From b02c8591c5f1a3bda006af8d75065db0775a3ed2 Mon Sep 17 00:00:00 2001
From: Aleks Kissinger <aleks0@gmail.com>
Date: Mon, 30 Dec 2024 17:00:10 +0000
Subject: [PATCH] extended pauli webs to represent errors and corrections

---
 demos/PauliWebs.ipynb    |  9979 +++++++++++++++++++++++++++++++--
 demos/PauliWebsRGB.ipynb | 11044 ++++++++++++++++++++++++++++++++++++-
 pyzx/gflow.py            |     2 +-
 pyzx/pauliweb.py         |    96 +-
 pyzx/simplify.py         |    14 +
 5 files changed, 20551 insertions(+), 584 deletions(-)

diff --git a/demos/PauliWebs.ipynb b/demos/PauliWebs.ipynb
index ba6738c8..10f0ea2f 100644
--- a/demos/PauliWebs.ipynb
+++ b/demos/PauliWebs.ipynb
@@ -7,10 +7,12 @@
    "outputs": [],
    "source": [
     "import sys, os, random\n",
+    "from fractions import Fraction\n",
     "sys.path.insert(0,os.path.expanduser('~/git/pyzx')) # git version\n",
     "sys.path.insert(0,'/workspaces/pyzx')\n",
     "import pyzx as zx\n",
     "from pyzx.pauliweb import PauliWeb, compute_pauli_webs\n",
+    "from pyzx import VertexType\n",
     "zx.settings.colors = zx.original_colors"
    ]
   },
@@ -54,7 +56,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9dj8FiGJ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-JqGKG78Z\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -418,7 +420,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-9dj8FiGJ',\n",
+       "showGraph('#graph-output-JqGKG78Z',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -451,7 +453,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-SnzbMlXA\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-JgIj0hlX\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -815,7 +817,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-SnzbMlXA',\n",
+       "showGraph('#graph-output-JgIj0hlX',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 3, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -830,7 +832,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-NaMJywMd\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-bQJ5btzO\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1194,7 +1196,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-NaMJywMd',\n",
+       "showGraph('#graph-output-bQJ5btzO',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1209,7 +1211,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Hokb0H2r\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-eV8WreQN\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1573,7 +1575,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Hokb0H2r',\n",
+       "showGraph('#graph-output-eV8WreQN',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1588,7 +1590,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ZeSLq1Sp\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-DX7kJwxE\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1952,7 +1954,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-ZeSLq1Sp',\n",
+       "showGraph('#graph-output-DX7kJwxE',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1981,7 +1983,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-LjtoNhmm\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-kmivAI3a\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2345,7 +2347,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-LjtoNhmm',\n",
+       "showGraph('#graph-output-kmivAI3a',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -2360,7 +2362,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9VAy6xYd\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-XG07nioX\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2724,7 +2726,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-9VAy6xYd',\n",
+       "showGraph('#graph-output-XG07nioX',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -2739,7 +2741,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-kxSr7u8g\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-pivIFVal\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3103,7 +3105,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-kxSr7u8g',\n",
+       "showGraph('#graph-output-pivIFVal',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3118,7 +3120,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-75Qf0jAA\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Yo6V8Tae\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3482,7 +3484,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-75Qf0jAA',\n",
+       "showGraph('#graph-output-Yo6V8Tae',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3515,7 +3517,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-v3dI7tCV\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ozpjnCVP\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3879,7 +3881,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-v3dI7tCV',\n",
+       "showGraph('#graph-output-ozpjnCVP',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3917,7 +3919,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wJg9KGzD\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Uu3qWPjb\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -4281,7 +4283,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-wJg9KGzD',\n",
+       "showGraph('#graph-output-Uu3qWPjb',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 8, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 8, \"target\": 4, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 5, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 5, \"t\": \"X\"}, {\"source\": 9, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 9, \"t\": \"X\"}, {\"source\": 15, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 15, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -4296,7 +4298,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-DWEtXQph\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Lv8lHxlh\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -4660,7 +4662,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-DWEtXQph',\n",
+       "showGraph('#graph-output-Lv8lHxlh',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 7, \"t\": \"Z\"}, {\"source\": 13, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 13, \"t\": \"Z\"}, {\"source\": 8, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 8, \"t\": \"Z\"}, {\"source\": 10, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 10, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -4675,7 +4677,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-sYKVf5Ub\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-K23n2ss7\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5039,7 +5041,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-sYKVf5Ub',\n",
+       "showGraph('#graph-output-K23n2ss7',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 9, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 9, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 16, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 16, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5054,7 +5056,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-cBXRSh0r\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-vnjx9lIw\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5418,7 +5420,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-cBXRSh0r',\n",
+       "showGraph('#graph-output-vnjx9lIw',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 7, \"t\": \"Z\"}, {\"source\": 9, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 9, \"t\": \"Z\"}, {\"source\": 11, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 11, \"t\": \"Z\"}, {\"source\": 8, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 8, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5433,7 +5435,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-mvQy8duQ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-bKVGcsau\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5797,7 +5799,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-mvQy8duQ',\n",
+       "showGraph('#graph-output-bKVGcsau',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 4, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 10, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 14, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"X\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 14, \"t\": \"X\"}, {\"source\": 9, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 9, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5812,7 +5814,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-mbaAihTO\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-PUsNncdr\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6176,7 +6178,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-mbaAihTO',\n",
+       "showGraph('#graph-output-PUsNncdr',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 17, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 17, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 7, \"t\": \"Z\"}, {\"source\": 4, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 4, \"t\": \"Z\"}, {\"source\": 10, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 10, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6207,7 +6209,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-av1x89gh\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-M2HjwiVP\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6571,7 +6573,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-av1x89gh',\n",
+       "showGraph('#graph-output-M2HjwiVP',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6599,7 +6601,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qF2SMlK3\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Ec2MTh3k\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6963,7 +6965,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-qF2SMlK3',\n",
+       "showGraph('#graph-output-Ec2MTh3k',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 15, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 15, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6978,7 +6980,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-eQ4YQufA\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-BMaiOaVM\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -7342,7 +7344,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-eQ4YQufA',\n",
+       "showGraph('#graph-output-BMaiOaVM',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}, {\"source\": 13, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 13, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -7357,7 +7359,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-TtbVE3mZ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-kRgBI3fD\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -7721,7 +7723,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-TtbVE3mZ',\n",
+       "showGraph('#graph-output-kRgBI3fD',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 16, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -7736,7 +7738,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-1H9Ry1BI\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-sZfH4keo\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8100,7 +8102,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-1H9Ry1BI',\n",
+       "showGraph('#graph-output-sZfH4keo',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 9, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 9, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8115,7 +8117,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-97M7ktIP\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-8svYi4Cp\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8479,7 +8481,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-97M7ktIP',\n",
+       "showGraph('#graph-output-8svYi4Cp',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 10, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 10, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8494,7 +8496,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-i2b1J2Yn\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-t5BFhDj5\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8858,7 +8860,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-i2b1J2Yn',\n",
+       "showGraph('#graph-output-t5BFhDj5',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}, {\"source\": 17, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 17, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8898,7 +8900,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-rMRH1mtT\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-izA2fjGv\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -9262,7 +9264,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-rMRH1mtT',\n",
+       "showGraph('#graph-output-izA2fjGv',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -9277,7 +9279,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-YNR311rS\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-K7geHk4W\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -9641,7 +9643,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-YNR311rS',\n",
+       "showGraph('#graph-output-K7geHk4W',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -9680,7 +9682,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ghxn1f0V\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Fu6y4YDm\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10044,7 +10046,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-ghxn1f0V',\n",
+       "showGraph('#graph-output-Fu6y4YDm',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 0, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 0, \"t\": \"Z\"}]}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -10059,7 +10061,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ZYb6bGlU\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-vHeWsCBV\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10423,7 +10425,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-ZYb6bGlU',\n",
+       "showGraph('#graph-output-vHeWsCBV',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}]}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -10463,7 +10465,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-6Tp04b0r\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-O758uDJA\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10827,7 +10829,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-6Tp04b0r',\n",
+       "showGraph('#graph-output-O758uDJA',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -10870,7 +10872,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Y8s8k6ID\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-WuqkFNJJ\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -11234,7 +11236,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Y8s8k6ID',\n",
+       "showGraph('#graph-output-WuqkFNJJ',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 3, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 6, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 6, \"t\": \"X\"}, {\"source\": 20, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 20, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 17, \"target\": 11, \"t\": \"X\"}, {\"source\": 17, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 17, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Z\"}, {\"source\": 12, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 12, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -11249,7 +11251,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-2sp4yjTz\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-msvZQyXk\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -11613,7 +11615,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-2sp4yjTz',\n",
+       "showGraph('#graph-output-msvZQyXk',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 2, \"t\": \"Y\"}, {\"source\": 4, \"target\": 0, \"t\": \"Y\"}, {\"source\": 0, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Y\"}, {\"source\": 6, \"target\": 7, \"t\": \"Y\"}, {\"source\": 7, \"target\": 6, \"t\": \"Y\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 7, \"t\": \"Y\"}, {\"source\": 9, \"target\": 10, \"t\": \"Y\"}, {\"source\": 10, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 9, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Y\"}, {\"source\": 10, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"Z\"}, {\"source\": 18, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 20, \"t\": \"Z\"}, {\"source\": 20, \"target\": 18, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 11, \"t\": \"Z\"}, {\"source\": 13, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 13, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -11628,7 +11630,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-q6wIXFG9\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Hk8HlNAE\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -11992,7 +11994,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-q6wIXFG9',\n",
+       "showGraph('#graph-output-Hk8HlNAE',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 3, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 6, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 6, \"t\": \"X\"}, {\"source\": 21, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 21, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 12, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 12, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -12007,7 +12009,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-8bf2Cg5s\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-P1K06SST\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -12371,7 +12373,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-8bf2Cg5s',\n",
+       "showGraph('#graph-output-P1K06SST',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 2, \"t\": \"Y\"}, {\"source\": 4, \"target\": 0, \"t\": \"Y\"}, {\"source\": 0, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Y\"}, {\"source\": 6, \"target\": 7, \"t\": \"Y\"}, {\"source\": 7, \"target\": 6, \"t\": \"Y\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 7, \"t\": \"Y\"}, {\"source\": 9, \"target\": 10, \"t\": \"Y\"}, {\"source\": 10, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 9, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Y\"}, {\"source\": 10, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"Z\"}, {\"source\": 12, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"Z\"}, {\"source\": 16, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 21, \"t\": \"Z\"}, {\"source\": 21, \"target\": 16, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 11, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -12386,7 +12388,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-J6advSRG\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-0kNRJ1fJ\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -12750,7 +12752,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-J6advSRG',\n",
+       "showGraph('#graph-output-0kNRJ1fJ',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 6, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 6, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"X\"}, {\"source\": 13, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 19, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 17, \"target\": 11, \"t\": \"X\"}, {\"source\": 17, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 17, \"t\": \"X\"}, {\"source\": 19, \"target\": 13, \"t\": \"X\"}, {\"source\": 19, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 19, \"t\": \"X\"}, {\"source\": 19, \"target\": 22, \"t\": \"X\"}, {\"source\": 22, \"target\": 19, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 7, \"t\": \"X\"}, {\"source\": 12, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 12, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -12765,7 +12767,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-4YftlOii\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-BqtBwqrx\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -13129,7 +13131,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-4YftlOii',\n",
+       "showGraph('#graph-output-BqtBwqrx',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 2, \"t\": \"Z\"}, {\"source\": 7, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Z\"}, {\"source\": 22, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 22, \"t\": \"Z\"}, {\"source\": 9, \"target\": 7, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 9, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}, {\"source\": 13, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 13, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -13161,7 +13163,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-dqWByjyL\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qP9QziFR\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -13525,7 +13527,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-dqWByjyL',\n",
+       "showGraph('#graph-output-qP9QziFR',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -13540,7 +13542,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-6QDEMZk5\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-rHE99a0M\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -13904,7 +13906,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-6QDEMZk5',\n",
+       "showGraph('#graph-output-rHE99a0M',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}, {\"source\": 0, \"target\": 1, \"t\": \"Y\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}]}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -13938,7 +13940,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wMvHqNBe\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qws0tsMT\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -14302,7 +14304,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-wMvHqNBe',\n",
+       "showGraph('#graph-output-qws0tsMT',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 28.571428571428573, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 28.571428571428573, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 28.571428571428573, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 28.571428571428573, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 57.142857142857146, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 85.71428571428572, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 85.71428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 114.28571428571429, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 114.28571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 142.85714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 171.42857142857144, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 200.0, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200.0, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 228.57142857142858, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 228.57142857142858, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 257.14285714285717, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 257.14285714285717, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 285.7142857142857, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 314.2857142857143, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 314.2857142857143, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 342.8571428571429, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 371.42857142857144, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 400.0, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 400.0, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 428.5714285714286, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 457.14285714285717, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 485.7142857142857, \"y\": 85.71428571428572, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 485.7142857142857, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 514.2857142857143, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 514.2857142857143, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 542.8571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 571.4285714285714, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 571.4285714285714, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 600.0, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 628.5714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 657.1428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 685.7142857142858, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 685.7142857142858, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 714.2857142857143, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 742.8571428571429, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 771.4285714285714, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 771.4285714285714, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 771.4285714285714, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 771.4285714285714, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 171.42857142857144, 28.571428571428573,\n",
        "  5.714285714285715, false, true, '');\n",
        "</script>"
@@ -14317,7 +14319,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-2Bd9OUhL\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-vcnZn8P5\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -14681,7 +14683,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-2Bd9OUhL',\n",
+       "showGraph('#graph-output-vcnZn8P5',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 28.571428571428573, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 28.571428571428573, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 28.571428571428573, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 28.571428571428573, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 57.142857142857146, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 85.71428571428572, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 85.71428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 114.28571428571429, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 114.28571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 142.85714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 171.42857142857144, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 200.0, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200.0, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 228.57142857142858, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 228.57142857142858, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 257.14285714285717, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 257.14285714285717, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 285.7142857142857, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 314.2857142857143, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 314.2857142857143, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 342.8571428571429, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 371.42857142857144, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 400.0, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 400.0, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 428.5714285714286, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 457.14285714285717, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 485.7142857142857, \"y\": 85.71428571428572, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 485.7142857142857, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 514.2857142857143, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 514.2857142857143, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 542.8571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 571.4285714285714, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 571.4285714285714, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 600.0, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 628.5714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 657.1428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 685.7142857142858, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 685.7142857142858, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 714.2857142857143, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 742.8571428571429, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 771.4285714285714, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 771.4285714285714, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 771.4285714285714, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 771.4285714285714, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Y\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Y\"}, {\"source\": 8, \"target\": 5, \"t\": \"Y\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 10, \"t\": \"Y\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 19, \"t\": \"X\"}, {\"source\": 10, \"target\": 8, \"t\": \"Y\"}, {\"source\": 10, \"target\": 14, \"t\": \"X\"}, {\"source\": 12, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"X\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 14, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 16, \"t\": \"X\"}, {\"source\": 19, \"target\": 9, \"t\": \"X\"}, {\"source\": 19, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 19, \"t\": \"X\"}, {\"source\": 19, \"target\": 21, \"t\": \"X\"}, {\"source\": 21, \"target\": 19, \"t\": \"X\"}, {\"source\": 21, \"target\": 25, \"t\": \"Y\"}, {\"source\": 24, \"target\": 23, \"t\": \"X\"}, {\"source\": 23, \"target\": 24, \"t\": \"Z\"}, {\"source\": 24, \"target\": 28, \"t\": \"X\"}, {\"source\": 28, \"target\": 24, \"t\": \"X\"}, {\"source\": 25, \"target\": 21, \"t\": \"Y\"}, {\"source\": 25, \"target\": 26, \"t\": \"X\"}, {\"source\": 26, \"target\": 25, \"t\": \"X\"}, {\"source\": 32, \"target\": 26, \"t\": \"X\"}, {\"source\": 26, \"target\": 32, \"t\": \"X\"}, {\"source\": 32, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 32, \"t\": \"X\"}, {\"source\": 32, \"target\": 34, \"t\": \"X\"}, {\"source\": 34, \"target\": 32, \"t\": \"Z\"}, {\"source\": 15, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 15, \"t\": \"Z\"}, {\"source\": 17, \"target\": 23, \"t\": \"Z\"}, {\"source\": 23, \"target\": 17, \"t\": \"Z\"}, {\"source\": 28, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 28, \"t\": \"X\"}, {\"source\": 34, \"target\": 35, \"t\": \"Z\"}, {\"source\": 35, \"target\": 34, \"t\": \"Z\"}, {\"source\": 35, \"target\": 37, \"t\": \"Z\"}, {\"source\": 37, \"target\": 35, \"t\": \"Z\"}, {\"source\": 0, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 0, \"t\": \"X\"}, {\"source\": 41, \"target\": 37, \"t\": \"Z\"}, {\"source\": 37, \"target\": 41, \"t\": \"Z\"}]}'), 800.0, 171.42857142857144, 28.571428571428573,\n",
        "  5.714285714285715, false, false, '');\n",
        "</script>"
@@ -14696,7 +14698,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9iAD5XWY\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-GEb6qry2\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -15060,7 +15062,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-9iAD5XWY',\n",
+       "showGraph('#graph-output-GEb6qry2',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 28.571428571428573, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 28.571428571428573, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 28.571428571428573, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 28.571428571428573, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 57.142857142857146, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 85.71428571428572, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 85.71428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 114.28571428571429, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 114.28571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 142.85714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 171.42857142857144, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 200.0, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200.0, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 228.57142857142858, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 228.57142857142858, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 257.14285714285717, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 257.14285714285717, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 285.7142857142857, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 314.2857142857143, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 314.2857142857143, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 342.8571428571429, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 371.42857142857144, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 400.0, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 400.0, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 428.5714285714286, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 457.14285714285717, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 485.7142857142857, \"y\": 85.71428571428572, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 485.7142857142857, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 514.2857142857143, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 514.2857142857143, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 542.8571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 571.4285714285714, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 571.4285714285714, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 600.0, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 628.5714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 657.1428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 685.7142857142858, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 685.7142857142858, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 714.2857142857143, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 742.8571428571429, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 771.4285714285714, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 771.4285714285714, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 771.4285714285714, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 771.4285714285714, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 2, \"t\": \"Y\"}, {\"source\": 2, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 10, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 19, \"t\": \"X\"}, {\"source\": 10, \"target\": 8, \"t\": \"X\"}, {\"source\": 10, \"target\": 14, \"t\": \"Y\"}, {\"source\": 12, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"Y\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 14, \"t\": \"Y\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 18, \"t\": \"Y\"}, {\"source\": 18, \"target\": 16, \"t\": \"Y\"}, {\"source\": 18, \"target\": 19, \"t\": \"Y\"}, {\"source\": 19, \"target\": 18, \"t\": \"Y\"}, {\"source\": 18, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 18, \"t\": \"Z\"}, {\"source\": 19, \"target\": 9, \"t\": \"X\"}, {\"source\": 19, \"target\": 21, \"t\": \"Y\"}, {\"source\": 21, \"target\": 19, \"t\": \"Y\"}, {\"source\": 21, \"target\": 25, \"t\": \"X\"}, {\"source\": 25, \"target\": 21, \"t\": \"X\"}, {\"source\": 25, \"target\": 26, \"t\": \"Y\"}, {\"source\": 26, \"target\": 25, \"t\": \"Y\"}, {\"source\": 26, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 26, \"t\": \"Z\"}, {\"source\": 26, \"target\": 32, \"t\": \"Y\"}, {\"source\": 32, \"target\": 26, \"t\": \"Y\"}, {\"source\": 32, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 32, \"t\": \"X\"}, {\"source\": 32, \"target\": 34, \"t\": \"Y\"}, {\"source\": 34, \"target\": 32, \"t\": \"Y\"}, {\"source\": 34, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"Y\"}, {\"source\": 35, \"target\": 37, \"t\": \"X\"}, {\"source\": 37, \"target\": 35, \"t\": \"X\"}, {\"source\": 37, \"target\": 36, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"X\"}, {\"source\": 37, \"target\": 41, \"t\": \"X\"}, {\"source\": 41, \"target\": 37, \"t\": \"X\"}, {\"source\": 11, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 11, \"t\": \"X\"}, {\"source\": 31, \"target\": 36, \"t\": \"X\"}, {\"source\": 36, \"target\": 31, \"t\": \"X\"}, {\"source\": 1, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 1, \"t\": \"Z\"}]}'), 800.0, 171.42857142857144, 28.571428571428573,\n",
        "  5.714285714285715, false, false, '');\n",
        "</script>"
@@ -15095,7 +15097,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-CDhkMZ48\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Ni5g2bn7\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -15459,7 +15461,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-CDhkMZ48',\n",
+       "showGraph('#graph-output-Ni5g2bn7',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"27\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 300, 300, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -15474,7 +15476,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9ZNNTFiU\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-XGLHi4G6\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -15838,7 +15840,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-9ZNNTFiU',\n",
+       "showGraph('#graph-output-XGLHi4G6',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"27\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 34, \"t\": \"X\"}, {\"source\": 34, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 4, \"t\": \"Z\"}, {\"source\": 0, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 0, \"t\": \"Z\"}, {\"source\": 41, \"target\": 34, \"t\": \"Z\"}, {\"source\": 34, \"target\": 41, \"t\": \"Z\"}]}'), 300, 300, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -15853,7 +15855,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-46G485iI\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ZHW2b6aB\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -16217,7 +16219,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-46G485iI',\n",
+       "showGraph('#graph-output-ZHW2b6aB',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"27\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 34, \"target\": 41, \"t\": \"X\"}, {\"source\": 41, \"target\": 34, \"t\": \"X\"}, {\"source\": 34, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 34, \"t\": \"Y\"}, {\"source\": 34, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 34, \"t\": \"Z\"}, {\"source\": 34, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 34, \"t\": \"Y\"}, {\"source\": 4, \"target\": 2, \"t\": \"Y\"}, {\"source\": 2, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 5, \"t\": \"Z\"}]}'), 300, 300, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -16256,20 +16258,24 @@
    "source": [
     "# Errors and corrections\n",
     "\n",
-    "Before moving on to Clifford+T examples, we'll show how to introduce errors into ZX-diagrams, correct them, and prove correctness.\n",
+    "Before moving on to Clifford+T examples, we'll show how to introduce errors into ZX-diagrams, correct them, and check the corrected diagram is equal to the original, error-free diagram, up to a global phase.\n",
     "\n",
-    "We can use the `PauliWeb` class to represent arbitrary Pauli errors on half edges. Note this will _not_ usually be a valid, closed Pauli web, but we can still use the `PauliWeb` class to hold this data."
+    "We can use the `PauliWeb` class to represent arbitrary Pauli errors on half edges. Note this will _not_ usually be a valid, closed Pauli web, but we can still use the `PauliWeb` class to hold this data. At some point, it might be worth adding an `is_valid` method to `PauliWeb` to check the Pauli web conditions are satisfied.\n",
+    "\n",
+    "The kinds of errors we are interested in here are logical flips coming from lattice surgery operations. Normally, these will non-deterministically introduce X errors next to Z nodes and Z errors next to X nodes.\n",
+    "\n",
+    "Since we know at runtime where these errors are, they are always correctable. Hence, the error rate and which subset of errors _actually_ occur is irrelevant. To demonstrate the corrections for arbitrary errors, we will call `PauliWeb.random` with its default arguments, which introduces a uniformly random Pauli X, Y, or Z with 30% probability on every half-edge."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-xT7LRFtp\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-opeNj15Y\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -16633,7 +16639,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-xT7LRFtp',\n",
+       "showGraph('#graph-output-opeNj15Y',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 650, 300, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -16648,7 +16654,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-fEOM57LR\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-aQeyHIbn\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -17012,8 +17018,8 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-fEOM57LR',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 11, \"target\": 0, \"t\": \"Z\"}, {\"source\": 7, \"target\": 12, \"t\": \"Z\"}, {\"source\": 8, \"target\": 10, \"t\": \"Z\"}, {\"source\": 14, \"target\": 10, \"t\": \"Z\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 14, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 14, \"t\": \"Y\"}, {\"source\": 15, \"target\": 17, \"t\": \"Z\"}, {\"source\": 18, \"target\": 22, \"t\": \"X\"}]}'), 650, 300, 50,\n",
+       "showGraph('#graph-output-aQeyHIbn',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"Y\"}, {\"source\": 7, \"target\": 8, \"t\": \"Y\"}, {\"source\": 8, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 8, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"Z\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"Y\"}, {\"source\": 13, \"target\": 23, \"t\": \"Y\"}, {\"source\": 15, \"target\": 17, \"t\": \"X\"}, {\"source\": 18, \"target\": 22, \"t\": \"Z\"}]}'), 650, 300, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
       ],
@@ -17031,83 +17037,19 @@
     "zx.draw(g, labels=True)\n",
     "\n",
     "# introduce random Pauli errors on edges and draw them\n",
-    "errors = PauliWeb(g)\n",
-    "for e in g.edges():\n",
-    "    s,t = g.edge_st(e)\n",
-    "    if random.random() > 0.75:\n",
-    "        errors.add_half_edge((s,t), random.choice(['X','Y','Z']))\n",
-    "    if random.random() > 0.75:\n",
-    "        errors.add_half_edge((t,s), random.choice(['X','Y','Z']))\n",
+    "errors = PauliWeb.random(g)\n",
     "zx.draw(g, pauli_web=errors)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Z-web 20: commutes\n",
-      "X-web 20: anti-commutes, corrected\n",
-      "Z-web 21: commutes\n",
-      "X-web 21: commutes\n",
-      "Z-web 22: anti-commutes, corrected\n",
-      "X-web 22: commutes\n",
-      "Z-web 23: commutes\n",
-      "X-web 23: commutes\n"
-     ]
-    }
-   ],
-   "source": [
-    "# To find the appropriate corrections, we should introduce Pauli X and Z gates at the outputs\n",
-    "# to make all 8 output webs commute with `errors`.\n",
-    "\n",
-    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
-    "output_es = [(o, next(iter(g.neighbors(o)))) for o in g.outputs()]\n",
-    "\n",
-    "\n",
-    "errors1 = errors.copy()\n",
-    "\n",
-    "# for each of the outputs, if the errors anti-commute with the associated Z-web, introduce\n",
-    "# an X-error at that output to make it commute, and do similar for X-webs.\n",
-    "for o,n in output_es:\n",
-    "    print(f'Z-web {o}: ', end='')\n",
-    "    if zwebs[o].commutes_with(errors):\n",
-    "        print('commutes')\n",
-    "    else:\n",
-    "        print('anti-commutes', end='')\n",
-    "        errors1.add_half_edge((o,n), 'X')\n",
-    "        if zwebs[o].commutes_with(errors1):\n",
-    "            print(', corrected')\n",
-    "    print(f'X-web {o}: ', end='')\n",
-    "    if xwebs[o].commutes_with(errors):\n",
-    "        print('commutes')\n",
-    "    else:\n",
-    "        print('anti-commutes', end='')\n",
-    "        errors1.add_half_edge((o,n), 'Z')\n",
-    "        if xwebs[o].commutes_with(errors1):\n",
-    "            print(', corrected')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Clifford+T Examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ruRdvBwG\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qRP5Huvn\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -17471,9 +17413,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-ruRdvBwG',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 26.666666666666668, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 26.666666666666668, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 26.666666666666668, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 53.333333333333336, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 53.333333333333336, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 80.0, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 80.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 106.66666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 106.66666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 133.33333333333334, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 160.0, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 160.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 186.66666666666669, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 186.66666666666669, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 186.66666666666669, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 213.33333333333334, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 213.33333333333334, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 240.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 240.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 240.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 266.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 266.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 293.33333333333337, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 293.33333333333337, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 266.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 320.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 320.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 346.6666666666667, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 346.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 373.33333333333337, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 373.33333333333337, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 373.33333333333337, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 400.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 400.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 426.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 426.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 453.33333333333337, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 453.33333333333337, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 480.0, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 480.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 480.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 506.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 506.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 533.3333333333334, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 560.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 586.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 613.3333333333334, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 613.3333333333334, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 640.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 640.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 666.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 506.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 533.3333333333334, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 666.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 560.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 586.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 693.3333333333334, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 693.3333333333334, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 720.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 720.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"60\", \"x\": 746.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 746.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 773.3333333333334, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 773.3333333333334, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 773.3333333333334, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"49\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"50\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"53\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"60\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"57\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"62\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"61\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 133.33333333333334, 26.666666666666668,\n",
-       "  5.333333333333334, false, false, '');\n",
+       "showGraph('#graph-output-qRP5Huvn',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 400.0, \"y\": 233.33333333333331, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 400.0, \"y\": 216.66666666666666, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 466.6666666666667, \"y\": 250.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 533.3333333333334, \"y\": 250.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 175.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 350.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 475.0, \"y\": 100.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 250.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 350.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 575.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 150.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 175.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 200.0, \"y\": 150.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 225.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200.0, \"y\": 240.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 200.0, \"y\": 229.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 200.0, \"y\": 219.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200.0, \"y\": 209.99999999999997, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"30\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 650, 300, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -17485,11 +17427,60 @@
     }
    ],
    "source": [
-    "# Generate a random CNOT, H, T circuit\n",
-    "random.seed(1330)\n",
-    "c = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=40)\n",
-    "# for g in c.gates: print(g)\n",
-    "zx.draw(c)"
+    "# The `PauliWeb.graph_with_errors()` method returns a copy of the original graph, where\n",
+    "# Pauli errors are inserted as pi-spiders on the edges colored by the web.\n",
+    "zx.draw(errors.graph_with_errors())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Z-web for output 20: commutes\n",
+      "X-web for output 20: anti-commutes, corrected\n",
+      "Z-web for output 21: anti-commutes, corrected\n",
+      "X-web for output 21: anti-commutes, corrected\n",
+      "Z-web for output 22: commutes\n",
+      "X-web for output 22: commutes\n",
+      "Z-web for output 23: anti-commutes, corrected\n",
+      "X-web for output 23: anti-commutes, corrected\n"
+     ]
+    }
+   ],
+   "source": [
+    "# To find the appropriate corrections, we should introduce Pauli X and Z gates at the outputs\n",
+    "# to make all 8 output webs commute with `errors`.\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "output_es = [(o, next(iter(g.neighbors(o)))) for o in g.outputs()]\n",
+    "\n",
+    "\n",
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# for each of the outputs, if the errors anti-commute with the associated Z-web, introduce\n",
+    "# an X-error at that output to make it commute, and do similar for X-webs.\n",
+    "for o,n in output_es:\n",
+    "    print(f'Z-web for output {o}: ', end='')\n",
+    "    if zwebs[o].commutes_with(errors1):\n",
+    "        print('commutes')\n",
+    "    else:\n",
+    "        print('anti-commutes', end='')\n",
+    "        errors1.add_half_edge((o,n), 'X')\n",
+    "        if zwebs[o].commutes_with(errors1):\n",
+    "            print(', corrected')\n",
+    "    print(f'X-web for output {o}: ', end='')\n",
+    "    if xwebs[o].commutes_with(errors1):\n",
+    "        print('commutes')\n",
+    "    else:\n",
+    "        print('anti-commutes', end='')\n",
+    "        errors1.add_half_edge((o,n), 'Z')\n",
+    "        if xwebs[o].commutes_with(errors1):\n",
+    "            print(', corrected')"
    ]
   },
   {
@@ -17500,7 +17491,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Tw6m2GYo\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-KJTLsliZ\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -17864,9 +17855,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Tw6m2GYo',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 350, 250, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-KJTLsliZ',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 400.0, \"y\": 233.33333333333331, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 400.0, \"y\": 216.66666666666666, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 550.0, \"y\": 100.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 440.00000000000006, \"y\": 250.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 480.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 520.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 560.0, \"y\": 250.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 175.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 350.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 566.6666666666667, \"y\": 150.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 583.3333333333334, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 475.0, \"y\": 100.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 250.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 350.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 575.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 150.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 175.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200.0, \"y\": 150.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 225.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 200.0, \"y\": 240.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200.0, \"y\": 229.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 200.0, \"y\": 219.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 200.0, \"y\": 209.99999999999997, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"35\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 650, 300, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -17875,84 +17866,11 @@
      },
      "metadata": {},
      "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# Convert to a ZX diagram and call the full_reduce procedure on it (PyZX's main ZX diagram optimisation pass)\n",
-    "g = c.to_graph()\n",
-    "zx.full_reduce(g)\n",
-    "zx.to_rg(g)\n",
-    "\n",
-    "# Normalise compacts the circuit visually and ensures every input/output is connected to a Z spider\n",
-    "g.normalize()\n",
-    "\n",
-    "# Compute the time-ordering on nodes (which is only important for the non-Clifford nodes) and compute the Pauli\n",
-    "# webs for every node.\n",
-    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
-    "\n",
-    "# Draw the simplified ZX diagram. Note blue edges correspond to edges with Hadamard gates\n",
-    "zx.draw(g, labels=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{(3, 1): 'Y',\n",
-       " (1, 3): 'Y',\n",
-       " (3, 43): 'Z',\n",
-       " (43, 3): 'Z',\n",
-       " (3, 5): 'Y',\n",
-       " (5, 3): 'Y',\n",
-       " (3, 58): 'Z',\n",
-       " (58, 3): 'X',\n",
-       " (3, 54): 'Z',\n",
-       " (54, 3): 'Z',\n",
-       " (3, 14): 'Y',\n",
-       " (14, 3): 'Y',\n",
-       " (5, 16): 'Y',\n",
-       " (16, 5): 'Y',\n",
-       " (5, 2): 'Y',\n",
-       " (2, 5): 'Y',\n",
-       " (5, 43): 'X',\n",
-       " (43, 5): 'Z',\n",
-       " (5, 58): 'X',\n",
-       " (58, 5): 'X',\n",
-       " (5, 54): 'X',\n",
-       " (54, 5): 'Z',\n",
-       " (14, 58): 'X',\n",
-       " (58, 14): 'X',\n",
-       " (14, 16): 'Y',\n",
-       " (16, 14): 'Y',\n",
-       " (16, 43): 'Z',\n",
-       " (43, 16): 'Z',\n",
-       " (16, 58): 'Z',\n",
-       " (58, 16): 'X'}"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pw = zwebs[43]\n",
-    "pw.half_edges()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
+    },
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-DqXCzq87\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-nUNQHPWl\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -18316,9 +18234,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-DqXCzq87',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Y\"}, {\"source\": 1, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 54, \"t\": \"Z\"}, {\"source\": 54, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 3, \"t\": \"Y\"}, {\"source\": 5, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 2, \"t\": \"Y\"}, {\"source\": 2, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 43, \"t\": \"X\"}, {\"source\": 43, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 54, \"t\": \"X\"}, {\"source\": 54, \"target\": 5, \"t\": \"Z\"}, {\"source\": 14, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 14, \"t\": \"Y\"}, {\"source\": 16, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 16, \"t\": \"X\"}]}'), 350, 250, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-nUNQHPWl',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 100, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 100, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 100, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 100, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 300, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -18330,29 +18248,45 @@
     }
    ],
    "source": [
-    "# Once the Pauli webs have been computed, a specific web can be highlighted by `zx.draw` by passing it in as\n",
-    "# an optional argument. Note that webs change color when they cross Hadamard edges.\n",
-    "zx.draw(g, labels=True, pauli_web=zwebs[43])"
+    "# All the errors have now been corrected, so the graph with Pauli errors given by `errors1` should\n",
+    "# be equal, up to a global phase to the origin graph\n",
+    "ge = errors1.graph_with_errors()\n",
+    "zx.draw(ge)\n",
+    "\n",
+    "# ...so if we compose `ge` with the adjoint of `g`, we should get the identity\n",
+    "h = g.adjoint() * ge\n",
+    "zx.full_reduce(h)\n",
+    "h.pack_circuit_rows()\n",
+    "zx.draw(h)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Clifford+T Examples"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We now show how this works in some simpler cases. The first is a single T gate.\n",
+    "Now, we'll move to some Clifford+T examples. By definition, spiders with phases that are not multiples of $\\pi/2$ must necessarily be on the boundary of a Pauli web.\n",
+    "\n",
+    "For our purposes, we will treat non-Clifford spiders as additional outputs that have been measured in the basis $\\{|T\\rangle, Z|T\\rangle \\}$, where $|T\\rangle := T|{+}\\rangle$ is a $T$ magic state.\n",
     "\n",
-    "The T gate becomes a single, 1-legged phase gadget, connected to the input. This can be implemented by Z-merging a T magic state, then doing either an X or a Y measurement, depending on the parity of the Pauli web."
+    "There are many equivalent ways to implement this fault-tolerantly in lattice surgery. One way to do this is to first perform a Z-merge between a data qubit and a $|T\\rangle$ magic state, then depending on the outcome of the merge, measure the remaining qubit in the X or Y basis."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-kyA8pdMW\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-YKkn4aXj\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -18716,9 +18650,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-kyA8pdMW',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
-       "  10.0, false, false, '');\n",
+       "showGraph('#graph-output-YKkn4aXj',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 250, 50,\n",
+       "  10.0, false, true, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -18731,7 +18665,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-4ZS1zzrq\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-c2LFHiOW\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -19095,9 +19029,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-4ZS1zzrq',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 0, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 0, \"t\": \"Z\"}]}'), 200, 150, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-c2LFHiOW',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 200, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -19109,36 +19043,29 @@
     }
    ],
    "source": [
-    "c = zx.qasm(\"\"\"\n",
-    "qreg q[1];\n",
-    "t q[0];\n",
-    "\"\"\")\n",
-    "zx.draw(c)\n",
+    "# Merge with parity 0, followed by an X measurement\n",
+    "g = zx.Graph()\n",
+    "g.add_vertex(qubit=0, row=0)\n",
+    "g.add_vertex(VertexType.Z, qubit=2, row=0, phase=Fraction(1/4))\n",
+    "g.add_vertex(VertexType.Z, qubit=1, row=1)\n",
+    "g.add_vertex(VertexType.Z, qubit=1, row=2)\n",
+    "for e in [(0,2), (1,2), (2,3)]: g.add_edge(e)\n",
+    "zx.draw(g, labels=True)\n",
     "\n",
-    "g = c.to_graph()\n",
+    "# ...is equivalent to a |T> measurement\n",
     "zx.full_reduce(g)\n",
-    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
-    "\n",
-    "# highlight the web associated to the T spider\n",
-    "zx.draw(g, labels=True, pauli_web=zwebs[1])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The next example is a circuit with some CNOT gates and a T gate, which can be simplified to a single phase gadget. I'm doing this manually here, since the automated simplifier comes up with a different answer (which is equivalent to this one, up to local Cliffords, but less clear what is going on)."
+    "zx.draw(g)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-QB0CIuve\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-EIphIKyl\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -19502,9 +19429,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-QB0CIuve',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 250, 50,\n",
-       "  10.0, false, false, '');\n",
+       "showGraph('#graph-output-EIphIKyl',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 75.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 250, 50,\n",
+       "  10.0, false, true, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -19517,7 +19444,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-NExmaneQ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-7k94vlWp\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -19881,9 +19808,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-NExmaneQ',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 110.00000000000001, \"y\": 300.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 80.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 350, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-7k94vlWp',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 200, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -19892,11 +19819,42 @@
      },
      "metadata": {},
      "output_type": "display_data"
-    },
+    }
+   ],
+   "source": [
+    "# Merge with parity 1, followed by an Y measurement\n",
+    "h = zx.Graph()\n",
+    "h.add_vertex(qubit=0, row=0)\n",
+    "h.add_vertex(VertexType.Z, qubit=2, row=0, phase=Fraction(1/4))\n",
+    "h.add_vertex(VertexType.Z, qubit=1, row=1)\n",
+    "h.add_vertex(VertexType.Z, qubit=1, row=2, phase=Fraction(1/2))\n",
+    "h.add_vertex(VertexType.X, qubit=1.5, row=0.5, phase=1)\n",
+    "for e in [(0,2), (1,4), (4,2), (2,3)]: h.add_edge(e)\n",
+    "zx.draw(h, labels=True)\n",
+    "\n",
+    "# ...is also equivalent to a |T> measurement\n",
+    "zx.full_reduce(h)\n",
+    "zx.draw(h)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In both cases above, we show the +1 outcome of the X/Y measurement. Getting the other outcome yields the same effect, up to a Pauli Z error, which can be corrected later.\n",
+    "\n",
+    "Using this primitive, we now look at implementing a single T gate."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-FRsGpofX\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-mnqt09Wz\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -20260,9 +20218,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-FRsGpofX',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 110.00000000000001, \"y\": 300.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 80.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 16, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 1, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 1, \"t\": \"Z\"}, {\"source\": 2, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 2, \"t\": \"Z\"}]}'), 400, 350, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-mnqt09Wz',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -20271,37 +20229,9408 @@
      },
      "metadata": {},
      "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "c = zx.qasm(\"\"\"\n",
-    "qreg q[3];\n",
-    "cx q[0], q[1];\n",
-    "cx q[1], q[2];\n",
-    "t q[2];\n",
-    "cx q[1], q[2];\n",
-    "cx q[0], q[1];\n",
-    "\"\"\")\n",
-    "zx.draw(c)\n",
-    "\n",
-    "# manual ZX simplification to get a single phase gadget\n",
-    "g = c.to_graph()\n",
-    "zx.simplify.gadgetize(g, graphlike=False)\n",
-    "zx.basicrules.strong_comp(g, 5, 7)\n",
-    "zx.simplify.spider_simp(g, quiet=True)\n",
-    "zx.basicrules.strong_comp(g, 3, 6)\n",
-    "zx.simplify.spider_simp(g, quiet=True)\n",
-    "zx.simplify.id_simp(g, quiet=True)\n",
-    "\n",
-    "zx.draw(g, labels=True)\n",
-    "\n",
-    "d = dict()\n",
-    "\n",
-    "# pauli web calculation\n",
-    "order, zwebs, xwebs = compute_pauli_webs(g, debug=d)\n",
-    "\n",
-    "# highlight the web associated to the T spider\n",
-    "zx.draw(g, labels=True, pauli_web=zwebs[15])"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-hKGH87TK\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-hKGH87TK',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[1];\n",
+    "t q[0];\n",
+    "\"\"\")\n",
+    "g = c.to_graph()\n",
+    "zx.draw(g)\n",
+    "\n",
+    "# Unfuse the non-Clifford spiders, so they look like outputs measured in {|T>, Z|T>}\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-P3eB6Pca\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-P3eB6Pca',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 0, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 0, \"t\": \"Z\"}, {\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-3pg03R4m\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-3pg03R4m',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-hzHPszFZ\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-hzHPszFZ',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 0, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# The relevant Pauli webs for this example are the Z and X webs of the output 2\n",
+    "# as well as the Z-web of the non-Clifford spider 3.\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[2])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[2])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Aeuct02S\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Aeuct02S',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-dehFpTOM\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-dehFpTOM',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# As we did in the Clifford examples, we can introduce random Pauli errors on all the edges\n",
+    "random.seed(1330)\n",
+    "errors = PauliWeb.random(g)\n",
+    "zx.draw(g, pauli_web=errors)\n",
+    "\n",
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# To implement the T-measurement at node 3, we need to look at the associated Z-web of 3\n",
+    "# If it anti-commutes with the errors, we should apply an X correction before we measure, or equivalently,\n",
+    "# flip whether we are measuring X or Y in the fault-tolerant gadget that injects a magic state.\n",
+    "if not zwebs[3].commutes_with(errors):\n",
+    "    errors1.add_half_edge((3,1), 'X')\n",
+    "\n",
+    "# a single Y error indeed anti-commutes with zweb[3], so a correction appears\n",
+    "zx.draw(g, pauli_web=errors1)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-bIJOEDws\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-bIJOEDws',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"Y\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-NufjldMt\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-NufjldMt',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "errors2 = errors1.copy()\n",
+    "\n",
+    "# The T-measurement itself will either apply <T| or <T|Z with uniform probability. We can simulate this by\n",
+    "# randomly introducing a Z error next to node 3.\n",
+    "if random.random() > 0.5:\n",
+    "    errors2.add_half_edge((v, n), 'Z')\n",
+    "\n",
+    "# Finally, we apply corrections on the output just like we did in the Clifford case\n",
+    "if not zwebs[2].commutes_with(errors2): errors2.add_half_edge((2,1), 'X')\n",
+    "if not xwebs[2].commutes_with(errors2): errors2.add_half_edge((2,1), 'Z')\n",
+    "\n",
+    "zx.draw(g, pauli_web=errors2)\n",
+    "\n",
+    "# The result, after we have applied corrections, should indeed be a single T gate\n",
+    "ge = errors2.graph_with_errors()\n",
+    "zx.full_reduce(ge)\n",
+    "zx.draw(ge)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The next example is a circuit with some CNOT gates and a T gate, which can be simplified to a single phase gadget. I'm doing this manually here, since the automated simplifier comes up with a different answer (which is equivalent to this one, up to local Cliffords, but less clear what is going on)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-DA7qw6xX\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-DA7qw6xX',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 250, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-2L4bs1g1\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-2L4bs1g1',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 110.00000000000001, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 200.0, \"y\": 190.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 80.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 300, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Tziq7OCs\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Tziq7OCs',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 110.00000000000001, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 200.0, \"y\": 190.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 80.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 2, \"t\": \"Z\"}, {\"source\": 19, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 20, \"t\": \"Z\"}, {\"source\": 20, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 19, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 1, \"target\": 20, \"t\": \"Z\"}, {\"source\": 20, \"target\": 1, \"t\": \"Z\"}]}'), 400, 300, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[3];\n",
+    "cx q[0], q[1];\n",
+    "cx q[1], q[2];\n",
+    "t q[2];\n",
+    "cx q[1], q[2];\n",
+    "cx q[0], q[1];\n",
+    "\"\"\")\n",
+    "zx.draw(c)\n",
+    "\n",
+    "# manual ZX simplification to get a single phase gadget\n",
+    "g = c.to_graph()\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.basicrules.strong_comp(g, 5, 7)\n",
+    "zx.simplify.spider_simp(g, quiet=True)\n",
+    "zx.basicrules.strong_comp(g, 3, 6)\n",
+    "zx.simplify.spider_simp(g, quiet=True)\n",
+    "zx.simplify.id_simp(g, quiet=True)\n",
+    "\n",
+    "zx.draw(g, labels=True)\n",
+    "\n",
+    "d = dict()\n",
+    "\n",
+    "# pauli web calculation\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g, debug=d)\n",
+    "\n",
+    "# highlight the web associated to the T spider\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[15])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This and the output Pauli webs is enough data to simulate running this computation and computing corrections. Rather than doing that explicitly, lets go straight to a random Clifford+T circuit."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ErqZdkUf\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-ErqZdkUf',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 48.484848484848484, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 48.484848484848484, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 121.21212121212122, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wINc2xTr\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-wINc2xTr',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Generate a random CNOT, H, T circuit\n",
+    "random.seed(1330)\n",
+    "c = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=30)\n",
+    "g = c.to_graph(compress_rows=False)\n",
+    "zx.draw(g)\n",
+    "\n",
+    "# Unfuse the non-Clifford spiders, so they look like outputs measured in {|T>, Z|T>}\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-QEffCAIh\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-QEffCAIh',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 8, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 15, \"target\": 12, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 18, \"target\": 14, \"t\": \"X\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 21, \"target\": 22, \"t\": \"Z\"}, {\"source\": 53, \"target\": 22, \"t\": \"X\"}, {\"source\": 28, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 27, \"t\": \"Y\"}, {\"source\": 28, \"target\": 29, \"t\": \"X\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 33, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"Y\"}, {\"source\": 37, \"target\": 40, \"t\": \"Y\"}, {\"source\": 38, \"target\": 49, \"t\": \"Y\"}, {\"source\": 40, \"target\": 41, \"t\": \"Y\"}, {\"source\": 41, \"target\": 42, \"t\": \"X\"}, {\"source\": 43, \"target\": 56, \"t\": \"Z\"}, {\"source\": 57, \"target\": 44, \"t\": \"Y\"}, {\"source\": 45, \"target\": 58, \"t\": \"Z\"}, {\"source\": 46, \"target\": 47, \"t\": \"X\"}, {\"source\": 47, \"target\": 50, \"t\": \"Z\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# as before, we can introduce random Pauli errors into the graph\n",
+    "random.seed(1337)\n",
+    "errors = PauliWeb.random(g)\n",
+    "zx.draw(g, pauli_web=errors)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{51: 1, 52: 1, 53: 1, 54: 1, 55: 2, 56: 2, 57: 2, 58: 2}\n"
+     ]
+    }
+   ],
+   "source": [
+    "# however, the correction strategy is more elaborate, since we have internal non-Clifford\n",
+    "# gadgets to handle. First, compute Pauli webs:\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "\n",
+    "# `order` tells us the order in which we should measure non-Clifford spiders. For Clifford diagrams,\n",
+    "# it was empty, since there were no non-Clifford spiders. In this example, it shows that we need to\n",
+    "# split the non-Clifford spiders into 2 time steps, where the last 4 measurements might depend on the\n",
+    "# outcomes of the first 4.\n",
+    "print(order)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-YJ9gvT9E\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-YJ9gvT9E',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 3, \"t\": \"Y\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Y\"}, {\"source\": 5, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 6, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 7, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 13, \"t\": \"Y\"}, {\"source\": 13, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 13, \"t\": \"Y\"}, {\"source\": 14, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 18, \"t\": \"Y\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 19, \"t\": \"Y\"}, {\"source\": 18, \"target\": 14, \"t\": \"Y\"}, {\"source\": 18, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 20, \"t\": \"Y\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 19, \"target\": 24, \"t\": \"Y\"}, {\"source\": 24, \"target\": 19, \"t\": \"Y\"}, {\"source\": 19, \"target\": 51, \"t\": \"X\"}, {\"source\": 20, \"target\": 18, \"t\": \"Y\"}, {\"source\": 20, \"target\": 23, \"t\": \"Y\"}, {\"source\": 23, \"target\": 20, \"t\": \"Y\"}, {\"source\": 20, \"target\": 52, \"t\": \"X\"}, {\"source\": 23, \"target\": 30, \"t\": \"Y\"}, {\"source\": 24, \"target\": 26, \"t\": \"Y\"}, {\"source\": 26, \"target\": 24, \"t\": \"Y\"}, {\"source\": 26, \"target\": 25, \"t\": \"X\"}, {\"source\": 25, \"target\": 26, \"t\": \"X\"}, {\"source\": 26, \"target\": 28, \"t\": \"Y\"}, {\"source\": 28, \"target\": 26, \"t\": \"Y\"}, {\"source\": 28, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 28, \"t\": \"X\"}, {\"source\": 28, \"target\": 29, \"t\": \"Y\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 29, \"target\": 30, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 29, \"target\": 34, \"t\": \"Z\"}, {\"source\": 30, \"target\": 23, \"t\": \"Y\"}, {\"source\": 30, \"target\": 33, \"t\": \"X\"}, {\"source\": 33, \"target\": 30, \"t\": \"Z\"}, {\"source\": 34, \"target\": 29, \"t\": \"Z\"}, {\"source\": 34, \"target\": 35, \"t\": \"Z\"}, {\"source\": 35, \"target\": 34, \"t\": \"Z\"}, {\"source\": 34, \"target\": 37, \"t\": \"Z\"}, {\"source\": 37, \"target\": 34, \"t\": \"Z\"}, {\"source\": 51, \"target\": 19, \"t\": \"X\"}, {\"source\": 52, \"target\": 20, \"t\": \"X\"}, {\"source\": 15, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 15, \"t\": \"X\"}, {\"source\": 25, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 25, \"t\": \"X\"}, {\"source\": 33, \"target\": 35, \"t\": \"Z\"}, {\"source\": 35, \"target\": 33, \"t\": \"Z\"}, {\"source\": 37, \"target\": 40, \"t\": \"Z\"}, {\"source\": 40, \"target\": 37, \"t\": \"Z\"}, {\"source\": 40, \"target\": 55, \"t\": \"Z\"}, {\"source\": 55, \"target\": 40, \"t\": \"Z\"}, {\"source\": 2, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 2, \"t\": \"Z\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# For example, if we look at the Z-web of spider 55, it touches 51 and 52, which means we need\n",
+    "# to be done with those spiders first.\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[55])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-rzAXBztq\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-rzAXBztq',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 8, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 15, \"target\": 12, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 18, \"target\": 14, \"t\": \"X\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 21, \"target\": 22, \"t\": \"Z\"}, {\"source\": 53, \"target\": 22, \"t\": \"X\"}, {\"source\": 28, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 27, \"t\": \"Y\"}, {\"source\": 28, \"target\": 29, \"t\": \"X\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 33, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"Y\"}, {\"source\": 37, \"target\": 40, \"t\": \"Y\"}, {\"source\": 38, \"target\": 49, \"t\": \"Y\"}, {\"source\": 40, \"target\": 41, \"t\": \"Y\"}, {\"source\": 41, \"target\": 42, \"t\": \"X\"}, {\"source\": 43, \"target\": 56, \"t\": \"Z\"}, {\"source\": 57, \"target\": 44, \"t\": \"Y\"}, {\"source\": 45, \"target\": 58, \"t\": \"Z\"}, {\"source\": 46, \"target\": 47, \"t\": \"X\"}, {\"source\": 47, \"target\": 50, \"t\": \"Z\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-pOTJEw8T\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-pOTJEw8T',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 8, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 15, \"target\": 12, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 18, \"target\": 14, \"t\": \"X\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 21, \"target\": 22, \"t\": \"Z\"}, {\"source\": 28, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 27, \"t\": \"Y\"}, {\"source\": 28, \"target\": 29, \"t\": \"X\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 33, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"Y\"}, {\"source\": 37, \"target\": 40, \"t\": \"Y\"}, {\"source\": 38, \"target\": 49, \"t\": \"Y\"}, {\"source\": 40, \"target\": 41, \"t\": \"Y\"}, {\"source\": 41, \"target\": 42, \"t\": \"X\"}, {\"source\": 43, \"target\": 56, \"t\": \"Z\"}, {\"source\": 45, \"target\": 58, \"t\": \"Z\"}, {\"source\": 46, \"target\": 47, \"t\": \"X\"}, {\"source\": 47, \"target\": 50, \"t\": \"Z\"}, {\"source\": 51, \"target\": 19, \"t\": \"Z\"}, {\"source\": 52, \"target\": 20, \"t\": \"X\"}, {\"source\": 54, \"target\": 31, \"t\": \"Z\"}, {\"source\": 55, \"target\": 40, \"t\": \"Y\"}, {\"source\": 49, \"target\": 38, \"t\": \"Z\"}, {\"source\": 50, \"target\": 47, \"t\": \"Y\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-HPUp5lOL\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-HPUp5lOL',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 53, \"target\": 22, \"t\": \"X\"}, {\"source\": 57, \"target\": 44, \"t\": \"Y\"}, {\"source\": 51, \"target\": 19, \"t\": \"Z\"}, {\"source\": 52, \"target\": 20, \"t\": \"X\"}, {\"source\": 54, \"target\": 31, \"t\": \"Z\"}, {\"source\": 55, \"target\": 40, \"t\": \"Y\"}, {\"source\": 49, \"target\": 38, \"t\": \"Z\"}, {\"source\": 50, \"target\": 47, \"t\": \"Y\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# traverse through the T spiders in the order given by `order`\n",
+    "for v in sorted(order.keys(), key=lambda v: order[v]):\n",
+    "    n = next(iter(g.neighbors(v)))\n",
+    "\n",
+    "    # if the Z-web associated with that spider anti-commutes with previous errors,\n",
+    "    # introduce an X error before the measurement. This has the same effect, up to Paulis\n",
+    "    # as choosing to measure Y rather than X in the fault-tolerant gadget\n",
+    "    if not zwebs[v].commutes_with(errors1):\n",
+    "        errors1.add_half_edge((v, n), 'X')\n",
+    "    \n",
+    "    # \"do\" the measurement, i.e. plug in |T> or Z|T> with uniform probability\n",
+    "    if random.random() > 0.5:\n",
+    "        errors1.add_half_edge((v, n), 'Z')\n",
+    "\n",
+    "# finally, use the output webs to correct outputs, as before\n",
+    "for o in g.outputs():\n",
+    "    n = next(iter(g.neighbors(o)))\n",
+    "    if not zwebs[o].commutes_with(errors1):\n",
+    "        errors1.add_half_edge((o,n), 'X')\n",
+    "    if not xwebs[o].commutes_with(errors1):\n",
+    "        errors1.add_half_edge((o,n), 'Z')\n",
+    "\n",
+    "# here is the original web\n",
+    "zx.draw(g, pauli_web=errors)\n",
+    "\n",
+    "# here is the corrected web\n",
+    "zx.draw(g, pauli_web=errors1)\n",
+    "\n",
+    "# n.b. we can multiply these two to just show the corrections\n",
+    "zx.draw(g, pauli_web=errors*errors1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-kTRDIEcE\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-kTRDIEcE',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"106\", \"x\": 100, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"107\", \"x\": 100, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"108\", \"x\": 100, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"106\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"107\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"108\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 250, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "h = g.adjoint() * errors1.graph_with_errors()\n",
+    "zx.full_reduce(h)\n",
+    "h.pack_circuit_rows()\n",
+    "zx.draw(h)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-YnaM1GDy\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-YnaM1GDy',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 25.806451612903224, \"y\": 51.61290322580645, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 25.806451612903224, \"y\": 77.41935483870967, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 25.806451612903224, \"y\": 103.2258064516129, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 51.61290322580645, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 77.41935483870967, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 51.61290322580645, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 51.61290322580645, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 103.2258064516129, \"y\": 103.2258064516129, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 103.2258064516129, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 129.03225806451613, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 129.03225806451613, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 154.83870967741933, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 154.83870967741933, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 180.64516129032256, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 180.64516129032256, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 206.4516129032258, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 232.25806451612902, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 258.06451612903226, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 283.8709677419355, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 283.8709677419355, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 309.67741935483866, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 206.4516129032258, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 335.4838709677419, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 335.4838709677419, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 361.2903225806451, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 361.2903225806451, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 387.09677419354836, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 387.09677419354836, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 412.9032258064516, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 412.9032258064516, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 412.9032258064516, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 438.7096774193548, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 438.7096774193548, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 464.51612903225805, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 464.51612903225805, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 490.3225806451613, \"y\": 103.2258064516129, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 490.3225806451613, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 516.1290322580645, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 516.1290322580645, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 516.1290322580645, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 541.9354838709677, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 567.741935483871, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 567.741935483871, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 593.5483870967741, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 593.5483870967741, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 541.9354838709677, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 619.3548387096773, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 567.741935483871, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 619.3548387096773, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 619.3548387096773, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 645.1612903225806, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 645.1612903225806, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 670.9677419354838, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 670.9677419354838, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 696.7741935483871, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 696.7741935483871, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 696.7741935483871, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 722.5806451612902, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 748.3870967741935, \"y\": 103.2258064516129, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 748.3870967741935, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"60\", \"x\": 722.5806451612902, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 774.1935483870967, \"y\": 51.61290322580645, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 774.1935483870967, \"y\": 77.41935483870967, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 774.1935483870967, \"y\": 103.2258064516129, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"20\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"46\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"47\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"49\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"50\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"53\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"60\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"57\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"57\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 129.03225806451613, 25.806451612903224,\n",
+       "  5.161290322580645, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-YSVnl23p\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-YSVnl23p',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 300, \"y\": 300, \"t\": 2, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 250, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 300, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"66\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"67\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"68\", \"x\": 300, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"18\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"65\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"67\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 350, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# The same procedure works with a reduced ZX-diagram, rather than a circuit, as input\n",
+    "random.seed(1337)\n",
+    "g = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=40).to_graph()\n",
+    "zx.draw(g)\n",
+    "zx.full_reduce(g)\n",
+    "g.normalize()\n",
+    "\n",
+    "# for simplicity, we'll make sure all the non-Clifford spiders are Z\n",
+    "zx.to_rg(g, init_z=set(v for v in g.vertices() if not zx.utils.phase_is_clifford(g.phase(v))))\n",
+    "\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-fS1JypQ0\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-fS1JypQ0',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 300, \"y\": 300, \"t\": 2, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 250, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 300, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"66\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"67\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"68\", \"x\": 300, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"18\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"65\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"67\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 39, \"t\": \"Y\"}, {\"source\": 38, \"target\": 18, \"t\": \"Z\"}, {\"source\": 38, \"target\": 63, \"t\": \"Y\"}, {\"source\": 45, \"target\": 38, \"t\": \"X\"}, {\"source\": 51, \"target\": 45, \"t\": \"Z\"}, {\"source\": 45, \"target\": 66, \"t\": \"Z\"}, {\"source\": 66, \"target\": 45, \"t\": \"X\"}, {\"source\": 67, \"target\": 51, \"t\": \"X\"}, {\"source\": 68, \"target\": 54, \"t\": \"Y\"}, {\"source\": 59, \"target\": 62, \"t\": \"Z\"}]}'), 400, 350, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-3R1iHwza\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-3R1iHwza',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 300, \"y\": 300, \"t\": 2, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 250, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 300, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"66\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"67\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"68\", \"x\": 300, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"18\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"65\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"67\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 67, \"target\": 51, \"t\": \"Y\"}, {\"source\": 68, \"target\": 54, \"t\": \"Z\"}, {\"source\": 64, \"target\": 41, \"t\": \"Z\"}, {\"source\": 65, \"target\": 39, \"t\": \"Y\"}, {\"source\": 61, \"target\": 54, \"t\": \"X\"}]}'), 400, 350, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9IkXu9GI\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#aabbff\", \"Zweb\": \"#99dd99\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-9IkXu9GI',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 100, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 100, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 100, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 250, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "random.seed(1337)\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "errors = PauliWeb.random(g)\n",
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# \"simulate\" the diagram and compute corrections, as before\n",
+    "for v in sorted(order.keys(), key=lambda v: order[v]):\n",
+    "    n = next(iter(g.neighbors(v)))\n",
+    "    if not zwebs[v].commutes_with(errors1): errors1.add_half_edge((v, n), 'X')\n",
+    "    if random.random() > 0.5: errors1.add_half_edge((v, n), 'Z')\n",
+    "for o in g.outputs():\n",
+    "    n = next(iter(g.neighbors(o)))\n",
+    "    if not zwebs[o].commutes_with(errors1): errors1.add_half_edge((o,n), 'X')\n",
+    "    if not xwebs[o].commutes_with(errors1): errors1.add_half_edge((o,n), 'Z')\n",
+    "\n",
+    "zx.draw(g, pauli_web=errors)\n",
+    "zx.draw(g, pauli_web=errors*errors1)\n",
+    "\n",
+    "h = g.adjoint() * errors1.graph_with_errors()\n",
+    "zx.full_reduce(h)\n",
+    "h.pack_circuit_rows()\n",
+    "zx.draw(h)"
    ]
   },
   {
diff --git a/demos/PauliWebsRGB.ipynb b/demos/PauliWebsRGB.ipynb
index bd9f8831..a9f9cfd4 100644
--- a/demos/PauliWebsRGB.ipynb
+++ b/demos/PauliWebsRGB.ipynb
@@ -7,10 +7,12 @@
    "outputs": [],
    "source": [
     "import sys, os, random\n",
+    "from fractions import Fraction\n",
     "sys.path.insert(0,os.path.expanduser('~/git/pyzx')) # git version\n",
     "sys.path.insert(0,'/workspaces/pyzx')\n",
     "import pyzx as zx\n",
     "from pyzx.pauliweb import PauliWeb, compute_pauli_webs\n",
+    "from pyzx import VertexType\n",
     "zx.settings.colors = zx.rgb_colors"
    ]
   },
@@ -18,21 +20,23 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This notebook demonstrates using PyZX's methods for automatically computing and drawing (bounded) Pauli webs. A Pauli web (a.k.a. _correlation surface_) is a coloring of the edges of ZX-diagram with the following properties for every Z spider `v`:\n",
+    "This notebook demonstrates using PyZX's methods for automatically computing and drawing bounded Pauli webs. A Pauli web (a.k.a. _correlation surface_) is a labelling of the edges of ZX-diagram from the set $\\{I, X, Y, Z\\}$ with certain properties. To explain these properties, it is useful to make some definitions.\n",
     "\n",
-    "- _all-or-nothing_: either no incident edges or all incident edges of `v` are labelled X or Y\n",
-    "- _parity_: an even number of incident edges of `v` are labelled Y or Z\n",
+    "To account for Hadmard edges, we label \"half-edges\" of a diagram. For a pair of connected vertices `v`, `w`, we represent the half-edge closest to `v` as `(v,w)` and the half-edge closest to `w` as `(w,v)`.\n",
     "\n",
-    "All X spiders satisfy analogous conditions, swapping the role of X and Z. A _bounded Pauli web_ is a Pauli web with a chosen set of spiders, called the _boundary_ where the parity condition is allowed to be violated.\n",
+    "We say a spider `v` is _stabilised_ by a Pauli web if `v` (considered as a state) is a +1 eigenstate of the Pauli string labelling its adjacent half-edges and we say `v` is _anti-stabilised_ by a Pauli web if it is a -1 eigenstate of its adjacent half-edges.\n",
     "\n",
-    "We say a spider `anti-commutes` with a Pauli web if it is touching an edge of a different colour.\n",
+    "A Pauli web is said to be _closed_ if:\n",
+    "1. every spider `v` in the ZX-diagram is stabilised or anti-stabilised\n",
+    "2. for every half-edge `(v,w)` labelled by a Pauli $P$, the other half-edge `(w,v)` is labelled by $P$ for a simple edge and $HPH$ for a Hadamard edge\n",
+    "\n",
+    "Otherwise, we say a Pauli web is _open_. The spiders and edges violating conditions 1 and 2 above are called the _boundary_ of a Pauli web.\n",
     "\n",
     "The function `compute_pauli_webs` automitically associates each non-input vertex `v` in the diagram to an integer `order[v]` giving a time-ordering, and one or two bounded Pauli webs, with the following properties:\n",
-    "1. the boundary of the web consists of only `v` itself and inputs\n",
+    "1. the boundary of the web consists of only `v` itself, earlier non-Clifford spiders `w` (`order[v] < order[w]>`), and inputs\n",
     "2. Z spiders have a web `zweb[v]` with a Z-colored edge incident to `v`\n",
     "3. X spiders have a web `xweb[v]` with a X-colored edge incident to `v`\n",
     "4. output vertices have two webs `zweb[v]` and `xweb[v]` corresponding to both colors at `v`\n",
-    "5. for non-Pauli spiders `v, w`, if `v` anti-commutes with the Pauli web of `w` then `order[v] < order[w]`\n",
     "\n",
     "Under the hood, this is using PyZX's gflow-finding algorithm to compute a focussed Pauli flow and translate this data into Pauli webs."
    ]
@@ -52,7 +56,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ctqpuKCV\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-cSSYEHxn\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -416,7 +420,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-ctqpuKCV',\n",
+       "showGraph('#graph-output-cSSYEHxn',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -449,7 +453,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-FjSWn0rt\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-u2inNqF1\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -813,7 +817,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-FjSWn0rt',\n",
+       "showGraph('#graph-output-u2inNqF1',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 3, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -828,7 +832,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-nIKIr1JV\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-vp9OeGiQ\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1192,7 +1196,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-nIKIr1JV',\n",
+       "showGraph('#graph-output-vp9OeGiQ',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1207,7 +1211,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ky88Hbzf\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-7jypfC5O\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1571,7 +1575,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-ky88Hbzf',\n",
+       "showGraph('#graph-output-7jypfC5O',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1586,7 +1590,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-4z4Q2iK4\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-0hMDduik\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1950,7 +1954,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-4z4Q2iK4',\n",
+       "showGraph('#graph-output-0hMDduik',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -1979,7 +1983,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-oGmutgmR\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-QYQO6HzP\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2343,7 +2347,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-oGmutgmR',\n",
+       "showGraph('#graph-output-QYQO6HzP',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -2358,7 +2362,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-mfICQp3A\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-zi0ZUvav\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2722,7 +2726,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-mfICQp3A',\n",
+       "showGraph('#graph-output-zi0ZUvav',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -2737,7 +2741,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ET8bW9C0\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-YEQeE5JM\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3101,7 +3105,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-ET8bW9C0',\n",
+       "showGraph('#graph-output-YEQeE5JM',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3116,7 +3120,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-vfu7lmST\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ZRxjUzvB\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3480,7 +3484,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-vfu7lmST',\n",
+       "showGraph('#graph-output-ZRxjUzvB',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3513,7 +3517,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-t8bQCX1y\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-32vh82TG\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -3877,7 +3881,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-t8bQCX1y',\n",
+       "showGraph('#graph-output-32vh82TG',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -3915,7 +3919,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9Kw77Uyc\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-nAKHAjzi\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -4279,7 +4283,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-9Kw77Uyc',\n",
+       "showGraph('#graph-output-nAKHAjzi',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 8, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 8, \"target\": 4, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 5, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 5, \"t\": \"X\"}, {\"source\": 9, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 9, \"t\": \"X\"}, {\"source\": 15, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 15, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -4294,7 +4298,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-xKNKlZy3\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qn37pNvc\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -4658,7 +4662,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-xKNKlZy3',\n",
+       "showGraph('#graph-output-qn37pNvc',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 7, \"t\": \"Z\"}, {\"source\": 13, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 13, \"t\": \"Z\"}, {\"source\": 8, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 8, \"t\": \"Z\"}, {\"source\": 10, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 10, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -4673,7 +4677,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-HUsPS3UI\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-emc0W581\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5037,7 +5041,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-HUsPS3UI',\n",
+       "showGraph('#graph-output-emc0W581',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 9, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 9, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 16, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 16, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5052,7 +5056,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-rmBRQmVy\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-kfNDluDh\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5416,7 +5420,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-rmBRQmVy',\n",
+       "showGraph('#graph-output-kfNDluDh',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 7, \"t\": \"Z\"}, {\"source\": 9, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 9, \"t\": \"Z\"}, {\"source\": 11, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 11, \"t\": \"Z\"}, {\"source\": 8, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 8, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5431,7 +5435,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-YPipQOZE\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-eP9ZvvUx\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -5795,7 +5799,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-YPipQOZE',\n",
+       "showGraph('#graph-output-eP9ZvvUx',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 4, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 10, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 14, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"X\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 14, \"t\": \"X\"}, {\"source\": 9, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 9, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -5810,7 +5814,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Gu2PzYgd\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-SmO0qCSB\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6174,7 +6178,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Gu2PzYgd',\n",
+       "showGraph('#graph-output-SmO0qCSB',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 17, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 17, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 7, \"t\": \"Z\"}, {\"source\": 4, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 4, \"t\": \"Z\"}, {\"source\": 10, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 10, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6205,7 +6209,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-V8J09Qxf\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-HYgCeXPj\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6569,7 +6573,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-V8J09Qxf',\n",
+       "showGraph('#graph-output-HYgCeXPj',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6597,7 +6601,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-U4pK0tMA\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-eDBq7dBQ\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -6961,7 +6965,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-U4pK0tMA',\n",
+       "showGraph('#graph-output-eDBq7dBQ',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 15, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 15, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -6976,7 +6980,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-V3bA71FO\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-jj211P32\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -7340,7 +7344,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-V3bA71FO',\n",
+       "showGraph('#graph-output-jj211P32',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}, {\"source\": 13, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 13, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -7355,7 +7359,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-alzbsLdS\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-TeVLG710\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -7719,7 +7723,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-alzbsLdS',\n",
+       "showGraph('#graph-output-TeVLG710',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 16, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -7734,7 +7738,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-l7TkEuFn\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-QWCkiBW4\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8098,7 +8102,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-l7TkEuFn',\n",
+       "showGraph('#graph-output-QWCkiBW4',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 9, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 9, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8113,7 +8117,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-TAvki1DG\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-BcXIwLoH\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8477,7 +8481,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-TAvki1DG',\n",
+       "showGraph('#graph-output-BcXIwLoH',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 10, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 10, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8492,7 +8496,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-tzmo6TYe\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qrFOTxB4\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -8856,7 +8860,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-tzmo6TYe',\n",
+       "showGraph('#graph-output-qrFOTxB4',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}, {\"source\": 17, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 17, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -8896,7 +8900,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-M2fgdZtL\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9huQxwNL\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -9260,7 +9264,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-M2fgdZtL',\n",
+       "showGraph('#graph-output-9huQxwNL',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -9275,7 +9279,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Je2HlWwp\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-pBrOywNg\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -9639,7 +9643,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Je2HlWwp',\n",
+       "showGraph('#graph-output-pBrOywNg',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -9678,7 +9682,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wmqF2kNr\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-5UAgIhGh\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10042,7 +10046,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-wmqF2kNr',\n",
+       "showGraph('#graph-output-5UAgIhGh',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 0, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 0, \"t\": \"Z\"}]}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -10057,7 +10061,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-l3RugtvI\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-gRA5YUR0\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10421,7 +10425,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-l3RugtvI',\n",
+       "showGraph('#graph-output-gRA5YUR0',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}]}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -10461,7 +10465,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-kAbniD68\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-UDhDDAhp\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -10825,7 +10829,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-kAbniD68',\n",
+       "showGraph('#graph-output-UDhDDAhp',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -10868,7 +10872,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-2ki5qtP6\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Q7W51rr8\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -11232,7 +11236,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-2ki5qtP6',\n",
+       "showGraph('#graph-output-Q7W51rr8',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 3, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 6, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 6, \"t\": \"X\"}, {\"source\": 20, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 20, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 17, \"target\": 11, \"t\": \"X\"}, {\"source\": 17, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 17, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Z\"}, {\"source\": 12, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 12, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -11247,7 +11251,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-B2DzTj24\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-71poUkup\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -11611,7 +11615,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-B2DzTj24',\n",
+       "showGraph('#graph-output-71poUkup',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 2, \"t\": \"Y\"}, {\"source\": 4, \"target\": 0, \"t\": \"Y\"}, {\"source\": 0, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Y\"}, {\"source\": 6, \"target\": 7, \"t\": \"Y\"}, {\"source\": 7, \"target\": 6, \"t\": \"Y\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 7, \"t\": \"Y\"}, {\"source\": 9, \"target\": 10, \"t\": \"Y\"}, {\"source\": 10, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 9, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Y\"}, {\"source\": 10, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"Z\"}, {\"source\": 18, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 20, \"t\": \"Z\"}, {\"source\": 20, \"target\": 18, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 11, \"t\": \"Z\"}, {\"source\": 13, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 13, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -11626,7 +11630,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-7EPSUU7d\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ZlzOZjZW\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -11990,7 +11994,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-7EPSUU7d',\n",
+       "showGraph('#graph-output-ZlzOZjZW',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 3, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 6, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 6, \"t\": \"X\"}, {\"source\": 21, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 21, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 8, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 12, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 12, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -12005,7 +12009,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-KtsBzgok\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-AfmYICeY\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -12369,7 +12373,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-KtsBzgok',\n",
+       "showGraph('#graph-output-AfmYICeY',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 2, \"t\": \"Y\"}, {\"source\": 4, \"target\": 0, \"t\": \"Y\"}, {\"source\": 0, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Y\"}, {\"source\": 6, \"target\": 7, \"t\": \"Y\"}, {\"source\": 7, \"target\": 6, \"t\": \"Y\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 7, \"t\": \"Y\"}, {\"source\": 9, \"target\": 10, \"t\": \"Y\"}, {\"source\": 10, \"target\": 9, \"t\": \"Y\"}, {\"source\": 9, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 9, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Y\"}, {\"source\": 10, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"Z\"}, {\"source\": 12, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 12, \"t\": \"Z\"}, {\"source\": 12, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"Z\"}, {\"source\": 16, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 21, \"t\": \"Z\"}, {\"source\": 21, \"target\": 16, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 11, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -12384,7 +12388,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-5v7wBYeV\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-mWWSMm5k\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -12748,7 +12752,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-5v7wBYeV',\n",
+       "showGraph('#graph-output-mWWSMm5k',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 6, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 6, \"t\": \"X\"}, {\"source\": 11, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 11, \"t\": \"Z\"}, {\"source\": 11, \"target\": 17, \"t\": \"X\"}, {\"source\": 13, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 19, \"t\": \"X\"}, {\"source\": 15, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 17, \"target\": 11, \"t\": \"X\"}, {\"source\": 17, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 17, \"t\": \"X\"}, {\"source\": 19, \"target\": 13, \"t\": \"X\"}, {\"source\": 19, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 19, \"t\": \"X\"}, {\"source\": 19, \"target\": 22, \"t\": \"X\"}, {\"source\": 22, \"target\": 19, \"t\": \"X\"}, {\"source\": 4, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 7, \"t\": \"X\"}, {\"source\": 12, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 12, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -12763,7 +12767,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-uZwHZeyQ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-xkwQLeA3\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -13127,7 +13131,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-uZwHZeyQ',\n",
+       "showGraph('#graph-output-xkwQLeA3',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 450, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 500, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 500, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 550, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 550, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 550, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"6\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"14\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 2, \"t\": \"Z\"}, {\"source\": 7, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Z\"}, {\"source\": 22, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 22, \"t\": \"Z\"}, {\"source\": 9, \"target\": 7, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 9, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}, {\"source\": 13, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 13, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}]}'), 600, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -13159,7 +13163,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-WLh4C6u1\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-0og3E1VW\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -13523,7 +13527,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-WLh4C6u1',\n",
+       "showGraph('#graph-output-0og3E1VW',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -13538,7 +13542,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-A5T2xA2W\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-lhRIna50\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -13902,7 +13906,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-A5T2xA2W',\n",
+       "showGraph('#graph-output-lhRIna50',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}, {\"source\": 0, \"target\": 1, \"t\": \"Y\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}]}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -13936,7 +13940,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-FheQNnF2\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-U6sEW1KE\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -14300,7 +14304,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-FheQNnF2',\n",
+       "showGraph('#graph-output-U6sEW1KE',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 28.571428571428573, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 28.571428571428573, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 28.571428571428573, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 28.571428571428573, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 57.142857142857146, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 85.71428571428572, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 85.71428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 114.28571428571429, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 114.28571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 142.85714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 171.42857142857144, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 200.0, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200.0, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 228.57142857142858, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 228.57142857142858, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 257.14285714285717, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 257.14285714285717, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 285.7142857142857, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 314.2857142857143, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 314.2857142857143, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 342.8571428571429, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 371.42857142857144, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 400.0, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 400.0, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 428.5714285714286, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 457.14285714285717, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 485.7142857142857, \"y\": 85.71428571428572, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 485.7142857142857, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 514.2857142857143, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 514.2857142857143, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 542.8571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 571.4285714285714, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 571.4285714285714, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 600.0, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 628.5714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 657.1428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 685.7142857142858, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 685.7142857142858, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 714.2857142857143, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 742.8571428571429, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 771.4285714285714, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 771.4285714285714, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 771.4285714285714, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 771.4285714285714, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 171.42857142857144, 28.571428571428573,\n",
        "  5.714285714285715, false, true, '');\n",
        "</script>"
@@ -14315,7 +14319,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Tns7u7AZ\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-DON1Wrlg\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -14679,7 +14683,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Tns7u7AZ',\n",
+       "showGraph('#graph-output-DON1Wrlg',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 28.571428571428573, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 28.571428571428573, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 28.571428571428573, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 28.571428571428573, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 57.142857142857146, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 85.71428571428572, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 85.71428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 114.28571428571429, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 114.28571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 142.85714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 171.42857142857144, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 200.0, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200.0, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 228.57142857142858, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 228.57142857142858, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 257.14285714285717, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 257.14285714285717, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 285.7142857142857, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 314.2857142857143, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 314.2857142857143, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 342.8571428571429, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 371.42857142857144, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 400.0, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 400.0, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 428.5714285714286, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 457.14285714285717, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 485.7142857142857, \"y\": 85.71428571428572, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 485.7142857142857, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 514.2857142857143, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 514.2857142857143, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 542.8571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 571.4285714285714, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 571.4285714285714, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 600.0, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 628.5714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 657.1428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 685.7142857142858, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 685.7142857142858, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 714.2857142857143, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 742.8571428571429, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 771.4285714285714, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 771.4285714285714, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 771.4285714285714, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 771.4285714285714, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Y\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Y\"}, {\"source\": 8, \"target\": 5, \"t\": \"Y\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 10, \"t\": \"Y\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 19, \"t\": \"X\"}, {\"source\": 10, \"target\": 8, \"t\": \"Y\"}, {\"source\": 10, \"target\": 14, \"t\": \"X\"}, {\"source\": 12, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"X\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 14, \"t\": \"X\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 16, \"t\": \"X\"}, {\"source\": 19, \"target\": 9, \"t\": \"X\"}, {\"source\": 19, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 19, \"t\": \"X\"}, {\"source\": 19, \"target\": 21, \"t\": \"X\"}, {\"source\": 21, \"target\": 19, \"t\": \"X\"}, {\"source\": 21, \"target\": 25, \"t\": \"Y\"}, {\"source\": 24, \"target\": 23, \"t\": \"X\"}, {\"source\": 23, \"target\": 24, \"t\": \"Z\"}, {\"source\": 24, \"target\": 28, \"t\": \"X\"}, {\"source\": 28, \"target\": 24, \"t\": \"X\"}, {\"source\": 25, \"target\": 21, \"t\": \"Y\"}, {\"source\": 25, \"target\": 26, \"t\": \"X\"}, {\"source\": 26, \"target\": 25, \"t\": \"X\"}, {\"source\": 32, \"target\": 26, \"t\": \"X\"}, {\"source\": 26, \"target\": 32, \"t\": \"X\"}, {\"source\": 32, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 32, \"t\": \"X\"}, {\"source\": 32, \"target\": 34, \"t\": \"X\"}, {\"source\": 34, \"target\": 32, \"t\": \"Z\"}, {\"source\": 15, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 15, \"t\": \"Z\"}, {\"source\": 17, \"target\": 23, \"t\": \"Z\"}, {\"source\": 23, \"target\": 17, \"t\": \"Z\"}, {\"source\": 28, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 28, \"t\": \"X\"}, {\"source\": 34, \"target\": 35, \"t\": \"Z\"}, {\"source\": 35, \"target\": 34, \"t\": \"Z\"}, {\"source\": 35, \"target\": 37, \"t\": \"Z\"}, {\"source\": 37, \"target\": 35, \"t\": \"Z\"}, {\"source\": 0, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 0, \"t\": \"X\"}, {\"source\": 41, \"target\": 37, \"t\": \"Z\"}, {\"source\": 37, \"target\": 41, \"t\": \"Z\"}]}'), 800.0, 171.42857142857144, 28.571428571428573,\n",
        "  5.714285714285715, false, false, '');\n",
        "</script>"
@@ -14694,7 +14698,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-SU2obGd2\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-thZd0Fs0\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -15058,7 +15062,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-SU2obGd2',\n",
+       "showGraph('#graph-output-thZd0Fs0',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 28.571428571428573, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 28.571428571428573, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 28.571428571428573, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 28.571428571428573, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 57.142857142857146, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 85.71428571428572, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 85.71428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 114.28571428571429, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 114.28571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 142.85714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 171.42857142857144, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 200.0, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 200.0, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 228.57142857142858, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 228.57142857142858, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 257.14285714285717, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 257.14285714285717, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 285.7142857142857, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 314.2857142857143, \"y\": 114.28571428571429, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 314.2857142857143, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 342.8571428571429, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 371.42857142857144, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 400.0, \"y\": 142.85714285714286, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 400.0, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 428.5714285714286, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 457.14285714285717, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 485.7142857142857, \"y\": 85.71428571428572, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 485.7142857142857, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 514.2857142857143, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 514.2857142857143, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 542.8571428571429, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 571.4285714285714, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 571.4285714285714, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 600.0, \"y\": 114.28571428571429, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 628.5714285714286, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 657.1428571428572, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 685.7142857142858, \"y\": 57.142857142857146, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 685.7142857142858, \"y\": 85.71428571428572, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 714.2857142857143, \"y\": 142.85714285714286, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 742.8571428571429, \"y\": 57.142857142857146, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 771.4285714285714, \"y\": 57.142857142857146, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 771.4285714285714, \"y\": 85.71428571428572, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 771.4285714285714, \"y\": 114.28571428571429, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 771.4285714285714, \"y\": 142.85714285714286, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 2, \"t\": \"Y\"}, {\"source\": 2, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 10, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 19, \"t\": \"X\"}, {\"source\": 10, \"target\": 8, \"t\": \"X\"}, {\"source\": 10, \"target\": 14, \"t\": \"Y\"}, {\"source\": 12, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 12, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 12, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"Y\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 14, \"t\": \"Y\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 18, \"t\": \"Y\"}, {\"source\": 18, \"target\": 16, \"t\": \"Y\"}, {\"source\": 18, \"target\": 19, \"t\": \"Y\"}, {\"source\": 19, \"target\": 18, \"t\": \"Y\"}, {\"source\": 18, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 18, \"t\": \"Z\"}, {\"source\": 19, \"target\": 9, \"t\": \"X\"}, {\"source\": 19, \"target\": 21, \"t\": \"Y\"}, {\"source\": 21, \"target\": 19, \"t\": \"Y\"}, {\"source\": 21, \"target\": 25, \"t\": \"X\"}, {\"source\": 25, \"target\": 21, \"t\": \"X\"}, {\"source\": 25, \"target\": 26, \"t\": \"Y\"}, {\"source\": 26, \"target\": 25, \"t\": \"Y\"}, {\"source\": 26, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 26, \"t\": \"Z\"}, {\"source\": 26, \"target\": 32, \"t\": \"Y\"}, {\"source\": 32, \"target\": 26, \"t\": \"Y\"}, {\"source\": 32, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 32, \"t\": \"X\"}, {\"source\": 32, \"target\": 34, \"t\": \"Y\"}, {\"source\": 34, \"target\": 32, \"t\": \"Y\"}, {\"source\": 34, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"Y\"}, {\"source\": 35, \"target\": 37, \"t\": \"X\"}, {\"source\": 37, \"target\": 35, \"t\": \"X\"}, {\"source\": 37, \"target\": 36, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"X\"}, {\"source\": 37, \"target\": 41, \"t\": \"X\"}, {\"source\": 41, \"target\": 37, \"t\": \"X\"}, {\"source\": 11, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 11, \"t\": \"X\"}, {\"source\": 31, \"target\": 36, \"t\": \"X\"}, {\"source\": 36, \"target\": 31, \"t\": \"X\"}, {\"source\": 1, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 1, \"t\": \"Z\"}]}'), 800.0, 171.42857142857144, 28.571428571428573,\n",
        "  5.714285714285715, false, false, '');\n",
        "</script>"
@@ -15093,7 +15097,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-RLvYytri\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-aZI3OEA7\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -15457,7 +15461,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-RLvYytri',\n",
+       "showGraph('#graph-output-aZI3OEA7',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"27\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 300, 300, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
@@ -15472,7 +15476,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-EzS29tgj\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-dfiqyrKo\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -15836,7 +15840,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-EzS29tgj',\n",
+       "showGraph('#graph-output-dfiqyrKo',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"27\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 34, \"t\": \"X\"}, {\"source\": 34, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 4, \"t\": \"Z\"}, {\"source\": 0, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 0, \"t\": \"Z\"}, {\"source\": 41, \"target\": 34, \"t\": \"Z\"}, {\"source\": 34, \"target\": 41, \"t\": \"Z\"}]}'), 300, 300, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -15851,7 +15855,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-lhbk9hhX\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-dNcBSe0x\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -16215,8 +16219,8 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-lhbk9hhX',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"27\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 34, \"target\": 41, \"t\": \"X\"}, {\"source\": 41, \"target\": 34, \"t\": \"X\"}, {\"source\": 34, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 34, \"t\": \"Y\"}, {\"source\": 34, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 34, \"t\": \"Z\"}, {\"source\": 34, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 34, \"t\": \"Y\"}, {\"source\": 4, \"target\": 2, \"t\": \"Y\"}, {\"source\": 2, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 1, \"t\": \"Y\"}, {\"source\": 1, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 5, \"t\": \"Z\"}]}'), 300, 300, 50,\n",
+       "showGraph('#graph-output-dNcBSe0x',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 200, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200, \"y\": 250, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"27\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"11\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"34\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"44\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 34, \"target\": 41, \"t\": \"X\"}, {\"source\": 41, \"target\": 34, \"t\": \"X\"}, {\"source\": 34, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 34, \"t\": \"Y\"}, {\"source\": 34, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 34, \"t\": \"Z\"}, {\"source\": 34, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 34, \"t\": \"Y\"}, {\"source\": 4, \"target\": 2, \"t\": \"Y\"}, {\"source\": 2, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 5, \"t\": \"Z\"}]}'), 300, 300, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
       ],
@@ -16243,6 +16247,7 @@
     "zx.draw(g1, labels=True)\n",
     "\n",
     "order, zwebs, xwebs = compute_pauli_webs(g1)\n",
+    "\n",
     "zx.draw(g1, pauli_web=zwebs[41])\n",
     "zx.draw(g1, pauli_web=xwebs[41])"
    ]
@@ -16251,7 +16256,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Clifford+T Examples"
+    "# Errors and corrections\n",
+    "\n",
+    "Before moving on to Clifford+T examples, we'll show how to introduce errors into ZX-diagrams, correct them, and check the corrected diagram is equal to the original, error-free diagram, up to a global phase.\n",
+    "\n",
+    "We can use the `PauliWeb` class to represent arbitrary Pauli errors on half edges. Note this will _not_ usually be a valid, closed Pauli web, but we can still use the `PauliWeb` class to hold this data. At some point, it might be worth adding an `is_valid` method to `PauliWeb` to check the Pauli web conditions are satisfied.\n",
+    "\n",
+    "The kinds of errors we are interested in here are logical flips coming from lattice surgery operations. Normally, these will non-deterministically introduce X errors next to Z nodes and Z errors next to X nodes.\n",
+    "\n",
+    "Since we know at runtime where these errors are, they are always correctable. Hence, the error rate and which subset of errors _actually_ occur is irrelevant. To demonstrate the corrections for arbitrary errors, we will call `PauliWeb.random` with its default arguments, which introduces a uniformly random Pauli X, Y, or Z with 30% probability on every half-edge."
    ]
   },
   {
@@ -16262,7 +16275,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-vze5LgdT\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-tIrxvtnG\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -16626,9 +16639,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-vze5LgdT',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 26.666666666666668, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 26.666666666666668, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 26.666666666666668, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 53.333333333333336, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 53.333333333333336, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 80.0, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 80.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 106.66666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 106.66666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 133.33333333333334, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 160.0, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 160.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 186.66666666666669, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 186.66666666666669, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 186.66666666666669, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 213.33333333333334, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 213.33333333333334, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 240.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 240.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 240.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 266.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 266.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 293.33333333333337, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 293.33333333333337, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 266.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 320.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 320.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 346.6666666666667, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 346.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 373.33333333333337, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 373.33333333333337, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 373.33333333333337, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 400.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 400.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 426.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 426.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 453.33333333333337, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 453.33333333333337, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 480.0, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 480.0, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 480.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 506.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 506.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 533.3333333333334, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 560.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 586.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 613.3333333333334, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 613.3333333333334, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 640.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 640.0, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 666.6666666666667, \"y\": 106.66666666666667, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 506.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 533.3333333333334, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 666.6666666666667, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 560.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 586.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 693.3333333333334, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 693.3333333333334, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 720.0, \"y\": 106.66666666666667, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 720.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"60\", \"x\": 746.6666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 746.6666666666667, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 773.3333333333334, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 773.3333333333334, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 773.3333333333334, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"49\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"50\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"53\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"60\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"57\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"62\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"61\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 133.33333333333334, 26.666666666666668,\n",
-       "  5.333333333333334, false, false, '');\n",
+       "showGraph('#graph-output-tIrxvtnG',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 650, 300, 50,\n",
+       "  10.0, false, true, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -16637,25 +16650,11 @@
      },
      "metadata": {},
      "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# Generate a random CNOT, H, T circuit\n",
-    "random.seed(1330)\n",
-    "c = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=40)\n",
-    "# for g in c.gates: print(g)\n",
-    "zx.draw(c)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
+    },
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Ghz5kFC6\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-waVRWGnk\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -17019,9 +17018,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Ghz5kFC6',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 350, 250, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-waVRWGnk',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"Y\"}, {\"source\": 7, \"target\": 8, \"t\": \"Y\"}, {\"source\": 8, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 8, \"t\": \"X\"}, {\"source\": 14, \"target\": 10, \"t\": \"Z\"}, {\"source\": 11, \"target\": 12, \"t\": \"X\"}, {\"source\": 13, \"target\": 14, \"t\": \"Y\"}, {\"source\": 13, \"target\": 23, \"t\": \"Y\"}, {\"source\": 15, \"target\": 17, \"t\": \"X\"}, {\"source\": 18, \"target\": 22, \"t\": \"Z\"}]}'), 650, 300, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -17033,81 +17032,24 @@
     }
    ],
    "source": [
-    "# Convert to a ZX diagram and call the full_reduce procedure on it (PyZX's main ZX diagram optimisation pass)\n",
-    "g = c.to_graph()\n",
-    "zx.full_reduce(g)\n",
-    "zx.to_rg(g)\n",
-    "\n",
-    "# Normalise compacts the circuit visually and ensures every input/output is connected to a Z spider\n",
-    "g.normalize()\n",
-    "\n",
-    "# Compute the time-ordering on nodes (which is only important for the non-Clifford nodes) and compute the Pauli\n",
-    "# webs for every node.\n",
-    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "random.seed(1337)\n",
+    "g = zx.generate.CNOT_HAD_PHASE_circuit(qubits=4, depth=10, clifford=True).to_graph(compress_rows=False)\n",
+    "zx.draw(g, labels=True)\n",
     "\n",
-    "# Draw the simplified ZX diagram. Note blue edges correspond to edges with Hadamard gates\n",
-    "zx.draw(g, labels=True)"
+    "# introduce random Pauli errors on edges and draw them\n",
+    "errors = PauliWeb.random(g)\n",
+    "zx.draw(g, pauli_web=errors)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{(3, 1): 'Y',\n",
-       " (1, 3): 'Y',\n",
-       " (3, 43): 'Z',\n",
-       " (43, 3): 'Z',\n",
-       " (3, 5): 'Y',\n",
-       " (5, 3): 'Y',\n",
-       " (3, 58): 'Z',\n",
-       " (58, 3): 'X',\n",
-       " (3, 54): 'Z',\n",
-       " (54, 3): 'Z',\n",
-       " (3, 14): 'Y',\n",
-       " (14, 3): 'Y',\n",
-       " (5, 16): 'Y',\n",
-       " (16, 5): 'Y',\n",
-       " (5, 2): 'Y',\n",
-       " (2, 5): 'Y',\n",
-       " (5, 43): 'X',\n",
-       " (43, 5): 'Z',\n",
-       " (5, 58): 'X',\n",
-       " (58, 5): 'X',\n",
-       " (5, 54): 'X',\n",
-       " (54, 5): 'Z',\n",
-       " (14, 58): 'X',\n",
-       " (58, 14): 'X',\n",
-       " (14, 16): 'Y',\n",
-       " (16, 14): 'Y',\n",
-       " (16, 43): 'Z',\n",
-       " (43, 16): 'Z',\n",
-       " (16, 58): 'Z',\n",
-       " (58, 16): 'X'}"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pw = zwebs[43]\n",
-    "pw.half_edges()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-xecjUQC7\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-8zMtaHu9\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -17471,9 +17413,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-xecjUQC7',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Y\"}, {\"source\": 1, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 54, \"t\": \"Z\"}, {\"source\": 54, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 3, \"t\": \"Y\"}, {\"source\": 5, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 2, \"t\": \"Y\"}, {\"source\": 2, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 43, \"t\": \"X\"}, {\"source\": 43, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 54, \"t\": \"X\"}, {\"source\": 54, \"target\": 5, \"t\": \"Z\"}, {\"source\": 14, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 14, \"t\": \"Y\"}, {\"source\": 16, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 16, \"t\": \"X\"}]}'), 350, 250, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-8zMtaHu9',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 400.0, \"y\": 233.33333333333331, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 400.0, \"y\": 216.66666666666666, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 466.6666666666667, \"y\": 250.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 533.3333333333334, \"y\": 250.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 175.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 350.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 475.0, \"y\": 100.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 250.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 350.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 575.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 150.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 175.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 200.0, \"y\": 150.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 225.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 200.0, \"y\": 240.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 200.0, \"y\": 229.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 200.0, \"y\": 219.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200.0, \"y\": 209.99999999999997, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"30\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 650, 300, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -17485,29 +17427,71 @@
     }
    ],
    "source": [
-    "# Once the Pauli webs have been computed, a specific web can be highlighted by `zx.draw` by passing it in as\n",
-    "# an optional argument. Note that webs change color when they cross Hadamard edges.\n",
-    "zx.draw(g, labels=True, pauli_web=zwebs[43])"
+    "# The `PauliWeb.graph_with_errors()` method returns a copy of the original graph, where\n",
+    "# Pauli errors are inserted as pi-spiders on the edges colored by the web.\n",
+    "zx.draw(errors.graph_with_errors())"
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": 18,
    "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Z-web for output 20: commutes\n",
+      "X-web for output 20: anti-commutes, corrected\n",
+      "Z-web for output 21: anti-commutes, corrected\n",
+      "X-web for output 21: anti-commutes, corrected\n",
+      "Z-web for output 22: commutes\n",
+      "X-web for output 22: commutes\n",
+      "Z-web for output 23: anti-commutes, corrected\n",
+      "X-web for output 23: anti-commutes, corrected\n"
+     ]
+    }
+   ],
    "source": [
-    "We now show how this works in some simpler cases. The first is a single T gate.\n",
+    "# To find the appropriate corrections, we should introduce Pauli X and Z gates at the outputs\n",
+    "# to make all 8 output webs commute with `errors`.\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "output_es = [(o, next(iter(g.neighbors(o)))) for o in g.outputs()]\n",
+    "\n",
     "\n",
-    "The T gate becomes a single, 1-legged phase gadget, connected to the input. This can be implemented by Z-merging a T magic state, then doing either an X or a Y measurement, depending on the parity of the Pauli web."
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# for each of the outputs, if the errors anti-commute with the associated Z-web, introduce\n",
+    "# an X-error at that output to make it commute, and do similar for X-webs.\n",
+    "for o,n in output_es:\n",
+    "    print(f'Z-web for output {o}: ', end='')\n",
+    "    if zwebs[o].commutes_with(errors1):\n",
+    "        print('commutes')\n",
+    "    else:\n",
+    "        print('anti-commutes', end='')\n",
+    "        errors1.add_half_edge((o,n), 'X')\n",
+    "        if zwebs[o].commutes_with(errors1):\n",
+    "            print(', corrected')\n",
+    "    print(f'X-web for output {o}: ', end='')\n",
+    "    if xwebs[o].commutes_with(errors1):\n",
+    "        print('commutes')\n",
+    "    else:\n",
+    "        print('anti-commutes', end='')\n",
+    "        errors1.add_half_edge((o,n), 'Z')\n",
+    "        if xwebs[o].commutes_with(errors1):\n",
+    "            print(', corrected')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-gNBMPV7y\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-fEMONsGh\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -17871,8 +17855,8 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-gNBMPV7y',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
+       "showGraph('#graph-output-fEMONsGh',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 400, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 450, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 450, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 500, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 550, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 550, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 600, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 600, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 600, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 600, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 400.0, \"y\": 233.33333333333331, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 400.0, \"y\": 216.66666666666666, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 550.0, \"y\": 100.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 440.00000000000006, \"y\": 250.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 480.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 520.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 560.0, \"y\": 250.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 175.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 350.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 566.6666666666667, \"y\": 150.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 583.3333333333334, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 475.0, \"y\": 100.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 250.0, \"y\": 200.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 350.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 575.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 150.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 175.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200.0, \"y\": 150.0, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 225.0, \"y\": 150.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 200.0, \"y\": 240.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 200.0, \"y\": 229.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 200.0, \"y\": 219.99999999999997, \"t\": 1, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 200.0, \"y\": 209.99999999999997, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"35\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 650, 300, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
       ],
@@ -17886,7 +17870,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-muW6ZGCx\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-nodpO6jt\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -18250,9 +18234,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-muW6ZGCx',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 0, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 0, \"t\": \"Z\"}]}'), 200, 150, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-nodpO6jt',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 100, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 100, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 100, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 100, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 300, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -18264,36 +18248,45 @@
     }
    ],
    "source": [
-    "c = zx.qasm(\"\"\"\n",
-    "qreg q[1];\n",
-    "t q[0];\n",
-    "\"\"\")\n",
-    "zx.draw(c)\n",
-    "\n",
-    "g = c.to_graph()\n",
-    "zx.full_reduce(g)\n",
-    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "# All the errors have now been corrected, so the graph with Pauli errors given by `errors1` should\n",
+    "# be equal, up to a global phase to the origin graph\n",
+    "ge = errors1.graph_with_errors()\n",
+    "zx.draw(ge)\n",
     "\n",
-    "# highlight the web associated to the T spider\n",
-    "zx.draw(g, labels=True, pauli_web=zwebs[1])"
+    "# ...so if we compose `ge` with the adjoint of `g`, we should get the identity\n",
+    "h = g.adjoint() * ge\n",
+    "zx.full_reduce(h)\n",
+    "h.pack_circuit_rows()\n",
+    "zx.draw(h)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The next example is a circuit with some CNOT gates and a T gate, which can be simplified to a single phase gadget. I'm doing this manually here, since the automated simplifier comes up with a different answer (which is equivalent to this one, up to local Cliffords, but less clear what is going on)."
+    "# Clifford+T Examples"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now, we'll move to some Clifford+T examples. By definition, spiders with phases that are not multiples of $\\pi/2$ must necessarily be on the boundary of a Pauli web.\n",
+    "\n",
+    "For our purposes, we will treat non-Clifford spiders as additional outputs that have been measured in the basis $\\{|T\\rangle, Z|T\\rangle \\}$, where $|T\\rangle := T|{+}\\rangle$ is a $T$ magic state.\n",
+    "\n",
+    "There are many equivalent ways to implement this fault-tolerantly in lattice surgery. One way to do this is to first perform a Z-merge between a data qubit and a $|T\\rangle$ magic state, then depending on the outcome of the merge, measure the remaining qubit in the X or Y basis."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-fV2wpKrl\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-jt5f94Xn\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -18657,9 +18650,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-fV2wpKrl',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 250, 50,\n",
-       "  10.0, false, false, '');\n",
+       "showGraph('#graph-output-jt5f94Xn',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 250, 50,\n",
+       "  10.0, false, true, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -18672,7 +18665,7 @@
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-fDrmxE4q\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-uOU0vUxv\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -19036,9 +19029,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-fDrmxE4q',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 110.00000000000001, \"y\": 300.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 80.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 16, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 1, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 1, \"t\": \"Z\"}, {\"source\": 2, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 2, \"t\": \"Z\"}]}'), 400, 350, 50,\n",
-       "  10.0, false, true, '');\n",
+       "showGraph('#graph-output-uOU0vUxv',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 200, 50,\n",
+       "  10.0, false, false, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -19050,38 +19043,10595 @@
     }
    ],
    "source": [
-    "c = zx.qasm(\"\"\"\n",
-    "qreg q[3];\n",
-    "cx q[0], q[1];\n",
-    "cx q[1], q[2];\n",
-    "t q[2];\n",
-    "cx q[1], q[2];\n",
-    "cx q[0], q[1];\n",
-    "\"\"\")\n",
-    "zx.draw(c)\n",
-    "\n",
-    "# manual ZX simplification to get a single phase gadget\n",
-    "g = c.to_graph()\n",
-    "zx.simplify.gadgetize(g, graphlike=False)\n",
-    "zx.basicrules.strong_comp(g, 5, 7)\n",
-    "zx.simplify.spider_simp(g, quiet=True)\n",
-    "zx.basicrules.strong_comp(g, 3, 6)\n",
-    "zx.simplify.spider_simp(g, quiet=True)\n",
-    "zx.simplify.id_simp(g, quiet=True)\n",
-    "\n",
-    "# pauli web calculation\n",
-    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "# Merge with parity 0, followed by an X measurement\n",
+    "g = zx.Graph()\n",
+    "g.add_vertex(qubit=0, row=0)\n",
+    "g.add_vertex(VertexType.Z, qubit=2, row=0, phase=Fraction(1/4))\n",
+    "g.add_vertex(VertexType.Z, qubit=1, row=1)\n",
+    "g.add_vertex(VertexType.Z, qubit=1, row=2)\n",
+    "for e in [(0,2), (1,2), (2,3)]: g.add_edge(e)\n",
+    "zx.draw(g, labels=True)\n",
     "\n",
-    "# highlight the web associated to the T spider\n",
-    "zx.draw(g, labels=True, pauli_web=zwebs[15])"
+    "# ...is equivalent to a |T> measurement\n",
+    "zx.full_reduce(g)\n",
+    "zx.draw(g)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-obN6Aa4f\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-obN6Aa4f',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 75.0, \"y\": 175.0, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-6UUpWDAx\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-6UUpWDAx',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Merge with parity 1, followed by an Y measurement\n",
+    "h = zx.Graph()\n",
+    "h.add_vertex(qubit=0, row=0)\n",
+    "h.add_vertex(VertexType.Z, qubit=2, row=0, phase=Fraction(1/4))\n",
+    "h.add_vertex(VertexType.Z, qubit=1, row=1)\n",
+    "h.add_vertex(VertexType.Z, qubit=1, row=2, phase=Fraction(1/2))\n",
+    "h.add_vertex(VertexType.X, qubit=1.5, row=0.5, phase=1)\n",
+    "for e in [(0,2), (1,4), (4,2), (2,3)]: h.add_edge(e)\n",
+    "zx.draw(h, labels=True)\n",
+    "\n",
+    "# ...is also equivalent to a |T> measurement\n",
+    "zx.full_reduce(h)\n",
+    "zx.draw(h)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In both cases above, we show the +1 outcome of the X/Y measurement. Getting the other outcome yields the same effect, up to a Pauli Z error, which can be corrected later.\n",
+    "\n",
+    "Using this primitive, we now look at implementing a single T gate."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-86tQJsWk\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-86tQJsWk',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-FgxuyXw1\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-FgxuyXw1',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[1];\n",
+    "t q[0];\n",
+    "\"\"\")\n",
+    "g = c.to_graph()\n",
+    "zx.draw(g)\n",
+    "\n",
+    "# Unfuse the non-Clifford spiders, so they look like outputs measured in {|T>, Z|T>}\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-n70lqyvy\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-n70lqyvy',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 0, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 0, \"t\": \"Z\"}, {\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-7iw3V0Uv\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-7iw3V0Uv',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-gv0SdnO8\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-gv0SdnO8',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 0, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 0, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# The relevant Pauli webs for this example are the Z and X webs of the output 2\n",
+    "# as well as the Z-web of the non-Clifford spider 3.\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[2])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[2])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-68BIjTYD\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-68BIjTYD',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-ZOdnCrY0\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-ZOdnCrY0',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# As we did in the Clifford examples, we can introduce random Pauli errors on all the edges\n",
+    "random.seed(1330)\n",
+    "errors = PauliWeb.random(g)\n",
+    "zx.draw(g, pauli_web=errors)\n",
+    "\n",
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# To implement the T-measurement at node 3, we need to look at the associated Z-web of 3\n",
+    "# If it anti-commutes with the errors, we should apply an X correction before we measure, or equivalently,\n",
+    "# flip whether we are measuring X or Y in the fault-tolerant gadget that injects a magic state.\n",
+    "if not zwebs[3].commutes_with(errors):\n",
+    "    errors1.add_half_edge((3,1), 'X')\n",
+    "\n",
+    "# a single Y error indeed anti-commutes with zweb[3], so a correction appears\n",
+    "zx.draw(g, pauli_web=errors1)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Y9pl4KCi\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Y9pl4KCi',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 1, \"target\": 0, \"t\": \"Y\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"Y\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-OsaJfy90\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-OsaJfy90',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "errors2 = errors1.copy()\n",
+    "\n",
+    "# The T-measurement itself will either apply <T| or <T|Z with uniform probability. We can simulate this by\n",
+    "# randomly introducing a Z error next to node 3.\n",
+    "if random.random() > 0.5:\n",
+    "    errors2.add_half_edge((v, n), 'Z')\n",
+    "\n",
+    "# Finally, we apply corrections on the output just like we did in the Clifford case\n",
+    "if not zwebs[2].commutes_with(errors2): errors2.add_half_edge((2,1), 'X')\n",
+    "if not xwebs[2].commutes_with(errors2): errors2.add_half_edge((2,1), 'Z')\n",
+    "\n",
+    "zx.draw(g, pauli_web=errors2)\n",
+    "\n",
+    "# The result, after we have applied corrections, should indeed be a single T gate\n",
+    "ge = errors2.graph_with_errors()\n",
+    "zx.full_reduce(ge)\n",
+    "zx.draw(ge)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The next example is a circuit with some CNOT gates and a T gate, which can be simplified to a single phase gadget. I'm doing this manually here, since the automated simplifier comes up with a different answer (which is equivalent to this one, up to local Cliffords, but less clear what is going on)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-3X54ThV6\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-3X54ThV6',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 250, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-W6wTVxam\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-W6wTVxam',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 110.00000000000001, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 200.0, \"y\": 190.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 80.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 300, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Rc6oSDf4\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Rc6oSDf4',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 110.00000000000001, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 200.0, \"y\": 190.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 80.0, \"y\": 200.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 2, \"t\": \"Z\"}, {\"source\": 19, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 20, \"t\": \"Z\"}, {\"source\": 20, \"target\": 19, \"t\": \"Z\"}, {\"source\": 19, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 19, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 1, \"target\": 20, \"t\": \"Z\"}, {\"source\": 20, \"target\": 1, \"t\": \"Z\"}]}'), 400, 300, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[3];\n",
+    "cx q[0], q[1];\n",
+    "cx q[1], q[2];\n",
+    "t q[2];\n",
+    "cx q[1], q[2];\n",
+    "cx q[0], q[1];\n",
+    "\"\"\")\n",
+    "zx.draw(c)\n",
+    "\n",
+    "# manual ZX simplification to get a single phase gadget\n",
+    "g = c.to_graph()\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.basicrules.strong_comp(g, 5, 7)\n",
+    "zx.simplify.spider_simp(g, quiet=True)\n",
+    "zx.basicrules.strong_comp(g, 3, 6)\n",
+    "zx.simplify.spider_simp(g, quiet=True)\n",
+    "zx.simplify.id_simp(g, quiet=True)\n",
+    "\n",
+    "zx.draw(g, labels=True)\n",
+    "\n",
+    "d = dict()\n",
+    "\n",
+    "# pauli web calculation\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g, debug=d)\n",
+    "\n",
+    "# highlight the web associated to the T spider\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[15])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This and the output Pauli webs is enough data to simulate running this computation and computing corrections. Rather than doing that explicitly, lets go straight to a random Clifford+T circuit."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-7RH1NAq9\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-7RH1NAq9',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 48.484848484848484, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 48.484848484848484, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 48.484848484848484, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 121.21212121212122, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-BPwOo212\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-BPwOo212',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Generate a random CNOT, H, T circuit\n",
+    "random.seed(1330)\n",
+    "c = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=30)\n",
+    "g = c.to_graph(compress_rows=False)\n",
+    "zx.draw(g)\n",
+    "\n",
+    "# Unfuse the non-Clifford spiders, so they look like outputs measured in {|T>, Z|T>}\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-BMT0hdEg\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-BMT0hdEg',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 8, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 15, \"target\": 12, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 18, \"target\": 14, \"t\": \"X\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 21, \"target\": 22, \"t\": \"Z\"}, {\"source\": 53, \"target\": 22, \"t\": \"X\"}, {\"source\": 28, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 27, \"t\": \"Y\"}, {\"source\": 28, \"target\": 29, \"t\": \"X\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 33, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"Y\"}, {\"source\": 37, \"target\": 40, \"t\": \"Y\"}, {\"source\": 38, \"target\": 49, \"t\": \"Y\"}, {\"source\": 40, \"target\": 41, \"t\": \"Y\"}, {\"source\": 41, \"target\": 42, \"t\": \"X\"}, {\"source\": 43, \"target\": 56, \"t\": \"Z\"}, {\"source\": 57, \"target\": 44, \"t\": \"Y\"}, {\"source\": 45, \"target\": 58, \"t\": \"Z\"}, {\"source\": 46, \"target\": 47, \"t\": \"X\"}, {\"source\": 47, \"target\": 50, \"t\": \"Z\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# as before, we can introduce random Pauli errors into the graph\n",
+    "random.seed(1337)\n",
+    "errors = PauliWeb.random(g)\n",
+    "zx.draw(g, pauli_web=errors)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{51: 1, 52: 1, 53: 1, 54: 1, 55: 2, 56: 2, 57: 2, 58: 2}\n"
+     ]
+    }
+   ],
+   "source": [
+    "# however, the correction strategy is more elaborate, since we have internal non-Clifford\n",
+    "# gadgets to handle. First, compute Pauli webs:\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "\n",
+    "# `order` tells us the order in which we should measure non-Clifford spiders. For Clifford diagrams,\n",
+    "# it was empty, since there were no non-Clifford spiders. In this example, it shows that we need to\n",
+    "# split the non-Clifford spiders into 2 time steps, where the last 4 measurements might depend on the\n",
+    "# outcomes of the first 4.\n",
+    "print(order)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-UPQgn1Y0\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-UPQgn1Y0',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Y\"}, {\"source\": 4, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 3, \"t\": \"Y\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Y\"}, {\"source\": 5, \"target\": 6, \"t\": \"Y\"}, {\"source\": 6, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 7, \"t\": \"Z\"}, {\"source\": 6, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 7, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 7, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 13, \"t\": \"Y\"}, {\"source\": 13, \"target\": 16, \"t\": \"Y\"}, {\"source\": 16, \"target\": 13, \"t\": \"Y\"}, {\"source\": 14, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 14, \"t\": \"X\"}, {\"source\": 14, \"target\": 18, \"t\": \"Y\"}, {\"source\": 16, \"target\": 15, \"t\": \"X\"}, {\"source\": 15, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 19, \"t\": \"Y\"}, {\"source\": 18, \"target\": 14, \"t\": \"Y\"}, {\"source\": 18, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 18, \"t\": \"X\"}, {\"source\": 18, \"target\": 20, \"t\": \"Y\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 19, \"target\": 24, \"t\": \"Y\"}, {\"source\": 24, \"target\": 19, \"t\": \"Y\"}, {\"source\": 19, \"target\": 51, \"t\": \"X\"}, {\"source\": 20, \"target\": 18, \"t\": \"Y\"}, {\"source\": 20, \"target\": 23, \"t\": \"Y\"}, {\"source\": 23, \"target\": 20, \"t\": \"Y\"}, {\"source\": 20, \"target\": 52, \"t\": \"X\"}, {\"source\": 23, \"target\": 30, \"t\": \"Y\"}, {\"source\": 24, \"target\": 26, \"t\": \"Y\"}, {\"source\": 26, \"target\": 24, \"t\": \"Y\"}, {\"source\": 26, \"target\": 25, \"t\": \"X\"}, {\"source\": 25, \"target\": 26, \"t\": \"X\"}, {\"source\": 26, \"target\": 28, \"t\": \"Y\"}, {\"source\": 28, \"target\": 26, \"t\": \"Y\"}, {\"source\": 28, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 28, \"t\": \"X\"}, {\"source\": 28, \"target\": 29, \"t\": \"Y\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 29, \"target\": 30, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 29, \"target\": 34, \"t\": \"Z\"}, {\"source\": 30, \"target\": 23, \"t\": \"Y\"}, {\"source\": 30, \"target\": 33, \"t\": \"X\"}, {\"source\": 33, \"target\": 30, \"t\": \"Z\"}, {\"source\": 34, \"target\": 29, \"t\": \"Z\"}, {\"source\": 34, \"target\": 35, \"t\": \"Z\"}, {\"source\": 35, \"target\": 34, \"t\": \"Z\"}, {\"source\": 34, \"target\": 37, \"t\": \"Z\"}, {\"source\": 37, \"target\": 34, \"t\": \"Z\"}, {\"source\": 51, \"target\": 19, \"t\": \"X\"}, {\"source\": 52, \"target\": 20, \"t\": \"X\"}, {\"source\": 15, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 15, \"t\": \"X\"}, {\"source\": 25, \"target\": 27, \"t\": \"X\"}, {\"source\": 27, \"target\": 25, \"t\": \"X\"}, {\"source\": 33, \"target\": 35, \"t\": \"Z\"}, {\"source\": 35, \"target\": 33, \"t\": \"Z\"}, {\"source\": 37, \"target\": 40, \"t\": \"Z\"}, {\"source\": 40, \"target\": 37, \"t\": \"Z\"}, {\"source\": 40, \"target\": 55, \"t\": \"Z\"}, {\"source\": 55, \"target\": 40, \"t\": \"Z\"}, {\"source\": 2, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 2, \"t\": \"Z\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# For example, if we look at the Z-web of spider 55, it touches 51 and 52, which means we need\n",
+    "# to be done with those spiders first.\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[55])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-gVPx1xKb\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-gVPx1xKb',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 8, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 15, \"target\": 12, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 18, \"target\": 14, \"t\": \"X\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 21, \"target\": 22, \"t\": \"Z\"}, {\"source\": 53, \"target\": 22, \"t\": \"X\"}, {\"source\": 28, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 27, \"t\": \"Y\"}, {\"source\": 28, \"target\": 29, \"t\": \"X\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 33, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"Y\"}, {\"source\": 37, \"target\": 40, \"t\": \"Y\"}, {\"source\": 38, \"target\": 49, \"t\": \"Y\"}, {\"source\": 40, \"target\": 41, \"t\": \"Y\"}, {\"source\": 41, \"target\": 42, \"t\": \"X\"}, {\"source\": 43, \"target\": 56, \"t\": \"Z\"}, {\"source\": 57, \"target\": 44, \"t\": \"Y\"}, {\"source\": 45, \"target\": 58, \"t\": \"Z\"}, {\"source\": 46, \"target\": 47, \"t\": \"X\"}, {\"source\": 47, \"target\": 50, \"t\": \"Z\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-1qvKxUhx\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-1qvKxUhx',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 8, \"t\": \"Y\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 7, \"t\": \"Y\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}, {\"source\": 15, \"target\": 12, \"t\": \"Z\"}, {\"source\": 13, \"target\": 14, \"t\": \"Z\"}, {\"source\": 14, \"target\": 13, \"t\": \"X\"}, {\"source\": 18, \"target\": 14, \"t\": \"X\"}, {\"source\": 19, \"target\": 16, \"t\": \"Y\"}, {\"source\": 17, \"target\": 18, \"t\": \"Z\"}, {\"source\": 21, \"target\": 22, \"t\": \"Z\"}, {\"source\": 28, \"target\": 27, \"t\": \"Z\"}, {\"source\": 27, \"target\": 31, \"t\": \"X\"}, {\"source\": 31, \"target\": 27, \"t\": \"Y\"}, {\"source\": 28, \"target\": 29, \"t\": \"X\"}, {\"source\": 29, \"target\": 28, \"t\": \"Y\"}, {\"source\": 30, \"target\": 29, \"t\": \"Y\"}, {\"source\": 33, \"target\": 35, \"t\": \"Y\"}, {\"source\": 35, \"target\": 34, \"t\": \"X\"}, {\"source\": 36, \"target\": 37, \"t\": \"Y\"}, {\"source\": 37, \"target\": 40, \"t\": \"Y\"}, {\"source\": 38, \"target\": 49, \"t\": \"Y\"}, {\"source\": 40, \"target\": 41, \"t\": \"Y\"}, {\"source\": 41, \"target\": 42, \"t\": \"X\"}, {\"source\": 43, \"target\": 56, \"t\": \"Z\"}, {\"source\": 45, \"target\": 58, \"t\": \"Z\"}, {\"source\": 46, \"target\": 47, \"t\": \"X\"}, {\"source\": 47, \"target\": 50, \"t\": \"Z\"}, {\"source\": 51, \"target\": 19, \"t\": \"Z\"}, {\"source\": 52, \"target\": 20, \"t\": \"X\"}, {\"source\": 54, \"target\": 31, \"t\": \"Z\"}, {\"source\": 55, \"target\": 40, \"t\": \"Y\"}, {\"source\": 49, \"target\": 38, \"t\": \"Z\"}, {\"source\": 50, \"target\": 47, \"t\": \"Y\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-nGrhraj0\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-nGrhraj0',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 24.242424242424242, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 24.242424242424242, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 24.242424242424242, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 48.484848484848484, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 48.484848484848484, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 72.72727272727272, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 72.72727272727272, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 96.96969696969697, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 96.96969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 121.21212121212122, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 145.45454545454544, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 145.45454545454544, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 169.6969696969697, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 193.93939393939394, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 193.93939393939394, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 218.1818181818182, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 218.1818181818182, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 242.42424242424244, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 242.42424242424244, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 266.6666666666667, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 290.9090909090909, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 315.1515151515151, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 339.3939393939394, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 363.6363636363636, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 387.8787878787879, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 412.1212121212121, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 412.1212121212121, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 436.3636363636364, \"y\": 121.21212121212122, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 436.3636363636364, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 460.6060606060606, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 460.6060606060606, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 484.8484848484849, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 509.09090909090907, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 533.3333333333334, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 557.5757575757576, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 557.5757575757576, \"y\": 96.96969696969697, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 581.8181818181818, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 581.8181818181818, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 606.060606060606, \"y\": 96.96969696969697, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 606.060606060606, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 630.3030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 654.5454545454545, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 654.5454545454545, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 678.7878787878788, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 703.030303030303, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 727.2727272727273, \"y\": 72.72727272727272, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 751.5151515151515, \"y\": 72.72727272727272, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 751.5151515151515, \"y\": 121.21212121212122, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 775.7575757575758, \"y\": 72.72727272727272, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 775.7575757575758, \"y\": 96.96969696969697, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 775.7575757575758, \"y\": 121.21212121212122, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 266.6666666666667, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 290.9090909090909, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 339.3939393939394, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 484.8484848484849, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 630.3030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 678.7878787878788, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 703.030303030303, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 727.2727272727273, \"y\": 48.484848484848484, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"24\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 53, \"target\": 22, \"t\": \"X\"}, {\"source\": 57, \"target\": 44, \"t\": \"Y\"}, {\"source\": 51, \"target\": 19, \"t\": \"Z\"}, {\"source\": 52, \"target\": 20, \"t\": \"X\"}, {\"source\": 54, \"target\": 31, \"t\": \"Z\"}, {\"source\": 55, \"target\": 40, \"t\": \"Y\"}, {\"source\": 49, \"target\": 38, \"t\": \"Z\"}, {\"source\": 50, \"target\": 47, \"t\": \"Y\"}]}'), 800.0, 145.45454545454544, 24.242424242424242,\n",
+       "  4.848484848484849, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# traverse through the T spiders in the order given by `order`\n",
+    "for v in sorted(order.keys(), key=lambda v: order[v]):\n",
+    "    n = next(iter(g.neighbors(v)))\n",
+    "\n",
+    "    # if the Z-web associated with that spider anti-commutes with previous errors,\n",
+    "    # introduce an X error before the measurement. This has the same effect, up to Paulis\n",
+    "    # as choosing to measure Y rather than X in the fault-tolerant gadget\n",
+    "    if not zwebs[v].commutes_with(errors1):\n",
+    "        errors1.add_half_edge((v, n), 'X')\n",
+    "    \n",
+    "    # \"do\" the measurement, i.e. plug in |T> or Z|T> with uniform probability\n",
+    "    if random.random() > 0.5:\n",
+    "        errors1.add_half_edge((v, n), 'Z')\n",
+    "\n",
+    "# finally, use the output webs to correct outputs, as before\n",
+    "for o in g.outputs():\n",
+    "    n = next(iter(g.neighbors(o)))\n",
+    "    if not zwebs[o].commutes_with(errors1):\n",
+    "        errors1.add_half_edge((o,n), 'X')\n",
+    "    if not xwebs[o].commutes_with(errors1):\n",
+    "        errors1.add_half_edge((o,n), 'Z')\n",
+    "\n",
+    "# here is the original web\n",
+    "zx.draw(g, pauli_web=errors)\n",
+    "\n",
+    "# here is the corrected web\n",
+    "zx.draw(g, pauli_web=errors1)\n",
+    "\n",
+    "# n.b. we can multiply these two to just show the corrections\n",
+    "zx.draw(g, pauli_web=errors*errors1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-XpsFdxlQ\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-XpsFdxlQ',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"106\", \"x\": 100, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"107\", \"x\": 100, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"108\", \"x\": 100, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"106\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"107\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"108\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 250, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "h = g.adjoint() * errors1.graph_with_errors()\n",
+    "zx.full_reduce(h)\n",
+    "h.pack_circuit_rows()\n",
+    "zx.draw(h)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Evimfaz3\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Evimfaz3',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 25.806451612903224, \"y\": 51.61290322580645, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 25.806451612903224, \"y\": 77.41935483870967, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 25.806451612903224, \"y\": 103.2258064516129, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 51.61290322580645, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 77.41935483870967, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 51.61290322580645, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 51.61290322580645, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 103.2258064516129, \"y\": 103.2258064516129, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 103.2258064516129, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 129.03225806451613, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 129.03225806451613, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 154.83870967741933, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 154.83870967741933, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 180.64516129032256, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 180.64516129032256, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 206.4516129032258, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 232.25806451612902, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 258.06451612903226, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 283.8709677419355, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 283.8709677419355, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 309.67741935483866, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 206.4516129032258, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": 335.4838709677419, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": 335.4838709677419, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": 361.2903225806451, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": 361.2903225806451, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": 387.09677419354836, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": 387.09677419354836, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": 412.9032258064516, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": 412.9032258064516, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": 412.9032258064516, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 438.7096774193548, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 438.7096774193548, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 464.51612903225805, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 464.51612903225805, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 490.3225806451613, \"y\": 103.2258064516129, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 490.3225806451613, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 516.1290322580645, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 516.1290322580645, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 516.1290322580645, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 541.9354838709677, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 567.741935483871, \"y\": 51.61290322580645, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 567.741935483871, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 593.5483870967741, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 593.5483870967741, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 541.9354838709677, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 619.3548387096773, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 567.741935483871, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 619.3548387096773, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 619.3548387096773, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 645.1612903225806, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 645.1612903225806, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 670.9677419354838, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 670.9677419354838, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 696.7741935483871, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 696.7741935483871, \"y\": 77.41935483870967, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 696.7741935483871, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 722.5806451612902, \"y\": 103.2258064516129, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 748.3870967741935, \"y\": 103.2258064516129, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 748.3870967741935, \"y\": 77.41935483870967, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"60\", \"x\": 722.5806451612902, \"y\": 51.61290322580645, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 774.1935483870967, \"y\": 51.61290322580645, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 774.1935483870967, \"y\": 77.41935483870967, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 774.1935483870967, \"y\": 103.2258064516129, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"15\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"20\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"46\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"47\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"49\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"50\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"53\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"60\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"57\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"57\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 129.03225806451613, 25.806451612903224,\n",
+       "  5.161290322580645, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Q7E0F7EA\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Q7E0F7EA',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 300, \"y\": 300, \"t\": 2, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 250, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 300, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"66\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"67\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"68\", \"x\": 300, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"18\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"65\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"67\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 350, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# The same procedure works with a reduced ZX-diagram, rather than a circuit, as input\n",
+    "random.seed(1337)\n",
+    "g = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=40).to_graph()\n",
+    "zx.draw(g)\n",
+    "zx.full_reduce(g)\n",
+    "g.normalize()\n",
+    "\n",
+    "# for simplicity, we'll make sure all the non-Clifford spiders are Z\n",
+    "zx.to_rg(g, init_z=set(v for v in g.vertices() if not zx.utils.phase_is_clifford(g.phase(v))))\n",
+    "\n",
+    "zx.simplify.unfuse_non_cliffords(g)\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-WnlR6jxO\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-WnlR6jxO',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 300, \"y\": 300, \"t\": 2, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 250, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 300, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"66\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"67\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"68\", \"x\": 300, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"18\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"65\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"67\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 39, \"t\": \"Y\"}, {\"source\": 38, \"target\": 18, \"t\": \"Z\"}, {\"source\": 38, \"target\": 63, \"t\": \"Y\"}, {\"source\": 45, \"target\": 38, \"t\": \"X\"}, {\"source\": 51, \"target\": 45, \"t\": \"Z\"}, {\"source\": 45, \"target\": 66, \"t\": \"Z\"}, {\"source\": 66, \"target\": 45, \"t\": \"X\"}, {\"source\": 67, \"target\": 51, \"t\": \"X\"}, {\"source\": 68, \"target\": 54, \"t\": \"Y\"}, {\"source\": 59, \"target\": 62, \"t\": \"Z\"}]}'), 400, 350, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-DwF2lmUI\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-DwF2lmUI',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 300, \"y\": 300, \"t\": 2, \"phase\": \"3\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 100, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 250, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"59\", \"x\": 300, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"61\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 100, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"66\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"67\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"68\", \"x\": 300, \"y\": 150, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"18\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"39\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"38\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"41\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"65\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"51\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"67\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 67, \"target\": 51, \"t\": \"Y\"}, {\"source\": 68, \"target\": 54, \"t\": \"Z\"}, {\"source\": 64, \"target\": 41, \"t\": \"Z\"}, {\"source\": 65, \"target\": 39, \"t\": \"Y\"}, {\"source\": 61, \"target\": 54, \"t\": \"X\"}]}'), 400, 350, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-toyEzsY9\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "var _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#ccffcc\", \"Z\": \"#aabbff\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xweb\": \"#ff8888\", \"Yweb\": \"#99dd99\", \"Zweb\": \"#aabbff\"}');\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return _settings_colors['boundary'];\n",
+       "    else if (t == 1) return _settings_colors['Z']; // \"#ccffcc\";\n",
+       "    else if (t == 2) return _settings_colors['X']; // \"#ff8888\";\n",
+       "    else if (t == 3) return _settings_colors['H']; // \"yellow\";\n",
+       "    else if (t == 4) return _settings_colors['W']; // \"black\";\n",
+       "    else if (t == 5) return _settings_colors['Walt']; // \"black\";\n",
+       "    else if (t == 6) return _settings_colors['Zalt']; // \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return _settings_colors['edge']; //\"black\";\n",
+       "    else if (t == 2) return _settings_colors['Hedge']; // \"#08f\";\n",
+       "    else if (t == 3) return _settings_colors['Xedge']; // \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return _settings_colors['Xweb'];\n",
+       "    else if (t == 'Y') return _settings_colors['Yweb'];\n",
+       "    else if (t == 'Z') return _settings_colors['Zweb'];\n",
+       "    else if (t == 'I') return '#dddddd';\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-toyEzsY9',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 100, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": 100, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": 100, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 150, 250, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "random.seed(1337)\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "errors = PauliWeb.random(g)\n",
+    "errors1 = errors.copy()\n",
+    "\n",
+    "# \"simulate\" the diagram and compute corrections, as before\n",
+    "for v in sorted(order.keys(), key=lambda v: order[v]):\n",
+    "    n = next(iter(g.neighbors(v)))\n",
+    "    if not zwebs[v].commutes_with(errors1): errors1.add_half_edge((v, n), 'X')\n",
+    "    if random.random() > 0.5: errors1.add_half_edge((v, n), 'Z')\n",
+    "for o in g.outputs():\n",
+    "    n = next(iter(g.neighbors(o)))\n",
+    "    if not zwebs[o].commutes_with(errors1): errors1.add_half_edge((o,n), 'X')\n",
+    "    if not xwebs[o].commutes_with(errors1): errors1.add_half_edge((o,n), 'Z')\n",
+    "\n",
+    "zx.draw(g, pauli_web=errors)\n",
+    "zx.draw(g, pauli_web=errors*errors1)\n",
+    "\n",
+    "h = g.adjoint() * errors1.graph_with_errors()\n",
+    "zx.full_reduce(h)\n",
+    "h.pack_circuit_rows()\n",
+    "zx.draw(h)"
+   ]
   },
   {
    "cell_type": "code",
@@ -19093,7 +29643,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "Python 3",
    "language": "python",
    "name": "python3"
   },
@@ -19107,7 +29657,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.0"
   }
  },
  "nbformat": 4,
diff --git a/pyzx/gflow.py b/pyzx/gflow.py
index bf432cff..b106021c 100644
--- a/pyzx/gflow.py
+++ b/pyzx/gflow.py
@@ -137,7 +137,7 @@ def gflow(
 
         if not correct:
             if len(vertices) == len(processed):
-                return {v: k - i - 1 for v,i in l.items()}, gflow
+                return {v: i if reverse else k - i - 1 for v,i in l.items()}, gflow
             return None
         else:
             processed.update(correct)
diff --git a/pyzx/pauliweb.py b/pyzx/pauliweb.py
index ba865e27..dcae3f48 100644
--- a/pyzx/pauliweb.py
+++ b/pyzx/pauliweb.py
@@ -17,10 +17,11 @@
 from __future__ import annotations
 
 from .gflow import gflow
-from .utils import EdgeType, VertexType, vertex_is_zx
+from .utils import EdgeType, VertexType, vertex_is_zx, phase_is_clifford
 from .graph.base import BaseGraph, VT, ET
 
 from typing import Any, Optional, Set, Dict, Tuple, Generic
+import random
 
 def multiply_paulis(p1: str, p2: str) -> str:
     if p1 == 'I': return p2
@@ -57,6 +58,22 @@ def __init__(self, g: BaseGraph[VT,ET]):
         self.g = g
         self.es: Dict[Tuple[VT,VT], str] = dict()
     
+    @staticmethod
+    def random(g: BaseGraph[VT,ET], pX=0.1, pY=0.1, pZ=0.1):
+        w = PauliWeb(g)
+        for e in g.edges():
+            s,t = g.edge_st(e)
+            for _ in range(2):
+                p = random.random()
+                if p < pX:
+                    w.add_half_edge((s,t), 'X')
+                elif p < pX + pY:
+                    w.add_half_edge((s,t), 'Y')
+                elif p < pX + pY + pZ:
+                    w.add_half_edge((s,t), 'Z')
+                s,t = (t,s)
+        return w
+    
     def copy(self) -> PauliWeb:
         pw = PauliWeb(self.g)
         pw.es = self.es.copy()
@@ -98,15 +115,73 @@ def commutes_with(self, other: PauliWeb):
             if p1 != 'I' and p2 != 'I' and p1 != p2:
                 comm = not comm
         return comm
+    
+    def graph_with_errors(self) -> BaseGraph[VT,ET]:
+        g = self.g.clone()
+        edges = set((s,t) if s < t else (t,s) for s,t in self.es)
+        for s,t in edges:
+            p0 = self.es.get((s,t), 'I')
+            p1 = self.es.get((t,s), 'I')
+
+            e = g.edge(s, t)
+            et = g.edge_type(e)
+            g.remove_edge(e)
+
+            spots = 1
+            for p in [p0,p1]:
+                if p == 'Y': spots += 2
+                elif p == 'X' or p == 'Z': spots += 1
+
+            q, r = (g.qubit(s), g.row(s))
+            dq, dr = ((g.qubit(t) - q)/spots, (g.row(t) - r)/spots)
+
+            v0 = s
+            v1 = t
+            if p0 == 'X':
+                q += dq; r += dr
+                v0 = g.add_vertex(VertexType.X, q, r, phase=1)
+                g.add_edge((s, v0))
+            elif p0 == 'Y':
+                q += dq; r += dr
+                v = g.add_vertex(VertexType.X, q, r, phase=1)
+                q += dq; r += dr
+                v0 = g.add_vertex(VertexType.Z, q, r, phase=1)
+                g.add_edge((s, v))
+                g.add_edge((v, v0))
+            elif p0 == 'Z':
+                q += dq; r += dr
+                v0 = g.add_vertex(VertexType.Z, q, r, phase=1)
+                g.add_edge((s, v0))
 
+            if p1 == 'X':
+                q += dq; r += dr
+                v1 = g.add_vertex(VertexType.X, q, r, phase=1)
+                g.add_edge((t, v1))
+            elif p1 == 'Y':
+                q += dq; r += dr
+                v1 = g.add_vertex(VertexType.Z, q, r, phase=1)
+                q += dq; r += dr
+                v = g.add_vertex(VertexType.X, q, r, phase=1)
+                g.add_edge((v1, v))
+                g.add_edge((v, t))
+            elif p1 == 'Z':
+                q += dq; r += dr
+                v1 = g.add_vertex(VertexType.Z, q, r, phase=1)
+                g.add_edge((t, v1))
+            
+            g.add_edge((v0,v1), et)
+        return g
 
-def transpose_corrections(c: Dict[VT, Set[VT]]) -> Dict[VT, Set[VT]]:
-    ct: Dict[VT, Set[VT]] = dict()
-    for k,s in c.items():
-        for v in s:
-            if v not in ct: ct[v] = set()
-            ct[v].add(k)
-    return ct
+
+
+
+# def transpose_corrections(c: Dict[VT, Set[VT]]) -> Dict[VT, Set[VT]]:
+#     ct: Dict[VT, Set[VT]] = dict()
+#     for k,s in c.items():
+#         for v in s:
+#             if v not in ct: ct[v] = set()
+#             ct[v].add(k)
+#     return ct
 
 def compute_pauli_webs(g: BaseGraph[VT,ET], backwards:bool=True, debug:Optional[Dict[str,Any]]=None) -> Tuple[Dict[VT, int], Dict[VT, PauliWeb[VT,ET]], Dict[VT, PauliWeb[VT,ET]]]:
     g1 = g.clone()
@@ -155,12 +230,11 @@ def compute_pauli_webs(g: BaseGraph[VT,ET], backwards:bool=True, debug:Optional[
     if not gf:
         raise ValueError("Graph must have gFlow")
     order, corr = gf
+    vset = g.vertex_set()
+    order = { v: i for v,i in order.items() if v in vset and not phase_is_clifford(g.phase(v)) }
 
     zwebs: Dict[VT, PauliWeb[VT,ET]] = dict()
     xwebs: Dict[VT, PauliWeb[VT,ET]] = dict()
-    vset = g.vertex_set()
-    # corr_t = transpose_corrections(corr)
-
     for v,c in corr.items():
         pw = PauliWeb(g)
         for v1 in c:
diff --git a/pyzx/simplify.py b/pyzx/simplify.py
index 1d4cdbe7..9823d77c 100644
--- a/pyzx/simplify.py
+++ b/pyzx/simplify.py
@@ -599,6 +599,20 @@ def to_graph_like(g: BaseGraph[VT,ET]) -> None:
 
     assert(is_graph_like(g,strict=True))
 
+def unfuse_non_cliffords(g: BaseGraph[VT,ET]) -> None:
+    """Unfuses any non-Clifford spider into a magic state connected to a phase-free spider
+
+    Replaces any spider with a non-Clifford phase p and degree n > 1 with a degree 1 spider with phase p connected to
+    a degree n+1 spider with phase 0.
+    """
+    for v in list(g.vertices()):
+        ty = g.type(v)
+        p = g.phase(v)
+        if vertex_is_zx(ty) and not phase_is_clifford(p) and g.vertex_degree(v) > 1:
+            v1 = g.add_vertex(ty, qubit=-1, row=g.row(v), phase=p)
+            g.set_phase(v, 0)
+            g.add_edge((v, v1))
+
 def to_clifford_normal_form_graph(g: BaseGraph[VT,ET]) -> None:
     """Converts a graph that is Clifford into the form described by the right-hand side of eq. (11) of
     *Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus* (https://arxiv.org/abs/1902.03178).