dynamic-circuits-3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bdcd6645",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-17T19:58:55.387212Z",
     "start_time": "2022-11-17T19:58:55.387195Z"
    }
   },
   "source": [
    "![beta](images/dynamic3/beta-version.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6288dd3",
   "metadata": {},
   "source": [
    "# Dynamic circuits - III\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    This notebook is requires installing the <tt>qiskit-ibm-provider</tt>:\n",
    "    <ul>\n",
    "        <li>IBM Qiskit Provider: <tt>pip install qiskit-ibm-provider</tt></li>\n",
    "    </ul>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf62c349",
   "metadata": {},
   "source": [
    "## Background\n",
    "\n",
    "Having stuck with the BV circuit for some time now, let us branch out to other uses of dynamic circuits.  There is a wide variety of examples that are impossible to implement without dynamic circuits.  One of the most cited examples is that of quantum teleportation, where entanglement between qubits and classical communication is used to move the state of one qubit to another.  Another prominent use case area for dynamic circuits is quantum error correction (QEC).  Here we will examine examples of both."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0be0d561",
   "metadata": {},
   "source": [
    "## Front matter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fb3705a3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:16:35.140767Z",
     "start_time": "2022-12-02T20:16:35.121875Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit import *\n",
    "\n",
    "# We will use random 1Q gates for teleportation\n",
    "from qiskit.quantum_info import random_unitary\n",
    "# We will have to look at marginal counts (subsets over a few bits)\n",
    "from qiskit.result import marginal_counts\n",
    "\n",
    "# Aer simulator\n",
    "from qiskit_aer import AerSimulator\n",
    "\n",
    "# Load a fake device\n",
    "from qiskit.providers.fake_provider import FakeHanoi\n",
    "\n",
    "\n",
    "# Load the QASM3 exporter\n",
    "from qiskit import qasm3\n",
    "\n",
    "\n",
    "# Plotting tools\n",
    "import matplotlib.pyplot as plt\n",
    "try:\n",
    "    plt.style.use('quantum-light')\n",
    "except:\n",
    "    pass\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38cf84ab",
   "metadata": {},
   "source": [
    "### Load IBM provider and select target backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3d9af14a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-30T17:01:58.777258Z",
     "start_time": "2022-11-30T17:01:42.767628Z"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_provider import IBMProvider\n",
    "\n",
    "provider = IBMProvider()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5b3e64d8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-30T17:01:58.785212Z",
     "start_time": "2022-11-30T17:01:58.781396Z"
    }
   },
   "outputs": [],
   "source": [
    "backend = provider.get_backend('ibm_peekskill')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af03c5cd",
   "metadata": {},
   "source": [
    "## Quantum teleportation\n",
    "\n",
    "Quantum teleportation is an example of utilizing quantum entanglement and classical resources to transfer quantum information from a sender to a receiver.  That we transfer the information, as oppose to copying it, is a requirement of the [No-cloning theorem](https://en.wikipedia.org/wiki/No-cloning_theorem), which forbids one from copy an unknown quantum state.\n",
    "\n",
    "Suppose we want to teleport the state for qubit C $|\\psi\\rangle_{\\rm C}= \\alpha|0\\rangle_{\\rm C} +\\beta|1\\rangle_{\\rm C}$ that is shared with qubit A (Alice) over to qubit B (Bob).  First we create a Bell pair (entanglement resource) between A and B, such that the state of the complete system is (in Qiskit bit-ordering):\n",
    "\n",
    "$$\n",
    "|\\Psi\\rangle_{\\rm BAC} = \\frac{1}{\\sqrt{2}}\\left[ |00\\rangle_{\\rm BA} + |11\\rangle_{\\rm BA}\\right]\\otimes \\left[\\alpha|0\\rangle_{\\rm C}+\\beta |1\\rangle_{\\rm C}\\right]\n",
    "$$\n",
    "\n",
    "\n",
    "Now to proceed, we will make use of the Bell basis (In Qiskit bit-ordering):\n",
    "\n",
    "$$\n",
    "|B_{0}\\rangle = \\mathbb{I}\\otimes \\mathbb{I}|B_{0}\\rangle = \\frac{1}{\\sqrt{2}}\\left[|00\\rangle+|11\\rangle\\right] \\\\\n",
    "|B_{1}\\rangle = Z\\otimes \\mathbb{I}|B_{0}\\rangle = \\frac{1}{\\sqrt{2}}\\left[|00\\rangle-|11\\rangle\\right]\\\\\n",
    "|B_{2}\\rangle = X\\otimes \\mathbb{I}|B_{0}\\rangle = \\frac{1}{\\sqrt{2}}\\left[|01\\rangle+|10\\rangle\\right]\\\\\n",
    "|B_{3}\\rangle = ZX\\otimes \\mathbb{I}|B_{0}\\rangle = \\frac{1}{\\sqrt{2}}\\left[|01\\rangle-|10\\rangle\\right]\\\\\n",
    "$$\n",
    "\n",
    "Thus, in circuit notation, each Bell state can be formed via:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "75b05b07",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T17:02:00.546587Z",
     "start_time": "2022-12-02T17:02:00.419263Z"
    }
   },
   "outputs": [],
   "source": [
    "def bell_basis(index):\n",
    "\n",
    "    bell = QuantumCircuit(2)\n",
    "    bell.h(0)\n",
    "    bell.cx(0, 1)\n",
    "    if index == 0:\n",
    "        pass\n",
    "    elif index == 1:\n",
    "        bell.z(1)\n",
    "    elif index == 2:\n",
    "        bell.x(1)\n",
    "    elif index == 3:\n",
    "        bell.x(1)\n",
    "        bell.z(1)\n",
    "    else:\n",
    "        raise ValueError('Index must be in [0,1,2,3]')\n",
    "    return bell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "445b953f",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 287.294x200.667 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 182,
       "width": 252
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fLQhNL1922aWaMGF80xYPoNFMcit5L71bztk3yFk+S8EVs+reMq51B5mcS+UZ8j2ZphhBBBAzBECovLxcGzcWh9r1WQBytIk3/5eCQUe/nvyifD6fCgoKw94n+J0rJozXk08+wZZQQDNm0jvKnPt9mXNulPbvVOCdXGnv1vCT2p8o77VPS+268OcZaKEIgNDqoiIFAoFQuz4LQI7137fcrFEXnKd33p2mzxYs0I4dO+X3+5WRkaFhQ4foqquu1Bmnj2jq0gFEiTFGatdFSm1TPQCmtpFp39WdwgA0CQIgVFAQ/vxffRaA1KRHjx7KnXS/cifd3xRlAQCAKGERCFR47ArgOnYAAQAALRsjgNBzzz6t55592u0yAABAjDACCAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUS3C4AiEfJrY2ue6aN22VYJbm1cbsEAGgxCIBAFBiPUUo6gQQA0DwxBQwAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgmQS3CwAAAFLQcVRaWeF2GVbpkJwijzFul+EKAiAAAM1AaWWFen401e0yrLJx/I3qmJLqdhmuYAoYAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsw17AAABJkuM40v4dcnask7NjnbRzg1RSXP3EkmIF3smVOveS6dJHpksfqV1XGWNiXzSABiEAAoDFnJJiBVfNk7atORz6Kg7UfZG/Qk7xUql4qZzvjqWky3TpLXXpK8+A82U694pi1QAaiwAIAJZxAn45az5XcNlMacvXTXPTigNyNuVLm/IV+OJd6cQB8gwdK9P/XJmEpKbpA0CTIQACgCWcb3cpmP+JnBWzpEN7o9vZ1lUKbl0lzf6dzOBL5Rl8uUy7LtHtE0C9EQABIM45VT4FP39LzqJ3JScY287L98tZ9K4CX0yTGXGlPOf+l0xicmxrAFANARAA4pizfa0Cf3tBKtnkciFBOV++r8D6L+W9/D6ZE091tx7AcrwGBgDikFPlU2D+6wq8ebf74e9oe7Yo8OefKpD3BzlVPrerAazFCCAAxBlnV7ECM55pXsHvaE5QzpfTFFj/hbzjJh1+jQyAmGIEEADiiPPvQgWm3tt8w9/R9mxR4K37FPxmhduVANYhAAJAnAhu/EqBdyZJlYfcLqX+fOUKvvuggusWuV0JYBUCIADEgeCmfAXf/4Xkr3S7lMgF/ApOf0LB9YvdrgSwBgEQAFo4Z+vqw+Ev4He7lIYLBhT84Ak5m1e6XQlgBQIgALRgzt7tCrz3sOSvcLuUxqvyKTDtUTl7NrtdCRD3CIAA0EI5TlCBT35dv/17GyGh9wi1uvaXanXtL5XQe0RU+5KvTIGPfy0nGIhuP4DlCIAA0EI5yz6WojxlmtB7hNImvqTkIZcpechlSpv4khJ6nRbVPrVttZwl06PbB2A5AiAAtEDO3u0Kzv1D1PtJGjZWxnvklbHGm6Ck4eOi3m9w/htMBQNRRAAEgBYmNPUbgxW/3g4n1utYkwv4mQoGooidQACghYnF1G+zsG21nMV/lTnjGrcrsd7cMdfr/Mxujb7PvG2bdcHHf2mCitBYBEBLFRcXa9XqIu3atUvl5RVq376d+vbpo5ycbCUk8L8F0Fw5Ab+CC6e6XUbMBBe9KzNsnExiitulAHGFn/QW8fl8+vPUtzXt/fe1fv2GGs/p0KGDfnDrLbpl4s3yer3KX75c/3HN9aHvTzmlu2b/8++xKhnAMZw1C6WyfW6XETsVB+Ssni+TfYnblVhtxjfrVbRvT8TXjcjoqqEdu4Taeyvj4HVFcYIAaIkvvlys3Acf1pYtW2o9r7S0VM89/4IWL16iKS//VkVFa8K+H5SVFc0yAdQhuGym2yXEXHDpTHkIgK568eslEV+Tc0KG/rP3gFB7T0W5frJoTlOWhUZgEYgFpk//UBNvubXG8OfxeNS2bVt5vd6w43PnzdfLU17R6qKisOMDBw6Maq0Ajs/ZVSxtKXC7jNjbsVbOtjV1n4dmo1NKK8285CqlJyVLkoKOo+/P/VibD37rcmX4DiOAce6jGTN1/6TcsGPt2rXVtddco/HjxqhHjx5KTEyU3+/X0mX5mjLlFf1r0ReSpNdef1OZmV3Drs3KIgACbrFx9O87wWUz5c3s53YZqAevMXrvwvE6Oa1N6Ngzyxdp1paNLlaFYzECGMdWrFipSbkPhR07b+S5mvW3mfr5ffeqb9++SkxMlCQlJibqjNNH6I3X/6irrrxCklRWVhb2rKAxRgMHDhCA2HMqy+QU2jt95qyeJ6eM0aOW4OkR54WtGJ6zdZMe/WqhixWhJgTAOFVWVqaf3Huf/P4jm8OPHj1Kr/7+FXXq1Om413k8Hj3+2KPq3Llzte+6d++m9LS0qNQLoHbOlq8lX7nbZbinyifnm+VuV4E6jOnWS/dlH9kucOuhA7p+zkwFHcfFqlATAmCcennK78Ke+evVs6de+s3kas/61SQlJUVXTBhf7XgWz/8B7tm+1u0KXOfsWOd2CahFt7Q2evP8y+UxRpLkDwZ07eyPVFJR5nJlqAkBMA6VlJTo9TfeDDv22GOPKjk5ud73GDp0cLVjWawABlxD+JG0gxDcXCV6PHrvwvHqkJIaOjbpy/n6fOdWF6tCbVgEEofe/NNU+Xy+UPucc87WmWecHtE9MjplVDtW2wKQnTt3qaCwUAUFhSooKFBBYaFKSnaHvp+XN1snnRSD7aOAOEUAlJwd6+U4jsz/H2FC8/HCGRfo9IzMUHt68RpNbsCrYxA7BMA4EwwG9cEHH4Ydu/7ayLdROnaquLYFIM//6td69Q//G3EfAOrHOVgqHYz8Jbxxp+KAtG+H1L5r3eciZq7q0U93Zw0PtdftL9XEeZ+4WBHqgyngOJOfv1w7d+0KtdPS0jR69KiI77Nv376wdm0LQHy+6hvSt2vXNuI+AdSM0b8j+G/RvPRMb6c/nndZqF1W5dfVn36ob/2+Wq5Cc8AIYJz5cvHisPbQIUMatLfvnj3how21LQBp06atzj77LGUNHKisrIHKGjhQJ598knr3PTXifgHUYPc3blfQbDi7N0ka6XYZkJTk8WraRePVNunI8+U//vxTrSwtcbEq1BcBMM4UFq4Ka9e0mKM+Vn4dvttAbc//3X3XnQ3qI1ZWrFypvLx5YSOjQEsyKunfGlX/NVwhCb1HKGnYWHk7NPz5W2+XXjUeS7/jtQbfM1C6Vb6lM1W1fnHdJx/js7zZ+ses+FwMUu71SFknu11Gvb109oVh+/y+tmalXl/ztYsVRe6XTz2j1EAw5v12zsjQqFHnKyc7O+Z9f4cAGGc2bw7f7q2m9/nVx9Kly8LaLXULuBUrV+rJp55VIBBwuxSgwU47sUzqUvd5R0voPUJpE1+S8Tb9X/MmubUSujf8B1dC92wlZV+kg6/dpaoNkS0UOLhvr9Zuqf7YSTzwJSW2mAB4Q+8Buu3UwaH28t07defCT90rqIE2bNioJJ+/7hOb2Nq16/SvRV/okYdylZ09KOb9SzwDGHf27d8f1u7QoUPE91i/foNWrFwZahtjWuwWcHl58wh/aPESG7DoNWnY2KiEv6ZivAlKGj4u4uuSDC8Udlu/th30+3MvCbX3VVbo6tkfqiJQ5WJVLU8gENCcvLmu9U8AjDNH7/whSVX+yH+zmfrW22FtdgAB3MWvMEdUObwCxk2p3gS9f9EEpSUmhY5NnP+JNny7z72i0CAEwDiTnh4e1HbujOy5t6KiNXr3vWlhx1ryDiCjRp1fr91PgObMH4w89PiWzpTTjEdknECVfF/NiPg6PwOArppyzsXK6nBkO9EXVizWh5tYmd0QXq9Xo0dd4Fr/zXd+AA3SsWNHFRdvCrWX5efrppturNe1lT6fch98uNooYkud/pWknOxsPfJQrubkzWURCFqsNklbJUW2o0LV+sU6+NpdSho+rtGLQExy67BjTuUhBXZsaPA9A6Vb5ftqRsTP/0lSersO6tuqZTwnF6lyr0efuV1ELW7pl62b+x15Xm3B9i2atHieewU1gV69erq2CGT0qAtce/5PIgDGnZzsbC1Z8lWoPSdvrvaUluqEOp4FrKqq0j333KuvCwqqfddSF4B8Jzt7kKt/yIDGCq74u4KfTI74uqoNSxoUso6Wfsdr1RZ8BHZs0IFXbmnUfRvqgjFXaPTwCa70HW27K8r1+kdT3S6jRoM6dNJvz74w1N5ZdkjXzpmhgNOyh2QfeShXHY/avs4mTAHHmfPOC38/Vnl5eY2jekfbtWuXfnDbHZo9Z06174wxyjrODiAAYsN06eN2Cc2G6dLX7RKsk5aYpGkXjlerhERJUlUwqOvzZmh72UGXK0NjEADjzJlnnK5+/cL/gszLm6sbbrxJCz//PBQE/X6/1q5bp1+9MFnfGzNOCxYslFR9urd7925KT0+PTfEAataxu+RNdLsK9xmP1Lmn21VY5w8jL1W/dieE2vcuytPcbZtdrAhNgSngOPTUk0/ouutvVFXVkQfA8/OX6+aJt8rr9SotLU0HDhxQMBj+3MOE8ePUv38/FRQUho615AUgQLww3gQpo6e0fY3bpbirYzeZxBS3q7DK6RmZuq7XkV2d9lVWaED7E/TKORc3+J6Tv16idfv3NkV5aAQCYBwanJOj5597Rg9MerDa1G8gEND+Y94VmJiYqLvv+rFuv+0H+tnPHwj7riUvAAHiienSR47lAZDp39hLOeYtCu2SU3T7gCGNuuc7G1YTAJsBpoDj1LixY/TO21N12mnDj3tOamqqrr7qSs36ZKbuuP2HMsao8KjRP6nlLwAB4oXpynOAPAsJNB1GAONYTk62/vLWn7Vt2zYt+WqpSkpK5PP51a5dW/Xq1VODBw9WctKRl3mWlZWpeNOmUJsFIEDzYU7kz6I58dS6T0KTmr99i8yrz7ldBqKAAGiBzMxMjR+XWed5q1atDnsusFu3k1kAAjQTpmN3KfNUadtqt0txR0ZPiRFAoMkwBYyQgsLw6V8WgADNi2foWLdLcI1n6FgZwzZwQFMhACKksHBVWHvQoCyXKgFQE3PqSCm1jdtlxF5yK5mBo9yuAogrTAEj5NgRwPouANlTWqpHf/F4ref84rHHlZIa/rb1Jx7/RZ07lAA4wiQkyeRcKueL99wuJaZM1kUySXbu1gBECwEQkg7vGLJxY3GoHckCkPKycv3jH/+s9Zz5ny2odiz3gfsl8h8QEc/gyxX4Ypqklr0FVyRsnvoGooUpYEiSVhcVKRAIhNosAAGaJ9O+q0zfM90uI2ZMj2EyHbu5XQYQdxgBhCSpoCD8+b9IFoCcdNKJWr/W0pWJgAs8F/5IgU3LJV+Z26VEV0KyPJfc5XYVQFxiBBCSpMJjVwCzAwjQbJm2GfKM/mFM+gqUbq3XsWjwnH+LTPu6X2EFIHKMAEKS9NyzT+u5Z592uwwA9WRyLpMpWiCneGlU+/Etnamk7IsO70csyQlUyffVjKj2KUk6eZDM8PHR7wewFCOAANACGWPkueynUlKrqPZTtX6xDr52lyrzZ6kyf5YOvnaXqjYsiWqfSkiW9/KfyRh+RAHRwgggALRQ300FB2f9Jqr9VG1YEv3QdxSmfoHo49crAGjBTM5lMkPGuF1GkzGDLmLqF4gBAiAAtGDGGHkuvlPm1PPdLqXRTN+z5fnevUz9AjHAnzIAaOGMxyvP2Ptl+rTc9wOansPlGZ8r4/G6XQpgBQIgAMQB402Q54pHZAaOdruUiJn+I+W5+nGZhCS3SwGsQQAEgDhhvAnyjP25zLCW8wydGXzZ4ZE/b6LbpQBWYRUwAMQRYzzyXnyngqcMUfDv/yMd2ut2STVLbSvPJXfJc+pItysBrEQABIA45Ol7lszJWQp+OkVOYZ7b5YQx/UfKc8mPZVq1c7sUwFoEQACIUya1jbzjJinYf2TzGA1k1A9oNgiAABDnQqOBn78t5+t/ShUHY1tAciuZrIvkOfsGmdbtY9s3gBoRAAHAAia1jbwX3i7nvJvlrJqn4LIZ0o710e00o6c8Q8fKDBwlk5Qa3b4ARIQACAAWMYkpMjmXymRfIm1fo+CymXJWfyZVVTZNB95Emf7nyjN0rHTiABljmua+AJoUARAALGSMkTL7y5vZX85lP5V2fyNnx7rQP9q5QQr4a7+JN1HK6CnTpU/oH3XqzitdgBaAAAgAljPeBKlzL5nOvaScSyVJTqBKKt0iVRyU4688HAYdR0pIkklMlpJbSyecTNgDWigCIACgGuNNkDr1OPzZ5VoAND12AgEAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMuYb/ftcdwuAgAA2wUdR6WVFW6XYZUOySnyGDt3u05wuwAAACB5jFHHlFS3y4AlmAIGAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsMz/AWuv4jDoYyNCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 370.906x200.667 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 182,
       "width": 320
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bmV6+6KILNXLkiPotHsAxMynp8l74azlnXi1n6UyFl82secu4Ji1lci6Up9/PZepjBBFA3BAAofLycq1fXxxp12YByMFuuP46hcOOfjfp9/L7/SooKIx6n+CPRo0coXHjHmNLKKABM5mtZM76L5mfXiPt2abQm7nS95ujT2rRQd4rn5Sat+P7GWikCIDQyqIihUKhSLs2C0AO9X9vvF5Dzh2sN6e9rc/nztXWrdsUCATUpk0bDejfT5dddqlOO3VQfZcOIEaMMVLzdlJa06oBMK2pTIvj3CkMQL0gAEIFBdHP/9VmAcjhdOnSRbn336vc+++tj7IAAECMsAgEKjx0BXANO4AAAIDGjRFAaOKEJzVxwpNulwEAAOKEEUAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAs43O7ACARpTQxGj2+qdtlWCWliXG7BABoNAiAQAwYj1FqJoEEANAwMQUMAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBmf2wUAAADJccJS+Q9ul2GXtKYyxs6xMAIgAAANQfkPCj13hdtVWMV7x1tSenO3y3CFnbEXAADAYgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsw17AAABJkuM40p6tcraukbN1jbRtnVRSXPXEkmKF3syV2naTaddDpl0PqflxMsbEv2gAR4UACAAWc0qKFV4xW9qyan/oq9hb80WBCjnFi6XixXJ+PJaaKdOuu9SupzwnnyPTtlsMqwZwrAiAAGAZJxSQs+oLhZfMkDZ9XT83rdgrZ0O+tCFfofnTpA4ny9N/mEyvs2R8yfXTB4B6QwAEAEs4P2xXOP9jOctmSqXfx7azzSsU3rxCmvUnmb4XytP3Ypnm7WLbJ4BaIwACQIJzgn6Fv3hdzpfTJCcc387L98j5cppC89+WGXSpPGddJ5OUEt8aAFRBAASABOZ8t1qhj56RSja4XEhYzlfvKLT2K3kvvkemw0nu1gNYjtfAAEACcoJ+hea8otCUX7sf/g62c5NCr92pUN5f5AT9blcDWIsRQABIMM72YoU+HN+wgt/BnLCcr95WaO18eYffv/81MgDiihFAAEggzreFCk29q+GGv4Pt3KTQ6/co/M0ytysBrEMABIAEEV6/SKE375cqS90upfb85QpPG6Pwmi/drgSwCgEQABJAeEO+wu88LAUq3S6l7kIBhac/pvDaBW5XAliDAAgAjZyzeeX+8BcKuF3K0QuHFH7vMTkbl7tdCWAFAiAANGLO998p9NYDUqDC7VKOXdCv0NsPydm50e1KgIRHAASARspxwgp9/Lva7d97DHzdByn9yseVfuXj8nUfFNO+5C9T6B+/kxMOxbYfwHIEQABopJwl/5BiPGXq6z5IGTc8r5R+Fyml30XKuOF5+bqdEtM+tWWlnIXTY9sHYDkCIAA0Qs733yn82V9i3k/ygGEy3gOvjDVen5IHDo95v+E5k5kKBmKIAAgAjUxk6jcOK369LTvU6li9CwWYCgZiiJ1AAKCRicfUb4OwZaWcBe/KnHaF25VYK+mks5Vx3aRIO1C8RPteukVynFrfw6RlKvP2qZFfHIIblmrvS7dIhHtXEQAtVVxcrBUri7R9+3aVl1eoRYvm6tmjh3JysuXz8b8F0FA5oYDC86a6XUbchL+cJjNguExSqtulWCmw8nNVzn9XKaddJklK6tJfqYOvU8XsybW+R/ovHomEv3Dpbu37+1jCXwPAT3qL+P1+vTb1Db39zjtau3bdYc9p2bKlfnnTjbrxhuvl9XqVv3SpfnHFVZHPO3fupFn//me8SgZwCGfVPKlst9tlxE/FXjkr58hkX+B2JdYq+2iSfF0HyNumsyQp9bxbFFj9pUJbVtV4bcpZ/0fJJw8+cK93HpWzZ1usSkUd8AygJeZ/tUAXXHSJxk+YeMTwJ0m7du3SxKee0a9uvU2BQEBFRdHf4H2ysmJdKoBqhJfMcLuEuAsvtu/P3KAEKlU67QE5wf0vGje+JDUZPU7ypVR7mbdjH6Vd8D+RdsW8NxRYOTempaL2CIAWmD79fd1w403atGlTlc88Ho+aNWsmr9cbdfyz2XP0xxde1MqioqjjvXv3jmmtAI7M2V4sbSpwu4z427paTi1GmxA7oc1Fqpj150jb26aL0i6+44jnm/Rmyrh6vIwvSZIU3FSo8pnPx7xO1B4BMMF98OEM3Xt/rgKBA1tENW/eTLfc/Et9/I8PVPj1Ui1eOF8Fy/M19bUpOuP00yLnvfzKFC1YsDDqfllZBEDALTaO/v3I5j97Q1ExZ4oC6xdH2qmnXyFfzzMOe26TKx6Vp3k7SZJTsU+lfx8jhYJxqRO1QwBMYMuWLdf9uWOjjg0++yzN/GiGfnvPXerZs6eSkvb/dpaUlKTTTh2kya/8TZddOkqSVFZWFjVdbIxR794nx+8PACDCqSyTU/ip22W4xlk5W07ZD26XYTfHUdlbDytcfmDnmSaXPyST3izqtJTB1ymp108j7dJ3xym8a3PcykTtEAATVFlZmX5z1z1RI39Dhw7RS39+Ua1btz7idR6PR48+8pDatm1b5bNOnToqMyMjJvUCqJ6z6WvJX+52Ge4J+uV8s9TtKqwX3r1VZe9PiLQ9TVspfdSYSNvbsY/SfnZrpF351XQFvp4V1xpROwTABPXHF/4U9cxft65d9fyzk6o863c4qampGjVyRJXjWTz/B7jnu9VuV+A6Z+sat0uApMCyf6ky/+NIO7nPUCXlXCAlp6nJ6HGRnWOC361R2Yxn3CoTNeA1MAmopKREr0yeEnXskUceUkpK9Su2Dta/f98qx7JYAQy4hvAjaSshuKEoe3+ifJ37ytuivSQp/eI7Feh5WuR9f05lmUrfuF8K+t0sE9UgACagKa9Old9/4Jvupz89U6efdmqd7tGmdZsqx6pbALJt23YVFBaqoKBQBQUFKigsVEnJjsjns/Nm6fjj47B9FJCgCICSs3WtHMeRMcbtUlBZqrJpDynj5j/LeLzyNG2llAHDIh+XfTBR4ZJvXCwQNSEAJphwOKz33ns/6thVV9Z9G6VDp4qrWwDy1NO/00t/+Wud+wBQO86+XdK+nW6X4b6KvdLurVKL49yuBNq/pVvF7ClKG3Jj1PHKJR/Jv+Qjl6pCbfEMYILJz1+qbdu3R9oZGRkaOnRIne+ze/fuqHZ1C0D8/qob0jdv3uwwZwI4Goz+HcC/i4alYs4UOYGKqGOB5Z+4VA3qghHABPPVggVR7f79+h3V3r47d0aPNlS3AKRp02Y688wzlNW7t7Kyeiurd2+dcMLx6t7zpDr3C+AwdjCV9iNnxwZJZ7tdBv6/9GF3V9mnOX1Urn549io55by2pyEjACaYwsIVUe3DLeaojeVfR+82UN3zf7++/baj6iNeli1frry82VEjo0BjMiT5Ww2p/RquCF/3QUoeMCzyYP7R8Lbrdthjmbe+fNT3DO3aLP/iGQquXVDzyYf4PG+W/jUzMReDpJuAxjSiN20l971QKQOHVznuadZW6ZeOVenr97lQVd08/sR4lTlJce+3bZs2GjLkHOVkZ8e97x8RABPMxo3R270d7n1+tbF48ZKodmPdAm7Z8uUa98QEhUIht0sBjtopHcqkdnW7xtd9kDJueD7ySo76ZFKayNfp6H9w+TplKzn7fO17+XYF1y2s+YKD7Nv9vVZvqvrYSSLI9IWlHLerqB3PT05Q+qjcSNtfkCeFw0rOPk/S/lfDBAaOkH/RB26VWCvr1q3X3mD8n4ZbvXqN/vPlfD04NlfZ2X3i3r/EM4AJZ/eePVHtli1b1vkea9eu07LlyyNtY0yj3QIuL2824Q+NXtJRLHpNHjAsJuGvvhivT8mHGT2qSbJxYlAN6sSbpCZXj5dJaSJJCpfvVdkHT6nsw6cVLjvwMyh92N3y/OQEt6ps8EKhkD7N+8y1/gmACebgnT8kKXhIuzamvv5GVJsdQAB38SvMAUGHV8C4Le3nd8jXoVekXf7BU3L27pCzb2fULiEmJV1NRo+TPDVvQID4IwAmmMzM6KC2bVvdnnsrKlqlaW+9HXWsMe8AMmTIObXa/QRoyALhuoce/+IZckLBGFRTP5xQUP5FH9b5ugADgK5KOnmwUs8cHWlX5n8s/9KZkXZg+SeqXHJglxDfCb2Vev4tca2xsfB6vRo65FzX+m+48wM4Kq1atVJx8YZIe0l+vq699ppaXVvp9yt3zANVRhEb6/SvJOVkZ+vBsbn6NO8zFoGg0WqavFnS5jpdE1y7QPtevl3JA4cf8yKQH6f6fuRUliq0dd1R3zO0a7P8iz6s8/N/kpTZvKV6pifmtGK6CUjKd7uMIzLN2ir98oci7dDOb1X2/sQq55V9MFG+Lgd2CUkdfJ2Cq79UsLjh/dm6devq2iKQoUPOde35P4kAmHBysrO1cOGiSPvTvM+0c9cu/aSGZwGDwaDuuOMufV1QUOWzxroA5EfZ2X1c/SYDjlV42T8V/nhSna8Lrlt4VCHrYJm3vlxlwUdo6zrtffHGI1wRW+deMkpDB450pe9Yc8p2K/Rc3V/cHxcerzKuelKe9P3veHVCQZVOe1CqLK167iG7hBiPV+lXPKa9z10lp2JfnAuv3oNjc2XSm7tdhiuYAk4wgwdHvx+rvLz8sKN6B9u+fbt+ecutmvXpp1U+M8Yo6wg7gACID9Ouh9slNBimXU+3S7BS6vm3yNf5wBLliry/KrTx6yOeH9ywVBVzXo20vS2OU/rI3COej/gjACaY0087VSeeGP0XZF7eZ7r6mms174svIkEwEAho9Zo1evqZSfr5JcM1d+48SVWnezt16qjMzMz4FA/g8Fp1krzxn6ZqcIxHatvV7Sqs4+t+qlIHXx9pB4rzVZFX83sgKz75k4Lfroy0k/teoOT+F8eiRBwFpoAT0BPjHtPoq65RMHjgAfD8/KW6/oab5PV6lZGRob179yocDkddN3LEcPXqdaIKCgojxxrzAhAgURivT2rTVfpulduluKtVxyq7TiC2TEZLNbnyURnP/vGicPkPKn3zAckJ13ClpHBIpdMeUNPbX5dJ3v/fLX34bxUszlf4+y2xLBu1wAhgAuqbk6OnJo5XUlLVEYNQKKQ9e/ZEhb+kpCTdfdedevqpCVqxsijq/Ma8AARIJEwDM/0bd8aoyZWPy5PZKnKo7L3xcvZsq/UtwiXfqPzj5w7cMjVDTUY/vn80F67iv0CCGj7sEr35xlSdcsrAI56Tlpamyy+7VDM/nqFbf3WzjDEqPGj0T2r8C0CARGGOIwASguMrdfD1SupxaqRduehDBZZ/Uuf7VM5/W4GiLyJtX6ccpQ69qV5qxNFjCjiB5eRk6++vv6YtW7Zo4aLFKikpkd8fUPPmzdStW1f17dtXKcnJkfPLyspUvGFDpM0CEKDhMB34XjQdTnK7BKtUzH5FFbNfqZd77Zt8R73cB/WHAGiB9u3ba8Tw9jWet2LFyqip4Y4dT2ABCNBAmFadpPYnSVtW1nxyImrTVWIEEKg3TAEjoqAwevqXBSBAw+LpP8ztElzj6T9MxrANHFBfCICIKCxcEdXu0yfLpUoAHI456WwpranbZcRfSrpM7yFuVwEkFKaAEXHoCGBtF4Ds3LVLDz38aLXnPPzIo0pNS4s69tijD9e4QwmAA4wvWSbnQjnz33K7lLgyWefLJKfVfCKAWiMAQtL+HUPWry+OtOuyAKS8rFz/+te/qz1nzudzqxzLve9eifwH1Imn78UKzX9bkuN2KXFj89Q3ECtMAUOStLKoSKFQKNJmAQjQMJkWx8n0PN3tMuLGdBkg06qj22UACYcRQEiSCgqin/+rywKQ44/voLWrLV2ZCLjAc95/K7RhqeQvc7uU2PKlyHPB7W5XASQkRgAhSSo8dAUwO4AADZZp1kaeoTfHpa/Qrs21OhYLnnNulGlR8yusANQdI4CQJE2c8KQmTnjS7TIA1JLJuUimaK6c4sUx7ce/eIaSs8/fvx+xJCcUlH/RhzHtU5J0Qh+ZgSNi3w9gKUYAAaARMsbIc9GdUnJ6TPsJrl2gfS/frsr8marMn6l9L9+u4LqFMe1TvhR5L75bhv1igZhhBBAAGqkfp4LDM5+NaT/BdQtjH/oOwtQvEHv8egUAjZjJuUim3yVul1FvTJ/zmfoF4oAACACNmDFGnp/dJnPSOW6XcsxMzzPl+fldTP0CccB3GQA0csbjlWfYvTI9Gu/7AU3XgfKMyJXxeN0uBbACARAAEoDx+uQZ9aBM76Ful1JnptfZ8lz+qIwv2e1SAGsQAAEgQRivT55hv5UZ0HieoTN9L9o/8udNcrsUwCqsAgaABGKMR96f3aZw534K//M5qfR7t0s6vLRm8lxwuzwnne12JYCVCIAAkIA8Pc+QOSFL4U9ekFOY53Y5UUyvs+W54H9k0pu7XQpgLQIgACQok9ZU3uH3K9zr7IYxGsioH9BgEAABIMFFRgO/eEPO1/+WKvbFt4CUdJms8+U582qZJi3i2zeAwyIAAoAFTFpTec/7lZzB18tZMVvhJR9KW9fGttM2XeXpP0ym9xCZ5LTY9gWgTgiAAGARk5Qqk3OhTPYF0nerFF4yQ87Kz6VgZf104E2S6XWWPP2HSR1OljGmfu4LoF4RAAHAQsYYqX0vedv3knPRndKOb+RsXRP5R9vWSaFA9TfxJkltusq06xH5R6078UoXoBEgAAKA5YzXJ7XtJtO2m5RzoSTJCQWlXZukin1yApX7w6DjSL5kmaQUKaWJ9JMTCHtAI0UABABUYbw+qXWX/V+7XAuA+sdOIAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBnzw+6djttFAABgO8cJS+U/uF2GXdKayhg7x8J8bhcAAAC0P4ikN3e7DFjCztgLAABgMQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYJn/BdUTfjqu7f3jAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 370.906x200.667 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 182,
       "width": 320
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 454.517x200.667 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 182,
       "width": 388
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    display(bell_basis(i).draw('mpl'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50cbbb88",
   "metadata": {},
   "source": [
    "If we do a basis change and express the combined state of qubits A & C in terms of the Bell states, then the full tripartite system can be written as (ignoring overall factor of 1/2):\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "|\\Psi\\rangle_{\\rm BAC} =& |\\psi\\rangle_{B}\\otimes|B_{0}\\rangle_{(AC)}+ \\\\\n",
    "&Z|\\psi\\rangle_{B}\\otimes|B_{1}\\rangle_{(AC)} + \\\\\n",
    "&X|\\psi\\rangle_{B}\\otimes |B_{2}\\rangle_{(AC)} + \\\\\n",
    "&ZX|\\psi\\rangle_{B}\\otimes |B_{3}\\rangle_{(AC)}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "That is to say that, if we measure the state of AC to be in the i-th Bell state, then qubit B is in the desired state modulo the same gates needed to construct the i-th Bell state.  If we know, i.e. measure, AC to be in the i-th Bell state, then we know which gates we need to apply to fix this.  We therefore need to figure out how to measure Bell states.  It is important to note that **we have not done anything but express A and C in a different basis and rearrange terms**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1099e51",
   "metadata": {},
   "source": [
    "In order to pick out the particular Bell state via measurements, we need to perform a Bell measurement on pair AC.  The circuit for this is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b11e83e3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T17:13:36.595760Z",
     "start_time": "2022-12-02T17:13:36.425766Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 580.387x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 490
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bell_meas = QuantumCircuit(2)\n",
    "bell_meas.cx(0, 1)\n",
    "bell_meas.h(0)\n",
    "bell_meas.measure_all()\n",
    "bell_meas.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6d521aa",
   "metadata": {},
   "source": [
    "In particular, it can be shown that a Bell measurement on the state $|B_{i}\\rangle$ yields the binary representation of the integer $i$, e.g. $i=2$ yields the bit-string `10`.  Whats more is that the resulting bit-string tells us which gate(s) we need to correct for. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9bee33b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = AerSimulator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "06f7d1f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bell measurement of B(0): {'00': 100}\n",
      "Bell measurement of B(1): {'01': 100}\n",
      "Bell measurement of B(2): {'10': 100}\n",
      "Bell measurement of B(3): {'11': 100}\n"
     ]
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    print(\"Bell measurement of B({}):\".format(i),\n",
    "          sim.run(bell_basis(i).compose(bell_meas),\n",
    "                  shots=100).result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4d1b61d",
   "metadata": {},
   "source": [
    " Here we make a circuit that generates a random initial state for qubit C, and teleports it to qubit B via the above method.  To verify that the state was generated, here we apply the inverse of the unitary used to generate the state, and look to see if we get back to the ground state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d1229aba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:57:27.645188Z",
     "start_time": "2022-12-02T18:57:27.641148Z"
    }
   },
   "outputs": [],
   "source": [
    "# Create a random state for qubit C\n",
    "random_1q_gate = random_unitary(2).to_instruction()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "841d554b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:57:28.370602Z",
     "start_time": "2022-12-02T18:57:27.979177Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1459.65x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "image/png": {
       "height": 317,
       "width": 1202
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a random state for qubit C\n",
    "random_1q_gate = random_unitary(2).to_instruction()\n",
    "\n",
    "# Create a register for each qubit of interest\n",
    "qrA = QuantumRegister(1, 'qA')\n",
    "qrB = QuantumRegister(1, 'qB')\n",
    "qrC = QuantumRegister(1, 'qC')\n",
    "\n",
    "# Create a single classical register\n",
    "cr = ClassicalRegister(2)\n",
    "\n",
    "# Create circuit\n",
    "qc = QuantumCircuit(qrC, qrA, qrB, cr)\n",
    "# Make C qubit in random quantum state\n",
    "qc.compose(random_1q_gate, qrC, inplace=True)\n",
    "# Form Bell pair between A and B\n",
    "qc.h(qrA)\n",
    "qc.cx(qrA, qrB)\n",
    "qc.barrier()\n",
    "\n",
    "# Bell measurement\n",
    "qc.cx(qrC, qrA)\n",
    "qc.h(qrC)\n",
    "qc.measure([0,1], [0,1])\n",
    "\n",
    "qc.barrier()\n",
    "# Corrective Pauli gates\n",
    "# If returned bit-string is 01 = 1\n",
    "qc.z(qrB).c_if(cr, 1)\n",
    "# If returned bit-string is 10 = 2\n",
    "qc.x(qrB).c_if(cr, 2)\n",
    "# If returned bit-string is 11 = 3\n",
    "qc.z(qrB).c_if(cr, 3)\n",
    "qc.x(qrB).c_if(cr, 3)\n",
    "\n",
    "qc.barrier()\n",
    "# Apply inverse of unitary that generated state C\n",
    "qc.compose(random_1q_gate.inverse(), qrB, inplace=True)\n",
    "# Measure the Z component of B (overwriting the previous result)\n",
    "# We should be back in the ground state\n",
    "qc.measure(qrB, 0)\n",
    "\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ded834dc",
   "metadata": {},
   "source": [
    "### Simulate the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cf49d749",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:57:28.523724Z",
     "start_time": "2022-12-02T18:57:28.520354Z"
    }
   },
   "outputs": [],
   "source": [
    "sim = AerSimulator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d84855c0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:57:29.069783Z",
     "start_time": "2022-12-02T18:57:28.812313Z"
    }
   },
   "outputs": [],
   "source": [
    "sim_counts = sim.run(qc, shots=10000).result().get_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adf68bf0",
   "metadata": {},
   "source": [
    "We only care about the zeroth bit here so need to marginalize here, returning only what we want"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "da55ba81",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:57:29.638512Z",
     "start_time": "2022-12-02T18:57:29.633795Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 10000}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marg_sim_counts = marginal_counts(sim_counts, [0])\n",
    "marg_sim_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89b72e25",
   "metadata": {},
   "source": [
    "### Run on hardware\n",
    "\n",
    "Now we are in a position to run on hardware."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a67fb753",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:57:34.385655Z",
     "start_time": "2022-12-02T18:57:34.350336Z"
    }
   },
   "outputs": [],
   "source": [
    "trans_qc = transpile(qc, backend, initial_layout=[0,1,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ece7ad1",
   "metadata": {},
   "source": [
    "Lets take the opportunity to see what a transpiled QASM3 circuit looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bed7dc6c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T19:11:42.059926Z",
     "start_time": "2022-12-02T19:11:42.052670Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OPENQASM 3;\n",
      "include \"stdgates.inc\";\n",
      "bit[2] c0;\n",
      "rz(-0.52767) $0;\n",
      "sx $0;\n",
      "rz(-0.77932) $0;\n",
      "sx $0;\n",
      "rz(1.9861) $0;\n",
      "rz(pi/2) $1;\n",
      "sx $1;\n",
      "rz(pi/2) $1;\n",
      "cx $1, $4;\n",
      "barrier $0, $1, $4;\n",
      "cx $0, $1;\n",
      "rz(pi/2) $0;\n",
      "sx $0;\n",
      "rz(pi/2) $0;\n",
      "c0[0] = measure $0;\n",
      "c0[1] = measure $1;\n",
      "barrier $0, $1, $4;\n",
      "if (c0 == 1) {\n",
      "  rz(pi) $4;\n",
      "}\n",
      "if (c0 == 2) {\n",
      "  x $4;\n",
      "}\n",
      "if (c0 == 3) {\n",
      "  rz(pi) $4;\n",
      "}\n",
      "if (c0 == 3) {\n",
      "  x $4;\n",
      "}\n",
      "barrier $0, $1, $4;\n",
      "rz(-1.9861) $4;\n",
      "sx $4;\n",
      "rz(-0.77932) $4;\n",
      "sx $4;\n",
      "rz(0.52767) $4;\n",
      "c0[0] = measure $4;\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(qasm3.dumps(trans_qc))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59066980",
   "metadata": {},
   "source": [
    "Now lets run the compiled circuit, remembering we need to set `dynamic=True`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9f4b00ec",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:57:36.094553Z",
     "start_time": "2022-12-02T18:57:35.262182Z"
    },
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "job1 = backend.run(trans_qc, shots=10000, dynamic=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2ea1aff",
   "metadata": {},
   "source": [
    "Marginalize counts and see if we are close to the above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3d74476b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T18:58:15.425979Z",
     "start_time": "2022-12-02T18:57:36.460929Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 7876, '1': 2124}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real_counts = job1.result().get_counts()\n",
    "marg_real_counts = marginal_counts(real_counts, [0])\n",
    "marg_real_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d3d9aa3",
   "metadata": {},
   "source": [
    "## Bit-flip code\n",
    "\n",
    "The bit-flip code is one of the simplest examples of a stabilizer code.  It is capable of protecting the encoded version of our state from single bit-flip (x-gate) errors. Here we will do a simple demonstration of this, correcting for a single-round of errors. \n",
    "\n",
    "Let the initial state be $|\\psi\\rangle = \\alpha|0\\rangle +\\beta|1\\rangle$.  The encoding needed for the bit-flip code mirrors this state onto the 3-qubit state\n",
    "\n",
    "\n",
    "$$\n",
    "|\\psi\\rangle_{\\rm rep} = \\alpha|000\\rangle +\\beta|111\\rangle\n",
    "$$\n",
    "\n",
    "We cannot measure the qubits in the state directly, or we would destroy the state.  Therefore, we will need additional ancilla qubits on which to write the parity of the qubits.  Moreover, measuring individual qubits does not give enough knowledge to determine on which qubit an error occurred.  Rather, we need to measure the parity of *pairs* of qubits to determine which qubit has been flipped.\n",
    "\n",
    "Here we will look at joint parity measurements of qubits $Q0\\oplus Q1$, as well as $Q1 \\oplus Q2$, stored as classical bits 0 and 1, respectively.  So see how this works, let us look at what the measurement yields for each possible case of a single bit-flip.\n",
    "\n",
    "- Error on Q0:\n",
    "     $$\n",
    "     \\alpha|001\\rangle+\\beta|110\\rangle\\ \\ \\rightarrow \\ \\ 01\n",
    "     $$\n",
    "     \n",
    "- Error on Q1:\n",
    "     $$\n",
    "     \\alpha|010\\rangle+\\beta|101\\rangle\\ \\ \\rightarrow \\ \\ 11\n",
    "     $$\n",
    "     \n",
    "- Error on Q2:\n",
    "     $$\n",
    "     \\alpha|100\\rangle+\\beta|011\\rangle\\ \\ \\rightarrow \\ \\ 10\n",
    "     $$\n",
    "     \n",
    "We see that the joint parity measurement information allows us to identify which of the three qubits had a error.  We can then use this measurement information to conditionally flip the erroneous bit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34172f1e",
   "metadata": {},
   "source": [
    "Here we start with an arbitrary 1Q state, encode it into the bit-flip code and correct any single-flips that might have occurred.  To check the validity of the correction, we attempt to undo the encoding and arbitrary state, and measure how close we return to the ground state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a4f4149",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate random 1Q gate\n",
    "random_1q_gate = random_unitary(2).to_instruction()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 534,
   "id": "6a6a28c6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:05:48.092465Z",
     "start_time": "2022-12-02T20:05:47.605063Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1952.02x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 534,
     "metadata": {
      "image/png": {
       "height": 453,
       "width": 1601
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a register for each qubit of interest\n",
    "qr1 = QuantumRegister(3, 'state')\n",
    "qr2 = QuantumRegister(2, 'ancilla')\n",
    "cr = ClassicalRegister(3, 'c')\n",
    "\n",
    "qc2 = QuantumCircuit(qr1, qr2, cr)\n",
    "\n",
    "# Encode state\n",
    "qc2.compose(random_1q_gate, [qr1[0]], inplace=True)\n",
    "qc2.cx(qr1[0], qr1[1])\n",
    "qc2.cx(qr1[0], qr1[2])\n",
    "\n",
    "qc2.barrier()\n",
    "# Joint party of 0 and 1 onto ancilla 0\n",
    "qc2.cx(qr1[0], qr2[0])\n",
    "qc2.cx(qr1[1], qr2[0])\n",
    "\n",
    "# Joint party of 1 and 2 onto ancilla 1\n",
    "qc2.cx(qr1[1], qr2[1])\n",
    "qc2.cx(qr1[2], qr2[1])\n",
    "\n",
    "qc2.barrier()\n",
    "# Perform the syndrome measurement\n",
    "qc2.measure(qr2[0], 0)\n",
    "qc2.measure(qr2[1], 1)\n",
    "\n",
    "# Conditionally flip bits\n",
    "# We need to use the old c_if syntax in order to do noisy simulations\n",
    "qc2.x(qr1[0]).c_if(cr,1)\n",
    "qc2.x(qr1[1]).c_if(cr,3)\n",
    "qc2.x(qr1[2]).c_if(cr,2)\n",
    "\n",
    "qc2.barrier()\n",
    "# Undo computation and measure if back in ground state\n",
    "qc2.cx(qr1[0], qr1[2])\n",
    "qc2.cx(qr1[0], qr1[1])\n",
    "qc2.compose(random_1q_gate.inverse(), [qr1[0]], inplace=True)\n",
    "\n",
    "# Record the probability of being back in the ground state\n",
    "qc2.measure(0, 2)\n",
    "qc2.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84fde9d6",
   "metadata": {},
   "source": [
    "### Simulation\n",
    "\n",
    "Because we are correcting noisy behavior, we will need a noisy simulator to inject bit-flip errors.  There is no Peekskill noisy simulator, and we currently cannot build one from the new provider backends, so we will use another system here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 535,
   "id": "5b4cfe9d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:15:46.929515Z",
     "start_time": "2022-12-02T20:15:46.918088Z"
    }
   },
   "outputs": [],
   "source": [
    "sim = FakeHanoi()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fff7f1f",
   "metadata": {},
   "source": [
    "We have two different pieces of information in our counts.  First, the ancilla bits contain the information on what errors, and how many occurred.  The second bit records how often our system should be in the ground state.  Ideally this is 100% of the time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "id": "bcb7e6a7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:15:54.467451Z",
     "start_time": "2022-12-02T20:15:50.172448Z"
    }
   },
   "outputs": [],
   "source": [
    "sim_counts2 = sim.run(qc2, shots=10000).result().get_counts()\n",
    "anc_counts = marginal_counts(sim_counts2, [0,1])\n",
    "ans_counts = marginal_counts(sim_counts2, [2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 542,
   "id": "2baebf94",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:24:33.566487Z",
     "start_time": "2022-12-02T20:24:33.562133Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Errors detected: {'01': 112, '10': 79, '00': 9767, '11': 42}\n"
     ]
    }
   ],
   "source": [
    "print('Errors detected:', anc_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef575315",
   "metadata": {},
   "source": [
    "We see that errors occur a couple hundred of time, but the vast majority of time there are no qubit errors.  Taken together with the fact that we are correcting errors, the final qubit should be found in the ground state with high-probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 538,
   "id": "322d3130",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:21:01.460407Z",
     "start_time": "2022-12-02T20:21:01.454768Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'1': 197, '0': 9803}"
      ]
     },
     "execution_count": 538,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ans_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1be67fb",
   "metadata": {},
   "source": [
    "### Hardware execution\n",
    "\n",
    "We can now transpile the circuit and execute on hardware."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 539,
   "id": "6243e3a0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:23:21.945995Z",
     "start_time": "2022-12-02T20:23:21.014366Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V+g//v+bj2Q//LynXpceInZIkPUbslDlbfSiz7/1PrUoEADqwFbpXajJv/+5d8/XNSqWSa6+7XqC3q7vzrrtz5Je+koaGhqUeq1u3btl4o40Wev+8odRRW2zepvHHjG65E+7GG22UcnnB38Jzx513tjjeZuut069v3zbNt6R1LWqH3qIoMu6RR1ucGz580eHcJenTns9r//4r5L3vfU9GDB+eESOGZ8Tw4VlrrTWzwbCNl3ruajnwgI9kizb+/rVGURQ59c+n5fnnX2hxfo89ds93j/r2Mp9vYVZYoX+ee+6d41dfe22Jxnltnn4rrNB/acoCAAAAAACAJEl5CUJ5nVWdn0XV1Opn281zWjV1S/BlAJ2V3zMAACB13dPn0J+n1GvuZ+QrMxoy/bLjk6KSbuuNSrnPikmS+n2/ncYJ96cy6blFDAYAdEV1tZq3C7/WO6exsWZzC/R2ALfffkc+f/gXM3v27BbnN9hgSHb4wAeyxRabZ8011sjgwYPSu3fv9OrVK3V17/xVvfuee/Kxjx/WfDx0gw3Ss2fPBc714osv5vXX39kKu3v37ovc9XVBRo+ZJzg7YuHB2UfmCcBuscVmbZqrtV599dW8/Morzcd9+vRZ6K7BSTJhwtOZNm1a8/Gqq66SVVdddZFztLVPez6vSfK1r355kfV3RFtvvVUOWMY7NhdFkWOO/eF8Yd4999wjJx7/m3Tr1n6XvfXXWy9jxryzI/aLL7zY5jEmT56cadOmtzi33nrrLXVtrbHTTh/M7XfcaZdeAAAAAACATqpxCT6nMfu+y9Jj5K4ddqfNoqkxs++9tM395lSk8qplTm02Fsjsrvs5pKqbU7T970tHvnYs6XUjSWbX6PcbAADoOHrv9fV0W/OdDZhm/OdXKRrmbuYz/eJfpO8nfpUkKfWsT59DfpqGUz6bVHw2FwB4x5wavZ7dld8b+cD73luzuTveq+RdzJQpU3LU977fIvS59tpr5yf/98O8973vadUYd955d4vjRQVs3x0uTOburtujR482VJyMnmeMRc337LMtv0FonXXWadNcra+pZch4+PBNUiot/KIydlzLXYqHb7LonXbb2qe9n1fmejvMe+5557c4X4swb5IMGbJ+i+PnX3ghRVEs8ndzXvMGk5NkgyFDlrq21ths5Mgce/T3c931N7QIzAMAAAAAsPxZYYUVqj7HoEGDMmfOnHTv3r3q87X1C2uBBavv+UySl9vUp/HJuzP1jK+mx1b7pW7AGks8d93gISn17NPiXDFrWpomjl/iMZtefyGz7700jePvaXPf/gMGZljfJX88LNzU7o8lebPd551Tv3KGDVur3eftCnr1ejLJ64tt924d9dqxNNeNJBmw6uAMW2mVJeoLQOt0tvVsYk0L0Bb1pTlJHqh1GQvVfZMd0uu9hzQfz7r/ysx+8L/Nx3PGXJdZ912enlvukyTpttbw9Nr1iMy8+k/tXmtrDRmyfqYX3WtdBsByo7OtWaxXamNK+ZEMTEO7z9vYb9UMG7Z6u8/b3hobG/PUUxNanNukFVnCahHorbGzzj4nL7/8zhuka665Rs4/798ZOGBAq8e46aabWxwvMtA7dp4w7qZtD4mOGd36HXrfnDKlxXG/vn3bPF+rahrTMmy76YgRi2w/duw84dzhrQj0tqFPez+vLDzMu9eee+SEGoR5k7m7Kr/b1KlT8+T48fOdX5QHHnxwvnPzBoWraeTITTNy5KbtNh8AAAAAANXxwIMPV32ObbfZuupzvO2Lh3+u3eaCzqzppr+luP3fbe7XOP6eJQ6/va3fkWek2zojW9YzcfzcXWpqYLc9984e2x5Yk7k7u6ab/5nitjPbfd4PHvy57LTxB9p93q6g6YrjUzx8dZv7dcZrxwEHHZKPDt+xJnMDdBWdbT2bWNMCtEUxfXKafndQrctYoNIKg1J/wLHNx02Tns/0//xqvnbTL/1Nuq23RfOXG/Xa4VNpfPyONE7omEHlY4/+fkr1K9a6DIDlRmdbs1iv1EbTtaemuOeidp93908emT2HtO+auBbefHNKPvO5L9S6jGblWhfQ1V162WUtjr/6lS+3KfQ5ZszYPPRwy4v/osKs8wZfR27atqDeq6++2mKnzvr6+gxZf+HhwsbGOS2OZ86a1ab5WmveHXoXF36dP5y7+LBsW/q09/Pa1XXEMG+SbLPN1qmrq2tx7r5772/TGPfd17L9Jpts3C7f4AIAAAAAAEDnVxpo99JmA9eudQWdVmm1YTWa104S1eLa8Y7Syq4dAADQJZXr0vfQn6XcZ8UkSdHUmGnnHpvMmjZ/21nTMu3c41JUmpIkpXJd6g/6cUq9qrNRFgCw/CmttmGN5vU6ei0I9NZQY2Njxo9/qsW5bbfZpk1j/O7k37c47t69ezbcaOF/iceOa9tOtvOaNzi78UYbpVxe+K9R//4tg4cvvfRSm+ZrrbHz7Dy86WICveMeeaTFcWt26G1tn1o8r13deedf0OHCvEmy4oorZquttmxx7oorr2p1/2nTpuWGG29qcW63XXdZJrUBAAAAAABAaXBtgpYdkQ+tVE9pvVFJ73b+0uLVN05pxdXad86uZLC/L0mSuu7JyuvUugoAAKAGeu16RLqtu3nz8czr/pKmZ0cvtH3TMw9l5k3/bD6uW2m11O//g2qWCAAsR0obbJP06N2+c647KqX6Fdt1TuYS6K2h116blEql0uJcnz71re5/4UUXzxf2GzZsaHr26LHA9i++9FImTZrUfNy7d+9ssMGQNlScjB49T3B200UHZ1dbbXCL4zvuvKtN87XGK6+8kldeebX5uF+/fllnnYW/YfLss8/lzTffbD5eaaWVsvpqi34jry192vt5JTnwgI9krz33aD7ee689c+IJv61pmPdtu++6a4vjO++6K089NaFVfS+77IpMm9bym7p2223XhbQGAAAAAACANhqwRtK9V62rqL1+K6fUZ6VaV9Fplbr1SGmzPRbfcBkqj9q3XefrakqDNqh1CR3DquunVFf7zyUAAADtq9sG26TXDp9qPp4z4YHMvOFvi+0383+npvGFR5uPe2y2W3qM2rsqNQIAy5dSzz4pjWjfDQBLW3odvVYEemuoZ8/5A5qPPPLoAlrO75Zbb8sxx/5wvvOL2nF37JiWYdxNNt44dXV1rZrvbWPm2aF3+PBFB3rn3Zn2pptuzuNPPNGmORdn9DyPa/jwTVIqlRbaft5dikcsZjfftvZp7+eVpK6uLiee8Nvstece2XuvPXPC8b9p8+92tRx44Eey8sorNx8XRZH/+/FPFtvvjTfeyIm/O7nFuR13/GCGDfVNxwAAAAAAdEx/Pf30nPS7k/PX00+vdSlAK5XKdYlgXkp2G6268hZ7z93NtD30HZDSxh9on7m6qFLvfsmKq9e6jJpz7QDoPKxnAWitUt8B6XPwj+e+ppKkMmNKpp1zTFJUFtMzSaUp0845JsXsmc2n6vc7KuUBa1SrXAA6CWuWrqG85YeSUjtFPVdcLaUNtmufuZiPQG8Nrbjiihk4cGCLc787+Q+ZPXv2QvtUKpX87e//yOFHHJk5c+bMd/+igqZjxs6zu+7ItodE5x1jcWHYPffcvUWwslKp5Mtf+VpeeOGFVs03deq0/OvMs3L9DTcstM3o0S1DxiMWEzIeO7ZlOHf4Jpssto629Gnv53V5csBH9s+Tjz/S/OeAj+y/zMZ+O9TbkcK8SVJfX58vffGIFuduu/2O/Po3v11on6lTp+VrX/9Wix21S6VSvv3Nb1SrTAAAAAAAWGpTp05LQ0NDpk6dVutSgDYQSPMzaA+lFQen/P7D2mWu8h7fSKnb/F/EzbJVWs3fG9cOgM7DehaA1upz0I9T7vfORj/TL/p5ijdfbnX/yqtPZ8Z/f998XOrVN30O/nH7hXcAWC5Zs3QNpZXXTmn7g9tlrvJe32r+ghLan3/51VCpVMoeu+/W4tx999+fj33isNx++x0tAqAvvvhi/n3Oudlrn/3ys5//MnPmzMmQ9ddP//79W/TfdNOFh3THzLOTbVt3fZ048eW8+uprzcf19fUZsv76i+yz7jrrzBfanDDh6eyz3/45/oSTMmbs2DQ2Njbf19jYmMceezznnX9BjvzSV7L9e9+f//vxT9O/X/95h242dt6g8mLCr/OGkocPX3ygty192vt55R11dXUdKsz7tkMPPXi+v2+n/eX0fPZzh+fue+5p/p1omDo1l152eQ746MG54847W7T/1GGfyEYbbdhuNQMAAAAAANA1COUlGTys1hV0CaVtD0xWq+57nqURu6Q81K4C7UGYNSmt5toBAABdSa8Pfibdh72z5px176WZM/raNo8z6/ZzM+ex25uPu62zWXrt/PllUiMAsHwrv/fjySrrVnWO0qj9Ul5ns6rOwaJ1q3UBXd2XjvxiLrv8ikyZMqX53IMPPpTDPv3ZdOvWLf369s3UadPm27V16NANcuLxv80++324+VyPHj0ybOjC3zAZO+6RFscj2xgSHT2m5U64m2y8ccrlxWfCj/7B/8u4Rx5pEShuaGjIKaf+Oaec+ueUy+X07ds3RVFk6tSpKYqiRf9yuZyNN95ooePPF7ZdTKB33Dw/h8Xt6LskfdrzeaXj6969e/74x5Nz6Mc+kRdeeLH5/M233JKbb7kl5XI5ffr0SUNDwwL7f+D978/3vntUe5ULAAAAAABAF1Jad4ukXJdUmmpdSm1075XSWot/z5ilVyrXpW7/Y9N05jeTKa8u+wlW3yjl3b6y7MdlgUrrb53c8Ndal1E7fQdW/YN1AABAxzLzxr9l5o1/WyZjTf3b15bJOABA51Lq1iN1H/lhms78VjLtjWU//tqbpbzTF5b5uLSNHXprbNCgVXPqKX9I375957uvsbExb0yePF/oc7/99s155/47kyZNanF+4402Svfu3Rc4z0sTJ+a1197ZXbdv375Zd91121TrmHkCvSNGLH5n2yTp06dP/nb6X7Lzzjst8P5KpZI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      "text/plain": [
       "<Figure size 2338.74x1120.39 with 1 Axes>"
      ]
     },
     "execution_count": 539,
     "metadata": {
      "image/png": {
       "height": 937,
       "width": 1914
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Transpile circuit with good transpiler seed\n",
    "trans_qc2 = transpile(qc2, backend, seed_transpiler=1514439656)\n",
    "trans_qc2.draw('mpl', idle_wires=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6dbb1206",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-01T15:08:15.684053Z",
     "start_time": "2022-12-01T15:07:24.189004Z"
    }
   },
   "outputs": [],
   "source": [
    "real_counts2 = backend.run(trans_qc2, shots=10000, dynamic=True).result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 540,
   "id": "05f481dd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:24:02.866934Z",
     "start_time": "2022-12-02T20:24:02.861912Z"
    }
   },
   "outputs": [],
   "source": [
    "real_anc_counts = marginal_counts(real_counts2, [0,1])\n",
    "real_ans_counts = marginal_counts(real_counts2, [2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 541,
   "id": "dd8aef5e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:24:22.807406Z",
     "start_time": "2022-12-02T20:24:22.802193Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Errors detected: {'00': 9298, '01': 200, '10': 362, '11': 140}\n"
     ]
    }
   ],
   "source": [
    "print('Errors detected:', real_anc_counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 543,
   "id": "fec5c363",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-12-02T20:24:48.108370Z",
     "start_time": "2022-12-02T20:24:48.103983Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 5194, '1': 4806}"
      ]
     },
     "execution_count": 543,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real_ans_counts "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b07b616c",
   "metadata": {},
   "source": [
    "Obviously this final result is far from what we want.  This is because there are many sources of error beyond simple bit-flips that need to be taken into account."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8145cda4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}