mytapering_examples.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "00970521",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mytapering import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a89e94b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane as qml\n",
    "from pennylane import qchem\n",
    "\n",
    "import numpy as np\n",
    "from time import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6c32f3b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(precision=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8feb84d9",
   "metadata": {},
   "source": [
    "# 1. Example: H2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5e23f864",
   "metadata": {},
   "outputs": [],
   "source": [
    "symbols = [\"H\", \"H\"]\n",
    "coordinates = np.array([0.0, 0.0, -0.6614, 0.0, 0.0, 0.6614])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c38535a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of qubits =  4\n",
      "The Hamiltonian is \n",
      "   (-0.24274501260941383) [Z2]\n",
      "+ (-0.24274501260941383) [Z3]\n",
      "+ (-0.042072551947440084) [I0]\n",
      "+ (0.1777135822909176) [Z0]\n",
      "+ (0.1777135822909176) [Z1]\n",
      "+ (0.12293330449299354) [Z0 Z2]\n",
      "+ (0.12293330449299354) [Z1 Z3]\n",
      "+ (0.1676833885560135) [Z0 Z3]\n",
      "+ (0.1676833885560135) [Z1 Z2]\n",
      "+ (0.17059759276836806) [Z0 Z1]\n",
      "+ (0.17627661394181787) [Z2 Z3]\n",
      "+ (-0.04475008406301996) [Y0 Y1 X2 X3]\n",
      "+ (-0.04475008406301996) [X0 X1 Y2 Y3]\n",
      "+ (0.04475008406301996) [Y0 X1 X2 Y3]\n",
      "+ (0.04475008406301996) [X0 Y1 Y2 X3]\n",
      "--------------------\n",
      "Number of terms:  15\n"
     ]
    }
   ],
   "source": [
    "# 基于JW变换构建的H2哈密顿量\n",
    "H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)\n",
    "print(\"Number of qubits = \", qubits)\n",
    "print(\"The Hamiltonian is \\n\", H)\n",
    "print(\"-\" * 20)\n",
    "print(\"Number of terms: \", len(H.ops))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4af414a6",
   "metadata": {},
   "source": [
    "## 1.1 Tapering using QML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "085ce22e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Lee\\anaconda3\\envs\\qchem\\lib\\site-packages\\pennylane\\operation.py:1886: UserWarning: Tensor object acts on overlapping wires; in some PennyLane functions this will lead to undefined behaviour\n",
      "  warnings.warn(\n",
      "C:\\Users\\Lee\\anaconda3\\envs\\qchem\\lib\\site-packages\\pennylane\\operation.py:2073: UserWarning: Tensor object acts on overlapping wires; in some PennyLane functions this will lead to undefined behaviour\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 0.5321645736694336\n",
      "Number of qubit after tapering = 1\n",
      "The tapered Hamiltonian is \n",
      "   ((-0.27643173133526805+0j)) [I0]\n",
      "+ ((0.17900033625207976+0j)) [X0]\n",
      "+ ((0.8409171898006624+0j)) [Z0]\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "generators_by_qml = qml.symmetry_generators(H)\n",
    "paulixops_by_qml = qml.paulix_ops(generators_by_qml, qubits)\n",
    "\n",
    "n_electrons = 2\n",
    "paulix_sector_by_qml = qml.qchem.optimal_sector(H, generators_by_qml, n_electrons)\n",
    "\n",
    "H_tapered = qml.taper(H, generators_by_qml, paulixops_by_qml, paulix_sector_by_qml)\n",
    "print(f'time cost: {time() - begin}')\n",
    "\n",
    "print(\"Number of qubit after tapering =\", len(H_tapered.wires))\n",
    "print(\"The tapered Hamiltonian is \\n\", H_tapered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "93f62f48",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.276431731335 I\n",
      " 0.840917189801 Z\n",
      " 0.179000336252 X\n"
     ]
    }
   ],
   "source": [
    "Hami_reduced_by_qml = create_pauliwords_from_hamilton(H_tapered, len(H_tapered.wires))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f9aebd1",
   "metadata": {},
   "source": [
    "## 1.2 Tapering using mytarpering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c3c2bc2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.042072551947 IIII\n",
      " 0.177713582291 ZIII\n",
      " 0.177713582291 IZII\n",
      " 0.170597592768 ZZII\n",
      " 0.044750084063 YXXY\n",
      "-0.044750084063 YYXX\n",
      "-0.044750084063 XXYY\n",
      " 0.044750084063 XYYX\n",
      "-0.242745012609 IIZI\n",
      " 0.122933304493 ZIZI\n",
      "-0.242745012609 IIIZ\n",
      " 0.167683388556 ZIIZ\n",
      " 0.167683388556 IZZI\n",
      " 0.122933304493 IZIZ\n",
      " 0.176276613942 IIZZ\n"
     ]
    }
   ],
   "source": [
    "Hami_ori = create_pauliwords_from_hamilton(H, qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9976adea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 0.026230335235595703\n",
      "Number of qubit after tapering = 1\n",
      "The tapered Hamiltonian is \n",
      " -0.27643173+0.00000000j I\n",
      "0.84091719+0.00000000j Z\n",
      "0.17900034+0.00000000j X\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "Hami_reduced_by_tapering = tapering(Hami_ori, n_electrons=2)\n",
    "print(f'time cost: {time() - begin}')\n",
    "print(\"Number of qubit after tapering =\", Hami_reduced_by_tapering.num_qubits)\n",
    "print(\"The tapered Hamiltonian is \\n\", Hami_reduced_by_tapering)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c8202e1",
   "metadata": {},
   "source": [
    "## 1.3 compare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8551f859",
   "metadata": {},
   "source": [
    "### 1.3.1 generators and paulixops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6fac88f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1:   (1.0) [Z0 Z1], paulix_op: PauliX(wires=[1])\n",
      "generator 2:   (1.0) [Z0 Z2], paulix_op: PauliX(wires=[2])\n",
      "generator 3:   (1.0) [Z0 Z3], paulix_op: PauliX(wires=[3])\n"
     ]
    }
   ],
   "source": [
    "for idx, generator in enumerate(generators_by_qml):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulixops_by_qml[idx]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1af8d1ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1: 1.00000000 ZZII, paulix_op: 1.00000000 IXII\n",
      "generator 2: 1.00000000 ZIZI, paulix_op: 1.00000000 IIXI\n",
      "generator 3: 1.00000000 ZIIZ, paulix_op: 1.00000000 IIIX\n"
     ]
    }
   ],
   "source": [
    "generators_by_tapering_ = get_generators_from_kernel(\n",
    "    kernel_of_E(create_parity_check_matrix_E(*create_binary_matrix_G(Hami_ori)))\n",
    ")\n",
    "generators_by_tapering, paulix_ops_by_tapering = get_paulix_ops_from_generators(generators_by_tapering_)\n",
    "\n",
    "for idx, generator in enumerate(generators_by_tapering.terms):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulix_ops_by_tapering.terms[idx]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc833ef4",
   "metadata": {},
   "source": [
    "### 1.3.2 optimal sectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "114d80b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sectors by qml: [1, -1, -1]\n",
      "sectors by tapering: [1, -1, -1]\n"
     ]
    }
   ],
   "source": [
    "print(f'sectors by qml: {paulix_sector_by_qml}')\n",
    "print(f'sectors by tapering: {optimal_sector(Hami_ori, generators_by_tapering, n_electrons)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1df20c19",
   "metadata": {},
   "source": [
    "### 1.3.3 final eigen values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "430833c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: Hami_reduced_by_qml\n",
      "\n",
      "Sorted Eigenvalues: \n",
      "[-1.136189+0.j  0.583326+0.j]\n",
      "min eigenvalue:  (-1.1361891625218794+0j)\n"
     ]
    }
   ],
   "source": [
    "print('Test: Hami_reduced_by_qml\\n')\n",
    "print(\"Sorted Eigenvalues: \")\n",
    "eigvals_reduced_by_qml = np.linalg.eigvals(Hami_reduced_by_qml.matrix)\n",
    "print(np.sort(eigvals_reduced_by_qml))\n",
    "print('min eigenvalue: ', min(eigvals_reduced_by_qml))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9e60d34b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: Hami_reduced_by_tapering\n",
      "\n",
      "Sorted Eigenvalues: \n",
      "[-1.136189+0.j  0.583326+0.j]\n",
      "min eigenvalue:  (-1.1361891625218794+0j)\n"
     ]
    }
   ],
   "source": [
    "print('Test: Hami_reduced_by_tapering\\n')\n",
    "print(\"Sorted Eigenvalues: \")\n",
    "eigvals_reduced_by_tapering = np.linalg.eigvals(Hami_reduced_by_tapering.matrix)\n",
    "print(np.sort(eigvals_reduced_by_tapering))\n",
    "print('min eigenvalue: ', min(eigvals_reduced_by_tapering))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fd06f8b",
   "metadata": {},
   "source": [
    "# 2. Example: LiH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7ebf9164",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://github.com/aoterodelaroza/refdata/blob/master/20_g3/lih.xyz\n",
    "symbols = [\"Li\", \"H\"]\n",
    "coordinates = np.array([0.0, 0.0, 0.403635, 0.0, 0.0, -1.210905])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "10cc82f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of qubits =  12\n",
      "The Hamiltonian is \n",
      "   (-3.844095589078443) [I0]\n",
      "+ (-0.38874433443438816) [Z11]\n",
      "+ (-0.38874433443438805) [Z10]\n",
      "+ (-0.21337079370277998) [Z9]\n",
      "+ (-0.21337079370277995) [Z8]\n",
      "+ (-0.21337079370270737) [Z7]\n",
      "+ (-0.21337079370270734) [Z6]\n",
      "+ (-0.18269688137599668) [Z5]\n",
      "+ (-0.18269688137599663) [Z4]\n",
      "+ (-0.08811650933952661) [Z3]\n",
      "+ (-0.0881165093395265) [Z2]\n",
      "+ (1.0657693942968418) [Z0]\n",
      "+ (1.0657693942968425) [Z1]\n",
      "+ (-0.0040328077024712255) [Y1 Y3]\n",
      "+ (-0.0040328077024712255) [X1 X3]\n",
      "+ (0.001121895797431289) [Y3 Y5]\n",
      "+ (0.001121895797431289) [X3 X5]\n",
      "+ (0.008829856445608452) [Y2 Y4]\n",
      "+ (0.008829856445608452) [X2 X4]\n",
      "+ (0.04515772747839051) [Y0 Y2]\n",
      "+ (0.04515772747839051) [X0 X2]\n",
      "+ (0.05516443343995296) [Z4 Z10]\n",
      "+ (0.05516443343995296) [Z5 Z11]\n",
      "+ (0.05992853198294553) [Z4 Z6]\n",
      "+ (0.05992853198294553) [Z5 Z7]\n",
      "+ (0.059928531982973314) [Z4 Z8]\n",
      "+ (0.059928531982973314) [Z5 Z9]\n",
      "+ (0.06101038170335723) [Z2 Z4]\n",
      "+ (0.06101038170335723) [Z3 Z5]\n",
      "+ (0.06195795786087671) [Z4 Z11]\n",
      "+ (0.06195795786087671) [Z5 Z10]\n",
      "+ (0.06332356811740786) [Z2 Z5]\n",
      "+ (0.06332356811740786) [Z3 Z4]\n",
      "+ (0.06558451169149097) [Z6 Z8]\n",
      "+ (0.06558451169149097) [Z7 Z9]\n",
      "+ (0.06564862385825075) [Z6 Z10]\n",
      "+ (0.06564862385825075) [Z7 Z11]\n",
      "+ (0.06564862385828116) [Z8 Z10]\n",
      "+ (0.06564862385828116) [Z9 Z11]\n",
      "+ (0.06897826425090509) [Z6 Z11]\n",
      "+ (0.06897826425090509) [Z7 Z10]\n",
      "+ (0.06897826425093703) [Z8 Z11]\n",
      "+ (0.06897826425093703) [Z9 Z10]\n",
      "+ (0.06957281650586862) [Z2 Z6]\n",
      "+ (0.06957281650586862) [Z3 Z7]\n",
      "+ (0.06957281650590084) [Z2 Z8]\n",
      "+ (0.06957281650590084) [Z3 Z9]\n",
      "+ (0.06980179563474762) [Z6 Z9]\n",
      "+ (0.06980179563474762) [Z7 Z8]\n",
      "+ (0.07066091764369015) [Z4 Z7]\n",
      "+ (0.07066091764369015) [Z5 Z6]\n",
      "+ (0.0706609176437229) [Z4 Z9]\n",
      "+ (0.0706609176437229) [Z5 Z8]\n",
      "+ (0.07669217590173041) [Z2 Z7]\n",
      "+ (0.07669217590173041) [Z3 Z6]\n",
      "+ (0.07669217590176594) [Z2 Z9]\n",
      "+ (0.07669217590176594) [Z3 Z8]\n",
      "+ (0.07823636352122464) [Z6 Z7]\n",
      "+ (0.07823636352129718) [Z8 Z9]\n",
      "+ (0.08345858154511318) [Z2 Z10]\n",
      "+ (0.08345858154511318) [Z3 Z11]\n",
      "+ (0.084330230456835) [Z4 Z5]\n",
      "+ (0.09340913252396751) [Z0 Z4]\n",
      "+ (0.09340913252396751) [Z1 Z5]\n",
      "+ (0.09649094730787496) [Z0 Z6]\n",
      "+ (0.09649094730787496) [Z1 Z7]\n",
      "+ (0.09649094730791966) [Z0 Z8]\n",
      "+ (0.09649094730791966) [Z1 Z9]\n",
      "+ (0.09785620160997842) [Z0 Z5]\n",
      "+ (0.09785620160997842) [Z1 Z4]\n",
      "+ (0.09898260831034297) [Z0 Z7]\n",
      "+ (0.09898260831034297) [Z1 Z6]\n",
      "+ (0.09898260831038883) [Z0 Z9]\n",
      "+ (0.09898260831038883) [Z1 Z8]\n",
      "+ (0.10115186115826806) [Z0 Z10]\n",
      "+ (0.10115186115826806) [Z1 Z11]\n",
      "+ (0.10620438977616045) [Z0 Z11]\n",
      "+ (0.10620438977616045) [Z1 Z10]\n",
      "+ (0.10914189586510814) [Z10 Z11]\n",
      "+ (0.11418967710312494) [Z2 Z11]\n",
      "+ (0.11418967710312494) [Z3 Z10]\n",
      "+ (0.11495128592984712) [Z0 Z2]\n",
      "+ (0.11495128592984712) [Z1 Z3]\n",
      "+ (0.1253853192333283) [Z0 Z3]\n",
      "+ (0.1253853192333283) [Z1 Z2]\n",
      "+ (0.13040594997586766) [Z2 Z3]\n",
      "+ (0.4082012700745567) [Z0 Z1]\n",
      "+ (-0.0079464965158474) [Y2 Z3 Y4]\n",
      "+ (-0.0079464965158474) [X2 Z3 X4]\n",
      "+ (-0.0079464965158474) [Y3 Z4 Y5]\n",
      "+ (-0.0079464965158474) [X3 Z4 X5]\n",
      "+ (0.027247318532926786) [Y1 Z2 Y3]\n",
      "+ (0.027247318532926786) [X1 Z2 X3]\n",
      "+ (0.027247318532926793) [Y0 Z1 Y2]\n",
      "+ (0.027247318532926793) [X0 Z1 X2]\n",
      "+ (-0.03073109555801176) [Y2 Y3 X10 X11]\n",
      "+ (-0.03073109555801176) [X2 X3 Y10 Y11]\n",
      "+ (-0.01073238566074959) [Y4 Y5 X8 X9]\n",
      "+ (-0.01073238566074959) [X4 X5 Y8 Y9]\n",
      "+ (-0.010732385660744616) [Y4 Y5 X6 X7]\n",
      "+ (-0.010732385660744616) [X4 X5 Y6 Y7]\n",
      "+ (-0.010434033303481197) [Y0 Y1 X2 X3]\n",
      "+ (-0.010434033303481197) [X0 X1 Y2 Y3]\n",
      "+ (-0.007119359395865093) [Y2 Y3 X8 X9]\n",
      "+ (-0.007119359395865093) [X2 X3 Y8 Y9]\n",
      "+ (-0.007119359395861792) [Y2 Y3 X6 X7]\n",
      "+ (-0.007119359395861792) [X2 X3 Y6 Y7]\n",
      "+ (-0.006793524420923752) [Y4 Y5 X10 X11]\n",
      "+ (-0.006793524420923752) [X4 X5 Y10 Y11]\n",
      "+ (-0.005052528617892376) [Y0 Y1 X10 X11]\n",
      "+ (-0.005052528617892376) [X0 X1 Y10 Y11]\n",
      "+ (-0.005002545304324002) [Y3 X4 X8 Y9]\n",
      "+ (-0.005002545304324002) [Y3 Y4 Y8 Y9]\n",
      "+ (-0.005002545304324002) [X3 X4 X8 X9]\n",
      "+ (-0.005002545304324002) [X3 Y4 Y8 X9]\n",
      "+ (-0.005002545304321684) [Y3 X4 X6 Y7]\n",
      "+ (-0.005002545304321684) [Y3 Y4 Y6 Y7]\n",
      "+ (-0.005002545304321684) [X3 X4 X6 X7]\n",
      "+ (-0.005002545304321684) [X3 Y4 Y6 X7]\n",
      "+ (-0.004447069086010908) [Y0 Y1 X4 X5]\n",
      "+ (-0.004447069086010908) [X0 X1 Y4 Y5]\n",
      "+ (-0.004217283943256648) [Y6 Y7 X8 X9]\n",
      "+ (-0.004217283943256648) [X6 X7 Y8 Y9]\n",
      "+ (-0.004169326928506781) [Y0 Z1 Y2 Z11]\n",
      "+ (-0.004169326928506781) [X0 Z1 X2 Z11]\n",
      "+ (-0.004169326928506781) [Y1 Z2 Y3 Z10]\n",
      "+ (-0.004169326928506781) [X1 Z2 X3 Z10]\n",
      "+ (-0.004032807702471225) [Y0 Z1 Y2 Z3]\n",
      "+ (-0.004032807702471225) [X0 Z1 X2 Z3]\n",
      "+ (-0.0033296403926558874) [Y8 Y9 X10 X11]\n",
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      "+ (-0.0014247714390429862) [Y0 Z1 Z2 Z3 Y4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0014247714390429862) [X0 Z1 Z2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.0014247714390429862) [X0 Z1 Z2 Z3 X4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0005448819335739082) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0005448819335739082) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X7 Z8 Z9 Z10 X11]\n",
      "+ (0.0005448819335739082) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0005448819335739082) [X0 Z1 Z2 Z3 Z4 Z5 X6 X7 Z8 Z9 Z10 X11]\n",
      "+ (0.0005448819335741604) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y9 Z10 Y11]\n",
      "+ (0.0005448819335741604) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 X9 Z10 X11]\n",
      "+ (0.0005448819335741604) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Y9 Z10 Y11]\n",
      "+ (0.0005448819335741604) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 X9 Z10 X11]\n",
      "+ (0.0036224668189408678) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z11]\n",
      "+ (0.0036224668189408678) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z11]\n",
      "+ (0.004551310975550443) [Y0 Z1 Z2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.004551310975550443) [X0 Z1 Z2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.006617582988978048) [Y0 Y1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.006617582988978048) [X0 X1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "--------------------\n",
      "Number of terms:  631\n"
     ]
    }
   ],
   "source": [
    "# 基于JW变换构建的H2哈密顿量\n",
    "H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)\n",
    "print(\"Number of qubits = \", qubits)\n",
    "print(\"The Hamiltonian is \\n\", H)\n",
    "print(\"-\" * 20)\n",
    "print(\"Number of terms: \", len(H.ops))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0949267d",
   "metadata": {},
   "source": [
    "## 2.1 Tapering using QML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "07cdd554",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 165.20137000083923\n",
      "Number of qubit after tapering = 8\n",
      "The tapered Hamiltonian is \n",
      "   ((-3.68762286203592+0j)) [I0]\n",
      "+ ((-0.42674158740555956+0j)) [Z8]\n",
      "+ ((-0.4267415874054145+0j)) [Z6]\n",
      "+ ((-0.18269688137599657+0j)) [Z4]\n",
      "+ ((-0.18269688137599657+0j)) [Z5]\n",
      "+ ((-0.08811650933952657+0j)) [Z3]\n",
      "+ ((-0.08811650933952643+0j)) [Z2]\n",
      "+ ((-0.009731378415249032+0j)) [X5]\n",
      "+ ((-0.0036224668189408647+0j)) [X0]\n",
      "+ ((0.003329640392654342+0j)) [X6]\n",
      "+ ((0.0033296403926558835+0j)) [X8]\n",
      "+ ((0.009033626870508097+0j)) [X4]\n",
      "+ ((0.030963141132992696+0j)) [X1]\n",
      "+ ((1.0657693942968405+0j)) [Z0]\n",
      "+ ((1.0657693942968416+0j)) [Z1]\n",
      "+ ((-0.030731095558011737+0j)) [Y2 Y3]\n",
      "+ ((-0.012871066449284539+0j)) [X4 Z5]\n",
      "+ ((-0.0067935244209237486+0j)) [Y4 Y5]\n",
      "+ ((-0.005052528617892372+0j)) [Y0 Y1]\n",
      "+ ((-0.004032807702471221+0j)) [Y1 Y3]\n",
      "+ ((-0.004032807702471221+0j)) [X1 X3]\n",
      "+ ((-0.0026554679625305938+0j)) [X1 X2]\n",
      "+ ((-0.002587745598082857+0j)) [Y5 Y8]\n",
      "+ ((-0.002587745598082857+0j)) [X5 X8]\n",
      "+ ((-0.0025877455980816587+0j)) [Y5 Y6]\n",
      "+ ((-0.0025877455980816587+0j)) [X5 X6]\n",
      "+ ((0.0005448819335739078+0j)) [X0 X6]\n",
      "+ ((0.0005448819335739078+0j)) [Y0 Y6]\n",
      "+ ((0.0005448819335741597+0j)) [X0 X8]\n",
      "+ ((0.0005448819335741597+0j)) [Y0 Y8]\n",
      "+ ((0.0011218957974312885+0j)) [Y3 Y5]\n",
      "+ ((0.0011218957974312885+0j)) [X3 X5]\n",
      "+ ((0.0016444357004715244+0j)) [Y0 Y5]\n",
      "+ ((0.007062539419022847+0j)) [X3 X4]\n",
      "+ ((0.008434567886513287+0j)) [Y6 Y8]\n",
      "+ ((0.008434567886513287+0j)) [X6 X8]\n",
      "+ ((0.008829856445608446+0j)) [Y2 Y4]\n",
      "+ ((0.008829856445608446+0j)) [X2 X4]\n",
      "+ ((0.025836613617428898+0j)) [Z0 X1]\n",
      "+ ((0.045157727478390496+0j)) [Y0 Y2]\n",
      "+ ((0.045157727478390496+0j)) [X0 X2]\n",
      "+ ((0.061010381703357174+0j)) [Z2 Z4]\n",
      "+ ((0.061010381703357174+0j)) [Z3 Z5]\n",
      "+ ((0.0633235681174078+0j)) [Z2 Z5]\n",
      "+ ((0.0633235681174078+0j)) [Z3 Z4]\n",
      "+ ((0.08433023045683495+0j)) [Z4 Z5]\n",
      "+ ((0.09340913252396744+0j)) [Z0 Z4]\n",
      "+ ((0.09340913252396744+0j)) [Z1 Z5]\n",
      "+ ((0.09785620160997838+0j)) [Z0 Z5]\n",
      "+ ((0.09785620160997838+0j)) [Z1 Z4]\n",
      "+ ((0.11495128592984699+0j)) [Z0 Z2]\n",
      "+ ((0.11495128592984699+0j)) [Z1 Z3]\n",
      "+ ((0.12538531923332824+0j)) [Z0 Z3]\n",
      "+ ((0.12538531923332824+0j)) [Z1 Z2]\n",
      "+ ((0.13040594997586757+0j)) [Z2 Z3]\n",
      "+ ((0.13058944962663557+0j)) [Z4 Z6]\n",
      "+ ((0.13058944962663557+0j)) [Z5 Z6]\n",
      "+ ((0.13058944962669614+0j)) [Z4 Z8]\n",
      "+ ((0.13058944962669614+0j)) [Z5 Z8]\n",
      "+ ((0.14626499240759894+0j)) [Z2 Z6]\n",
      "+ ((0.14626499240759894+0j)) [Z3 Z6]\n",
      "+ ((0.14626499240766666+0j)) [Z2 Z8]\n",
      "+ ((0.14626499240766666+0j)) [Z3 Z8]\n",
      "+ ((0.19547355561821783+0j)) [Z0 Z6]\n",
      "+ ((0.19547355561821783+0j)) [Z1 Z6]\n",
      "+ ((0.1954735556183084+0j)) [Z0 Z8]\n",
      "+ ((0.1954735556183084+0j)) [Z1 Z8]\n",
      "+ ((0.27077261465247693+0j)) [Z6 Z8]\n",
      "+ ((0.4082012700745565+0j)) [Z0 Z1]\n",
      "+ ((-0.040245314482897136+0j)) [Z0 Z1 X3]\n",
      "+ ((-0.038996566444017396+0j)) [Z0 Z1 X2]\n",
      "+ ((-0.035855923839514976+0j)) [Z1 Z2 X3]\n",
      "+ ((-0.029238340850536945+0j)) [Z0 Z2 X3]\n",
      "+ ((-0.01151563868231543+0j)) [Z3 X4 Z5]\n",
      "+ ((-0.010732385660749579+0j)) [Y4 Y5 X8]\n",
      "+ ((-0.010732385660744609+0j)) [Y4 Y5 X6]\n",
      "+ ((-0.007946496515847392+0j)) [Y2 Z3 Y4]\n",
      "+ ((-0.007946496515847392+0j)) [X2 Z3 X4]\n",
      "+ ((-0.007946496515847392+0j)) [Y3 Z4 Y5]\n",
      "+ ((-0.007946496515847392+0j)) [X3 Z4 X5]\n",
      "+ ((-0.007119359395865086+0j)) [Y2 Y3 X8]\n",
      "+ ((-0.007119359395861783+0j)) [Y2 Y3 X6]\n",
      "+ ((-0.00679491257848039+0j)) [X2 X3 X5]\n",
      "+ ((-0.00679491257848039+0j)) [X2 Y3 Y5]\n",
      "+ ((-0.006617582988978046+0j)) [X0 Y1 Y2]\n",
      "+ ((-0.005002545304323999+0j)) [Y3 X4 Y8]\n",
      "+ ((-0.005002545304323999+0j)) [X3 X4 X8]\n",
      "+ ((-0.005002545304323999+0j)) [X3 Y4 Y8]\n",
      "+ ((-0.0050025453043216804+0j)) [Y3 X4 Y6]\n",
      "+ ((-0.0050025453043216804+0j)) [X3 X4 X6]\n",
      "+ ((-0.0050025453043216804+0j)) [X3 Y4 Y6]\n",
      "+ ((-0.0047207261038350375+0j)) [Z2 X4 Z5]\n",
      "+ ((-0.004551310975550439+0j)) [Y0 Y3 X4]\n",
      "+ ((-0.004551310975550439+0j)) [Y1 Y2 X5]\n",
      "+ ((-0.0030575190914644422+0j)) [X0 X2 X3]\n",
      "+ ((-0.0030575190914644422+0j)) [Y0 Y2 X3]\n",
      "+ ((-0.002491661002469169+0j)) [Y0 Y1 X8]\n",
      "+ ((-0.0024916610024680133+0j)) [Y0 Y1 X6]\n",
      "+ ((-0.0022463325743191783+0j)) [Z0 X1 Z2]\n",
      "+ ((-0.002169428202930941+0j)) [Y1 X2 Y8]\n",
      "+ ((-0.002169428202930941+0j)) [X1 X2 X8]\n",
      "+ ((-0.002169428202930941+0j)) [X1 Y2 Y8]\n",
      "+ ((-0.002169428202929935+0j)) [Y1 X2 Y6]\n",
      "+ ((-0.002169428202929935+0j)) [X1 X2 X6]\n",
      "+ ((-0.002169428202929935+0j)) [X1 Y2 Y6]\n",
      "+ ((-0.0014247714390429852+0j)) [X0 X4 X5]\n",
      "+ ((-0.0014247714390429852+0j)) [Y0 Y4 X5]\n",
      "+ ((-0.000984207546844383+0j)) [X3 Y4 Y5]\n",
      "+ ((0.0008111865171452626+0j)) [Z0 X1 Z3]\n",
      "+ ((0.000984207546844383+0j)) [Y3 Y4 X5]\n",
      "+ ((0.0011856975737429584+0j)) [Z0 X1 Z4]\n",
      "+ ((0.0017588408593159223+0j)) [Z0 X1 Z6]\n",
      "+ ((0.001758840859316749+0j)) [Z0 X1 Z8]\n",
      "+ ((0.002169428202929935+0j)) [Y1 Y2 X6]\n",
      "+ ((0.002169428202930941+0j)) [Y1 Y2 X8]\n",
      "+ ((0.0024916610024680133+0j)) [Y0 X1 Y6]\n",
      "+ ((0.0024916610024680133+0j)) [X0 X1 X6]\n",
      "+ ((0.0024916610024680133+0j)) [X0 Y1 Y6]\n",
      "+ ((0.002491661002469169+0j)) [Y0 X1 Y8]\n",
      "+ ((0.002491661002469169+0j)) [X0 X1 X8]\n",
      "+ ((0.002491661002469169+0j)) [X0 Y1 Y8]\n",
      "+ ((0.002503156012440724+0j)) [Z0 X4 Z5]\n",
      "+ ((0.002610469012785943+0j)) [Z0 X1 Z5]\n",
      "+ ((0.0027464680929830446+0j)) [X4 Z5 Z6]\n",
      "+ ((0.0027464680929842806+0j)) [X4 Z5 Z8]\n",
      "+ ((0.0031541708948857957+0j)) [X0 X1 X5]\n",
      "+ ((0.0031541708948857957+0j)) [X0 Y1 Y5]\n",
      "+ ((0.004551310975550439+0j)) [X0 Y3 Y4]\n",
      "+ ((0.004551310975550439+0j)) [X1 Y2 Y5]\n",
      "+ ((0.0050025453043216804+0j)) [Y3 Y4 X6]\n",
      "+ ((0.005002545304323999+0j)) [Y3 Y4 X8]\n",
      "+ ((0.0052874004029997155+0j)) [X2 Z3 Z5]\n",
      "+ ((0.005657326907326522+0j)) [Z1 X4 Z5]\n",
      "+ ((0.006271607949844104+0j)) [X2 Z3 Z4]\n",
      "+ ((0.006617582988978046+0j)) [Y0 Y1 X2]\n",
      "+ ((0.007119359395861783+0j)) [Y2 X3 Y6]\n",
      "+ ((0.007119359395861783+0j)) [X2 X3 X6]\n",
      "+ ((0.007119359395861783+0j)) [X2 Y3 Y6]\n",
      "+ ((0.007119359395865086+0j)) [Y2 X3 Y8]\n",
      "+ ((0.007119359395865086+0j)) [X2 X3 X8]\n",
      "+ ((0.007119359395865086+0j)) [X2 Y3 Y8]\n",
      "+ ((0.010732385660744609+0j)) [Y4 X5 Y6]\n",
      "+ ((0.010732385660744609+0j)) [X4 X5 X6]\n",
      "+ ((0.010732385660744609+0j)) [X4 Y5 Y6]\n",
      "+ ((0.010732385660749579+0j)) [Y4 X5 Y8]\n",
      "+ ((0.010732385660749579+0j)) [X4 X5 X8]\n",
      "+ ((0.010732385660749579+0j)) [X4 Y5 Y8]\n",
      "+ ((0.027247318532926775+0j)) [Y0 Z1 Y2]\n",
      "+ ((0.027247318532926775+0j)) [X0 Z1 X2]\n",
      "+ ((0.027247318532926775+0j)) [Y1 Z2 Y3]\n",
      "+ ((0.027247318532926775+0j)) [X1 Z2 X3]\n",
      "+ ((0.038996566444017396+0j)) [X3 Z4 Z5]\n",
      "+ ((0.040245314482897136+0j)) [X2 Z4 Z5]\n",
      "+ ((-0.014538212066460167+0j)) [Z0 Z1 Z2 X3]\n",
      "+ ((-0.010434033303481192+0j)) [Y0 Y1 X2 X3]\n",
      "+ ((-0.010434033303481192+0j)) [X0 X1 Y2 Y3]\n",
      "+ ((-0.004447069086010905+0j)) [Y0 Y1 X4 X5]\n",
      "+ ((-0.004447069086010905+0j)) [X0 X1 Y4 Y5]\n",
      "+ ((-0.00403280770247122+0j)) [Y0 Z1 Y2 Z3]\n",
      "+ ((-0.00403280770247122+0j)) [X0 Z1 X2 Z3]\n",
      "+ ((-0.003452142424549066+0j)) [Y3 Z4 Z5 Y8]\n",
      "+ ((-0.003452142424549066+0j)) [X3 Z4 Z5 X8]\n",
      "+ ((-0.003452142424547465+0j)) [Y3 Z4 Z5 Y6]\n",
      "+ ((-0.003452142424547465+0j)) [X3 Z4 Z5 X6]\n",
      "+ ((-0.0032993028799647097+0j)) [Y0 X1 X3 Y4]\n",
      "+ ((-0.0032993028799647097+0j)) [Y0 Y1 Y3 Y4]\n",
      "+ ((-0.0032993028799647097+0j)) [X0 X1 X3 X4]\n",
      "+ ((-0.0032993028799647097+0j)) [X0 Y1 Y3 X4]\n",
      "+ ((-0.0026554679625305938+0j)) [Y0 Z1 Z2 Y3]\n",
      "+ ((-0.0026554679625305938+0j)) [Y0 Y3 Z4 Z5]\n",
      "+ ((-0.002313186414050624+0j)) [Y2 Y3 X4 X5]\n",
      "+ ((-0.002313186414050624+0j)) [X2 X3 Y4 Y5]\n",
      "+ ((-0.0018733067177044704+0j)) [Y1 X2 X3 Y4]\n",
      "+ ((-0.0018733067177044704+0j)) [X1 Y2 Y3 X4]\n",
      "+ ((-0.00100142867336504+0j)) [Y1 Z2 Z3 Y5]\n",
      "+ ((-0.00100142867336504+0j)) [X1 Z2 Z3 X5]\n",
      "+ ((-0.00024379407383964726+0j)) [Y1 X2 X4 Y5]\n",
      "+ ((-0.00024379407383964726+0j)) [Y1 Y2 Y4 Y5]\n",
      "+ ((-0.00024379407383964726+0j)) [X1 X2 X4 X5]\n",
      "+ ((-0.00024379407383964726+0j)) [X1 Y2 Y4 X5]\n",
      "+ ((0.0006866719904938414+0j)) [Z0 Y3 Z4 Y5]\n",
      "+ ((0.0006866719904938414+0j)) [Z0 X3 Z4 X5]\n",
      "+ ((0.0006866719904938414+0j)) [Z1 Y2 Z3 Y4]\n",
      "+ ((0.0006866719904938414+0j)) [Z1 X2 Z3 X4]\n",
      "+ ((0.0011218957974312885+0j)) [Y2 Z3 Y4 Z5]\n",
      "+ ((0.0011218957974312885+0j)) [X2 Z3 X4 Z5]\n",
      "+ ((0.0016444357004715244+0j)) [Z0 X1 X4 Z5]\n",
      "+ ((0.0016444357004715244+0j)) [X1 Z2 Z3 X4]\n",
      "+ ((0.0018733067177044704+0j)) [Y1 Y2 X3 X4]\n",
      "+ ((0.0018733067177044704+0j)) [X1 X2 Y3 Y4]\n",
      "+ ((0.002313186414050624+0j)) [Y2 X3 X4 Y5]\n",
      "+ ((0.002313186414050624+0j)) [X2 Y3 Y4 X5]\n",
      "+ ((0.003452142424547465+0j)) [Z0 Z1 X2 X6]\n",
      "+ ((0.003452142424547465+0j)) [Z0 Z1 Y2 Y6]\n",
      "+ ((0.003452142424549066+0j)) [Z0 Z1 X2 X8]\n",
      "+ ((0.003452142424549066+0j)) [Z0 Z1 Y2 Y8]\n",
      "+ ((0.003985974870458554+0j)) [Z0 Y2 Z3 Y4]\n",
      "+ ((0.003985974870458554+0j)) [Z0 X2 Z3 X4]\n",
      "+ ((0.003985974870458554+0j)) [Z1 Y3 Z4 Y5]\n",
      "+ ((0.003985974870458554+0j)) [Z1 X3 Z4 X5]\n",
      "+ ((0.004389807991361528+0j)) [Y0 Z1 Y2 Z5]\n",
      "+ ((0.004389807991361528+0j)) [X0 Z1 X2 Z5]\n",
      "+ ((0.004389807991361528+0j)) [Y1 Z2 Y3 Z4]\n",
      "+ ((0.004389807991361528+0j)) [X1 Z2 X3 Z4]\n",
      "+ ((0.004447069086010905+0j)) [Y0 X1 X4 Y5]\n",
      "+ ((0.004447069086010905+0j)) [X0 Y1 Y4 X5]\n",
      "+ ((0.004633602065201174+0j)) [Y0 Z1 Y2 Z4]\n",
      "+ ((0.004633602065201174+0j)) [X0 Z1 X2 Z4]\n",
      "+ ((0.004633602065201174+0j)) [Y1 Z2 Y3 Z5]\n",
      "+ ((0.004633602065201174+0j)) [X1 Z2 X3 Z5]\n",
      "+ ((0.005068351597496554+0j)) [Y2 Z3 Y4 Z6]\n",
      "+ ((0.005068351597496554+0j)) [X2 Z3 X4 Z6]\n",
      "+ ((0.005068351597496554+0j)) [Y3 Z4 Y5 Z6]\n",
      "+ ((0.005068351597496554+0j)) [X3 Z4 X5 Z6]\n",
      "+ ((0.0050683515974989+0j)) [Y2 Z3 Y4 Z8]\n",
      "+ ((0.0050683515974989+0j)) [X2 Z3 X4 Z8]\n",
      "+ ((0.0050683515974989+0j)) [Y3 Z4 Y5 Z8]\n",
      "+ ((0.0050683515974989+0j)) [X3 Z4 X5 Z8]\n",
      "+ ((0.005179115575182565+0j)) [Y0 Z1 Z3 Y4]\n",
      "+ ((0.005179115575182565+0j)) [X0 Z1 Z3 X4]\n",
      "+ ((0.005179115575182565+0j)) [Y1 Z2 Z4 Y5]\n",
      "+ ((0.005179115575182565+0j)) [X1 Z2 Z4 X5]\n",
      "+ ((0.005268688553060664+0j)) [Y0 Z1 Y2 Z6]\n",
      "+ ((0.005268688553060664+0j)) [X0 Z1 X2 Z6]\n",
      "+ ((0.005268688553060664+0j)) [Y1 Z2 Y3 Z6]\n",
      "+ ((0.005268688553060664+0j)) [X1 Z2 X3 Z6]\n",
      "+ ((0.005268688553063102+0j)) [Y0 Z1 Y2 Z8]\n",
      "+ ((0.005268688553063102+0j)) [X0 Z1 X2 Z8]\n",
      "+ ((0.005268688553063102+0j)) [Y1 Z2 Y3 Z8]\n",
      "+ ((0.005268688553063102+0j)) [X1 Z2 X3 Z8]\n",
      "+ ((0.007052422292887036+0j)) [Y0 Z1 Z2 Y4]\n",
      "+ ((0.007052422292887036+0j)) [X0 Z1 Z2 X4]\n",
      "+ ((0.007052422292887036+0j)) [Y1 Z3 Z4 Y5]\n",
      "+ ((0.007052422292887036+0j)) [X1 Z3 Z4 X5]\n",
      "+ ((0.007062539419022847+0j)) [Y2 Z3 Z4 Y5]\n",
      "+ ((0.007062539419022847+0j)) [Z0 Z1 Y2 Y5]\n",
      "+ ((0.008829856445608446+0j)) [Z2 Y3 Z4 Y5]\n",
      "+ ((0.008829856445608446+0j)) [Z2 X3 Z4 X5]\n",
      "+ ((0.010434033303481192+0j)) [Y0 X1 X2 Y3]\n",
      "+ ((0.010434033303481192+0j)) [X0 Y1 Y2 X3]\n",
      "+ ((0.014538212066460195+0j)) [X2 Z3 Z4 Z5]\n",
      "+ ((0.028997285064880748+0j)) [Y0 Z2 Z3 Y4]\n",
      "+ ((0.028997285064880748+0j)) [X0 Z2 Z3 X4]\n",
      "+ ((0.045157727478390496+0j)) [Z0 Y1 Z2 Y3]\n",
      "+ ((0.045157727478390496+0j)) [Z0 X1 Z2 X3]\n",
      "+ ((0.05516443343995292+0j)) [Z0 Z2 Z6 Z8]\n",
      "+ ((0.05516443343995292+0j)) [Z1 Z3 Z6 Z8]\n",
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      "+ ((-0.035855923839514976+0j)) [Z0 Z1 X2 Z3 Z5 Z6 Z8]\n",
      "+ ((-0.00679491257848039+0j)) [Z0 X2 Y3 Y4 Z5 Z6 Z8]\n",
      "+ ((-0.006617582988978046+0j)) [X0 X1 Z2 X3 Z5 Z6 Z8]\n",
      "+ ((-0.006617582988978046+0j)) [X0 Y1 Z2 Y3 Z5 Z6 Z8]\n",
      "+ ((-0.006617582988978046+0j)) [Y0 Y1 X2 Z3 Z5 Z6 Z8]\n",
      "+ ((-0.005657326907326522+0j)) [Z0 Z1 Z2 X4 Z5 Z6 Z8]\n",
      "+ ((-0.0052874004029997155+0j)) [Z0 X2 Z3 Z4 Z5 Z6 Z8]\n",
      "+ ((-0.0047207261038350375+0j)) [Z0 Z2 Z3 Z4 X5 Z6 Z8]\n",
      "+ ((-0.004551310975550439+0j)) [X0 Z1 Y3 Y4 Z5 Z6 Z8]\n",
      "+ ((-0.004551310975550439+0j)) [Z0 X1 Y2 Z4 Y5 Z6 Z8]\n",
      "+ ((-0.003598240923459001+0j)) [X0 Z1 X2 Z4 X5 Z6 Z8]\n",
      "+ ((-0.003598240923459001+0j)) [Y0 Z1 Y2 Z4 X5 Z6 Z8]\n",
      "+ ((-0.003598240923459001+0j)) [Z0 Y1 Y3 X4 Z5 Z6 Z8]\n",
      "+ ((-0.003598240923459001+0j)) [Z0 X1 X3 X4 Z5 Z6 Z8]\n",
      "+ ((-0.0031541708948857957+0j)) [X0 X1 Z2 Z4 X5 Z6 Z8]\n",
      "+ ((-0.0031541708948857957+0j)) [X0 Y1 Z2 Z4 Y5 Z6 Z8]\n",
      "+ ((-0.0031541708948857952+0j)) [Y0 Y1 Z2 X4 Z5 Z6 Z8]\n",
      "+ ((-0.0030575190914644422+0j)) [Z0 Y1 Y2 X3 Z5 Z6 Z8]\n",
      "+ ((-0.0027464680929842806+0j)) [Z0 Z1 Z2 Z3 Z4 X5 Z8]\n",
      "+ ((-0.0027464680929830446+0j)) [Z0 Z1 Z2 Z3 Z4 X5 Z6]\n",
      "+ ((-0.0025537920074065667+0j)) [Y0 Z1 Z2 Z3 Z4 Y5 X8]\n",
      "+ ((-0.002553792007405382+0j)) [Y0 Z1 Z2 Z3 Z4 Y5 X6]\n",
      "+ ((-0.001758840859316749+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z8]\n",
      "+ ((-0.0017588408593159223+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6]\n",
      "+ ((-0.0014247714390429852+0j)) [Z0 Y1 Z3 Y4 X5 Z6 Z8]\n",
      "+ ((-0.0011856975737429584+0j)) [Z0 X1 Z3 Z4 Z5 Z6 Z8]\n",
      "+ ((-0.000984207546844383+0j)) [Z0 Z2 Y3 Y4 X5 Z6 Z8]\n",
      "+ ((-0.0009530700520914373+0j)) [Y0 Z1 Y2 X4 Z5 Z6 Z8]\n",
      "+ ((-0.0009530700520914373+0j)) [Z0 Y1 Y3 Z4 X5 Z6 Z8]\n",
      "+ ((0.0008111865171452626+0j)) [X0 Z1 Z2 Z3 Z5 Z6 Z8]\n",
      "+ ((0.000984207546844383+0j)) [Z0 X2 Z3 X4 X5 Z6 Z8]\n",
      "+ ((0.000984207546844383+0j)) [Z0 Y2 Z3 Y4 X5 Z6 Z8]\n",
      "+ ((0.000984207546844383+0j)) [Z0 Z2 X3 Y4 Y5 Z6 Z8]\n",
      "+ ((0.0014247714390429852+0j)) [X0 Z1 Z3 X4 X5 Z6 Z8]\n",
      "+ ((0.0014247714390429852+0j)) [Y0 Z1 Z3 Y4 X5 Z6 Z8]\n",
      "+ ((0.0014247714390429852+0j)) [Z0 X1 Z3 Y4 Y5 Z6 Z8]\n",
      "+ ((0.0016815362811012614+0j)) [X0 Z1 X3 Z4 X5 Z6 Z8]\n",
      "+ ((0.0016815362811012614+0j)) [X0 Z1 Y3 Z4 Y5 Z6 Z8]\n",
      "+ ((0.0016815362811012614+0j)) [Z0 X1 Y2 Y4 Z5 Z6 Z8]\n",
      "+ ((0.0016815362811012614+0j)) [Z0 X1 X2 X4 Z5 Z6 Z8]\n",
      "+ ((0.0019167046423577414+0j)) [X0 Z1 X2 X4 Z5 Z6 Z8]\n",
      "+ ((0.0019167046423577414+0j)) [Z0 X1 X3 Z4 X5 Z6 Z8]\n",
      "+ ((0.0022463325743191783+0j)) [Z0 X1 Z2 Z3 Z5 Z6 Z8]\n",
      "+ ((0.002503156012440724+0j)) [Z0 Z1 Z2 Z4 X5 Z6 Z8]\n",
      "+ ((0.002553792007405382+0j)) [Y0 Z1 Z2 Z3 Z4 X5 Y6]\n",
      "+ ((0.002553792007405382+0j)) [X0 Z1 Z2 Z3 Z4 X5 X6]\n",
      "+ ((0.002553792007405382+0j)) [X0 Z1 Z2 Z3 Z4 Y5 Y6]\n",
      "+ ((0.0025537920074065667+0j)) [Y0 Z1 Z2 Z3 Z4 X5 Y8]\n",
      "+ ((0.0025537920074065667+0j)) [X0 Z1 Z2 Z3 Z4 X5 X8]\n",
      "+ ((0.0025537920074065667+0j)) [X0 Z1 Z2 Z3 Z4 Y5 Y8]\n",
      "+ ((0.002610469012785943+0j)) [X0 Z1 Z3 Z4 Z5 Z6 Z8]\n",
      "+ ((0.002869774694449178+0j)) [X0 Z1 Y2 Y4 Z5 Z6 Z8]\n",
      "+ ((0.002869774694449178+0j)) [Z0 X1 Y3 Z4 Y5 Z6 Z8]\n",
      "+ ((0.0030575190914644422+0j)) [X0 Z1 X2 X3 Z5 Z6 Z8]\n",
      "+ ((0.0030575190914644422+0j)) [Y0 Z1 Y2 X3 Z5 Z6 Z8]\n",
      "+ ((0.0030575190914644422+0j)) [Z0 X1 Y2 Y3 Z5 Z6 Z8]\n",
      "+ ((0.0031541708948857952+0j)) [X0 Y1 Z2 Y4 Z5 Z6 Z8]\n",
      "+ ((0.003329640392654342+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 X6]\n",
      "+ ((0.0033296403926558835+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 X8]\n",
      "+ ((0.004551310975550439+0j)) [Y0 Z1 Y3 X4 Z5 Z6 Z8]\n",
      "+ ((0.004551310975550439+0j)) [Z0 Y1 Y2 Z4 X5 Z6 Z8]\n",
      "+ ((0.006271607949844104+0j)) [Z0 Z2 X3 Z4 Z5 Z6 Z8]\n",
      "+ ((0.006617582988978046+0j)) [X0 Y1 Y2 Z3 Z5 Z6 Z8]\n",
      "+ ((0.00679491257848039+0j)) [Z0 X2 X3 Z4 X5 Z6 Z8]\n",
      "+ ((0.00679491257848039+0j)) [Z0 X2 Y3 Z4 Y5 Z6 Z8]\n",
      "+ ((0.00679491257848039+0j)) [Z0 Y2 Y3 X4 Z5 Z6 Z8]\n",
      "+ ((0.01151563868231543+0j)) [Z0 Z2 Z3 X4 Z5 Z6 Z8]\n",
      "+ ((0.029238340850536945+0j)) [Z0 Z1 Z2 X3 Z5 Z6 Z8]\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "generators_by_qml = qml.symmetry_generators(H)\n",
    "paulixops_by_qml = qml.paulix_ops(generators_by_qml, qubits)\n",
    "\n",
    "n_electrons = 4\n",
    "paulix_sector_by_qml = qml.qchem.optimal_sector(H, generators_by_qml, n_electrons)\n",
    "\n",
    "H_tapered = qml.taper(H, generators_by_qml, paulixops_by_qml, paulix_sector_by_qml)\n",
    "print(f'time cost: {time() - begin}')\n",
    "\n",
    "print(\"Number of qubit after tapering =\", len(H_tapered.wires))\n",
    "print(\"The tapered Hamiltonian is \\n\", H_tapered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5322378d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      " 0.045157727478 XIXIIIIII\n",
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      " 0.028997285065 YIZZYIIII\n",
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      " 0.001916704642 ZXIXZXIII\n",
      "-0.000953070052 ZYIYZXZIZ\n",
      "-0.000953070052 ZYIYZXIII\n",
      " 0.001916704642 ZXIXZXZIZ\n",
      " 0.002869774694 ZXIYZYZIZ\n",
      " 0.097856201610 IZIIZIIII\n",
      " 0.004389807991 IYZYZIIII\n",
      " 0.004389807991 IXZXZIIII\n",
      "-0.001001428673 IYZZIYIII\n",
      "-0.001001428673 IXZZIXIII\n",
      " 0.001185697574 ZXIIZIIII\n",
      "-0.001185697574 ZXIZZZZIZ\n",
      "-0.002553792007 IYZZXIYII\n",
      " 0.002553792007 IYZZYIXII\n",
      "-0.002553792007 IXZZXIXII\n",
      "-0.002553792007 IXZZYIYII\n",
      "-0.002553792007 IYZZXIIIY\n",
      " 0.002553792007 IYZZYIIIX\n",
      "-0.002553792007 IXZZXIIIX\n",
      "-0.002553792007 IXZZYIIIY\n",
      "-0.005657326907 ZZZIXZZIZ\n",
      " 0.005657326907 IZIIXZIII\n",
      "-0.003598240923 ZYIYXZZIZ\n",
      " 0.003598240923 IYZYXZIII\n",
      "-0.003598240923 ZXIXXZZIZ\n",
      " 0.003598240923 IXZXXZIII\n",
      "-0.001424771439 ZYIZYXZIZ\n",
      " 0.001424771439 IYZZYXIII\n",
      " 0.001424771439 ZXIZYYZIZ\n",
      "-0.001424771439 IXZZYYIII\n",
      "-0.001644435700 IXZIXZZIZ\n",
      " 0.001644435700 ZXIIXZIII\n",
      " 0.001644435700 IXZZXIIII\n",
      "-0.001644435700 ZXIZXIZIZ\n",
      " 0.093409132524 IZIIIZIII\n",
      "-0.002503156012 ZIZZZXIII\n",
      " 0.002503156012 ZZZIZXZIZ\n",
      " 0.004633602065 IYZYIZIII\n",
      " 0.004633602065 IXZXIZIII\n",
      " 0.002610469013 ZXIIIZIII\n",
      "-0.002610469013 ZXIZIIZIZ\n",
      " 0.195473555618 IZIIIIZII\n",
      " 0.005268688553 IYZYIIZII\n",
      " 0.005268688553 IXZXIIZII\n",
      " 0.004473090589 IYZZZYZII\n",
      " 0.004473090589 IXZZZXZII\n",
      " 0.001758840859 ZXIIIIZII\n",
      "-0.001758840859 ZXIZIZIIZ\n",
      " 0.000544881934 ZYIZIZYIZ\n",
      "-0.000544881934 IYZZZZYII\n",
      " 0.000544881934 ZXIZIZXIZ\n",
      "-0.000544881934 IXZZZZXII\n",
      " 0.195473555618 IZIIIIIIZ\n",
      " 0.005268688553 IYZYIIIIZ\n",
      " 0.005268688553 IXZXIIIIZ\n",
      " 0.004473090589 IYZZZYIIZ\n",
      " 0.004473090589 IXZZZXIIZ\n",
      " 0.001758840859 ZXIIIIIIZ\n",
      "-0.001758840859 ZXIZIZZII\n",
      " 0.000544881934 ZYIZIZZIY\n",
      "-0.000544881934 IYZZZZIIY\n",
      " 0.000544881934 ZXIZIZZIX\n",
      "-0.000544881934 IXZZZZIIX\n",
      " 0.106204389776 ZZZIZIZIZ\n",
      "-0.004169326929 ZYIYZIZIZ\n",
      "-0.004169326929 ZXIXZIZIZ\n",
      " 0.005344247480 ZYIZIYZIZ\n",
      " 0.005344247480 ZXIZIXZIZ\n",
      "-0.003622466819 IXZIZIZIZ\n",
      " 0.003622466819 IXZZZZIII\n",
      " 0.101151861158 IIIZIZZIZ\n",
      " 0.001513858966 IXZXIZZIZ\n",
      " 0.001513858966 IYZYIZZIZ\n",
      "-0.003699811780 IXZIZXZIZ\n",
      "-0.003699811780 IYZIZYZIZ\n",
      " 0.130405949976 IIZZIIIII\n",
      " 0.008829856446 IIYIYIIII\n",
      " 0.008829856446 IIXIXIIII\n",
      "-0.040245314483 ZIXIIZZIZ\n",
      " 0.040245314483 IIXIZZIII\n",
      " 0.008829856446 IIZYZYIII\n",
      " 0.008829856446 IIZXZXIII\n",
      " 0.002313186414 IIYXXYIII\n",
      "-0.002313186414 IIYYXXIII\n",
      "-0.002313186414 IIXXYYIII\n",
      " 0.002313186414 IIXYYXIII\n",
      " 0.006794912578 ZIXXZXZIZ\n",
      " 0.006794912578 ZIXYZYZIZ\n",
      "-0.006794912578 IIXXIXIII\n",
      "-0.006794912578 IIXYIYIII\n",
      " 0.007119359396 IIYXIIYII\n",
      "-0.007119359396 IIYYIIXII\n",
      " 0.007119359396 IIXXIIXII\n",
      " 0.007119359396 IIXYIIYII\n",
      " 0.007119359396 IIYXIIIIY\n",
      "-0.007119359396 IIYYIIIIX\n",
      " 0.007119359396 IIXXIIIIX\n",
      " 0.007119359396 IIXYIIIIY\n",
      "-0.040245314483 ZZIXIIIII\n",
      " 0.040245314483 ZIIXIZZIZ\n",
      " 0.006794912578 ZZXYYIIII\n",
      "-0.006794912578 ZIXYYZZIZ\n",
      "-0.006794912578 ZZYYXIIII\n",
      " 0.006794912578 ZIYYXZZIZ\n",
      " 0.030731095558 IZYYIZZIZ\n",
      "-0.030731095558 IIYYIIIII\n",
      "-0.030731095558 ZZYYZZIII\n",
      " 0.030731095558 ZIYYZIZIZ\n",
      " 0.061010381703 IIZIZIIII\n",
      " 0.004720726104 ZIIIXZZIZ\n",
      "-0.004720726104 IIZIXZIII\n",
      "-0.005287400403 ZIXZZZZIZ\n",
      " 0.005287400403 IIXZIZIII\n",
      " 0.063323568117 IIZIIZIII\n",
      " 0.001121895797 IIYZYZIII\n",
      " 0.001121895797 IIXZXZIII\n",
      "-0.006271607950 ZIXZIIZIZ\n",
      " 0.006271607950 IIXZZIIII\n",
      " 0.005002545304 IIYZZXYII\n",
      "-0.005002545304 IIYZZYXII\n",
      " 0.005002545304 IIXZZXXII\n",
      " 0.005002545304 IIXZZYYII\n",
      " 0.005002545304 IIYZZXIIY\n",
      "-0.005002545304 IIYZZYIIX\n",
      " 0.005002545304 IIXZZXIIX\n",
      " 0.005002545304 IIXZZYIIY\n",
      " 0.011515638682 ZZIZZXIII\n",
      "-0.011515638682 ZIIIZXZIZ\n",
      "-0.000984207547 ZZXIXXIII\n",
      " 0.000984207547 ZIXZXXZIZ\n",
      "-0.000984207547 ZZYIYXIII\n",
      " 0.000984207547 ZIYZYXZIZ\n",
      "-0.007062539419 IZYIZYZIZ\n",
      " 0.007062539419 IIYZZYIII\n",
      " 0.007062539419 ZZYIIYIII\n",
      "-0.007062539419 ZIYZIYZIZ\n",
      " 0.146264992408 IIZIIIZII\n",
      " 0.005068351597 IIYZYIZII\n",
      " 0.005068351597 IIXZXIZII\n",
      "-0.020122896224 ZIXZIZIIZ\n",
      " 0.020122896224 IIXZZZZII\n",
      " 0.003452142425 ZZXIIIXII\n",
      "-0.003452142425 ZIXZIZXIZ\n",
      " 0.003452142425 ZZYIIIYII\n",
      "-0.003452142425 ZIYZIZYIZ\n",
      " 0.146264992408 IIZIIIIIZ\n",
      " 0.005068351597 IIYZYIIIZ\n",
      " 0.005068351597 IIXZXIIIZ\n",
      "-0.020122896224 ZIXZIZZII\n",
      " 0.020122896224 IIXZZZIIZ\n",
      " 0.003452142425 ZZXIIIIIX\n",
      "-0.003452142425 ZIXZIZZIX\n",
      " 0.003452142425 ZZYIIIIIY\n",
      "-0.003452142425 ZIYZIZZIY\n",
      " 0.083458581545 ZIIIZIZIZ\n",
      "-0.001563930323 ZIXZXIZIZ\n",
      "-0.001563930323 ZIYZYIZIZ\n",
      " 0.114189677103 IZZZIZZIZ\n",
      " 0.008626469742 IZYIYZZIZ\n",
      " 0.008626469742 IZXIXZZIZ\n",
      "-0.038996566444 ZZXIIIIII\n",
      " 0.038996566444 IZXIZIZIZ\n",
      " 0.063323568117 IIIZZIIII\n",
      " 0.001121895797 IIIYIYIII\n",
      " 0.001121895797 IIIXIXIII\n",
      "-0.006271607950 ZZZXZIIII\n",
      " 0.006271607950 ZIZXZZZIZ\n",
      "-0.005002545304 IIIYXIYII\n",
      " 0.005002545304 IIIYYIXII\n",
      "-0.005002545304 IIIXXIXII\n",
      "-0.005002545304 IIIXYIYII\n",
      "-0.005002545304 IIIYXIIIY\n",
      " 0.005002545304 IIIYYIIIX\n",
      "-0.005002545304 IIIXXIIIX\n",
      "-0.005002545304 IIIXYIIIY\n",
      " 0.011515638682 ZIZZXZZIZ\n",
      "-0.011515638682 IIIZXZIII\n",
      "-0.000984207547 ZIZYYXZIZ\n",
      " 0.000984207547 IIIYYXIII\n",
      " 0.000984207547 ZIZXYYZIZ\n",
      "-0.000984207547 IIIXYYIII\n",
      "-0.007062539419 IZIXXZZIZ\n",
      " 0.007062539419 ZZZXXZIII\n",
      " 0.007062539419 IIIXXIIII\n",
      "-0.007062539419 ZIZXXIZIZ\n",
      " 0.061010381703 IIIZIZIII\n",
      " 0.004720726104 ZZZIZXIII\n",
      "-0.004720726104 ZIZZZXZIZ\n",
      "-0.005287400403 ZZZXIZIII\n",
      " 0.005287400403 ZIZXIIZIZ\n",
      " 0.146264992408 IIIZIIZII\n",
      " 0.005068351597 IIIYZYZII\n",
      " 0.005068351597 IIIXZXZII\n",
      "-0.020122896224 ZZZXIIZII\n",
      " 0.020122896224 ZIZXIZIIZ\n",
      " 0.003452142425 ZIZYIZYIZ\n",
      "-0.003452142425 IIIYZZYII\n",
      " 0.003452142425 ZIZXIZXIZ\n",
      "-0.003452142425 IIIXZZXII\n",
      " 0.146264992408 IIIZIIIIZ\n",
      " 0.005068351597 IIIYZYIIZ\n",
      " 0.005068351597 IIIXZXIIZ\n",
      "-0.020122896224 ZZZXIIIIZ\n",
      " 0.020122896224 ZIZXIZZII\n",
      " 0.003452142425 ZIZYIZZIY\n",
      "-0.003452142425 IIIYZZIIY\n",
      " 0.003452142425 ZIZXIZZIX\n",
      "-0.003452142425 IIIXZZIIX\n",
      " 0.114189677103 ZIZZZIZIZ\n",
      " 0.008626469742 ZIZYIYZIZ\n",
      " 0.008626469742 ZIZXIXZIZ\n",
      "-0.038996566444 IZIXZIZIZ\n",
      " 0.038996566444 IIIXZZIII\n",
      " 0.083458581545 IZIIIZZIZ\n",
      "-0.001563930323 IZIXZXZIZ\n",
      "-0.001563930323 IZIYZYZIZ\n",
      " 0.084330230457 IIIIZZIII\n",
      "-0.009033626871 ZIZIXIZIZ\n",
      " 0.009033626871 IIIIXIIII\n",
      " 0.010732385661 IIIIYXYII\n",
      "-0.010732385661 IIIIYYXII\n",
      " 0.010732385661 IIIIXXXII\n",
      " 0.010732385661 IIIIXYYII\n",
      " 0.010732385661 IIIIYXIIY\n",
      "-0.010732385661 IIIIYYIIX\n",
      " 0.010732385661 IIIIXXIIX\n",
      " 0.010732385661 IIIIXYIIY\n",
      "-0.009033626871 ZZZZIXIII\n",
      " 0.009033626871 ZIZIIXZIZ\n",
      " 0.006793524421 IZIZYYZIZ\n",
      "-0.006793524421 IIIIYYIII\n",
      "-0.006793524421 ZZZZYYIII\n",
      " 0.006793524421 ZIZIYYZIZ\n",
      " 0.130589449627 IIIIZIZII\n",
      "-0.002746468093 ZIZIXZIIZ\n",
      " 0.002746468093 IIIIXZZII\n",
      " 0.002587745598 ZZZZXIXII\n",
      "-0.002587745598 ZIZIXZXIZ\n",
      " 0.002587745598 ZZZZYIYII\n",
      "-0.002587745598 ZIZIYZYIZ\n",
      " 0.130589449627 IIIIZIIIZ\n",
      "-0.002746468093 ZIZIXZZII\n",
      " 0.002746468093 IIIIXZIIZ\n",
      " 0.002587745598 ZZZZXIIIX\n",
      "-0.002587745598 ZIZIXZZIX\n",
      " 0.002587745598 ZZZZYIIIY\n",
      "-0.002587745598 ZIZIYZZIY\n",
      " 0.055164433440 ZIZIIIZIZ\n",
      " 0.061957957861 IZIZZZZIZ\n",
      " 0.009731378415 ZZZZXIIII\n",
      "-0.009731378415 IZIZXIZIZ\n",
      " 0.130589449627 IIIIIZZII\n",
      "-0.002746468093 ZZZZZXZII\n",
      " 0.002746468093 ZIZIZXIIZ\n",
      " 0.002587745598 ZIZIZYYIZ\n",
      "-0.002587745598 IIIIIYYII\n",
      " 0.002587745598 ZIZIZXXIZ\n",
      "-0.002587745598 IIIIIXXII\n",
      " 0.130589449627 IIIIIZIIZ\n",
      "-0.002746468093 ZZZZZXIIZ\n",
      " 0.002746468093 ZIZIZXZII\n",
      " 0.002587745598 ZIZIZYZIY\n",
      "-0.002587745598 IIIIIYIIY\n",
      " 0.002587745598 ZIZIZXZIX\n",
      "-0.002587745598 IIIIIXIIX\n",
      " 0.061957957861 ZIZIZZZIZ\n",
      " 0.009731378415 IZIZIXZIZ\n",
      "-0.009731378415 IIIIIXIII\n",
      " 0.055164433440 IZIZIIZIZ\n",
      " 0.008434567887 IIIIIIYIY\n",
      " 0.008434567887 IIIIIIXIX\n",
      "-0.003329640393 IZIZIZXIZ\n",
      " 0.003329640393 IIIIIIXII\n",
      " 0.003329640393 ZZZZZZXII\n",
      "-0.003329640393 ZIZIZIXIZ\n",
      " 0.270772614652 IIIIIIZIZ\n",
      " 0.134626888109 ZIZIZIIIZ\n",
      " 0.134626888109 IZIZIZIIZ\n",
      "-0.003329640393 IZIZIZZIX\n",
      " 0.003329640393 IIIIIIIIX\n",
      " 0.003329640393 ZZZZZZIIX\n",
      "-0.003329640393 ZIZIZIZIX\n",
      " 0.134626888109 ZIZIZIZII\n",
      " 0.134626888109 IZIZIZZII\n",
      " 0.109141895865 ZZZZZZIII\n"
     ]
    }
   ],
   "source": [
    "Hami_reduced_by_qml = create_pauliwords_from_hamilton(H_tapered, 9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e9e0dca",
   "metadata": {},
   "source": [
    "## 2.2 Tapering using mytarpering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "37bb5287",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      " 1.065769394297 ZIIIIIIIIIII\n",
      " 1.065769394297 IZIIIIIIIIII\n",
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      " 0.027247318533 YZYIIIIIIIII\n",
      " 0.045157727478 YIYIIIIIIIII\n",
      " 0.027247318533 XZXIIIIIIIII\n",
      " 0.045157727478 XIXIIIIIIIII\n",
      " 0.024240011239 YZZZYIIIIIII\n",
      " 0.028997285065 YIZZYIIIIIII\n",
      " 0.024240011239 XZZZXIIIIIII\n",
      " 0.028997285065 XIZZXIIIIIII\n",
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      "-0.030963141133 XIZZZZZZZZXI\n",
      " 0.027247318533 IYZYIIIIIIII\n",
      " 0.045157727478 ZYZYIIIIIIII\n",
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      " 0.010434033303 YXXYIIIIIIII\n",
      "-0.010434033303 YYXXIIIIIIII\n",
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      "-0.003299302880 YXIXYIIIIIII\n",
      "-0.003299302880 YYIYYIIIIIII\n",
      "-0.003299302880 XXIXXIIIIIII\n",
      "-0.003299302880 XYIYXIIIIIII\n",
      " 0.006617582989 YXIXZZZZZZYI\n",
      " 0.006617582989 YYIYZZZZZZYI\n",
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      " 0.006617582989 XYIYZZZZZZXI\n",
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      " 0.028997285065 ZYZZZYIIIIII\n",
      " 0.024240011239 IXZZZXIIIIII\n",
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      " 0.003299302880 YXXZZYIIIIII\n",
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      "-0.003299302880 XXYZZYIIIIII\n",
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      "-0.004447069086 YYIIXXIIIIII\n",
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      " 0.003154170895 YXIIIXZZZZYI\n",
      " 0.003154170895 YYIIIYZZZZYI\n",
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      " 0.003154170895 XYIIIYZZZZXI\n",
      " 0.002491661002 YXIIIIXYIIII\n",
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      " 0.002491661002 YXIIIIIIXYII\n",
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      "-0.002491661002 XXIIIIIIYYII\n",
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      " 0.003985974870 ZIXZXIIIIIII\n",
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      " 0.029238340851 ZIYZZZZZZZYI\n",
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      " 0.029238340851 ZIXZZZZZZZXI\n",
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      "-0.000811186517 YZIZZZZZZZYI\n",
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      " 0.001916704642 YZYIYZZZZZYI\n",
      "-0.000953070052 YZYIXZZZZZXI\n",
      "-0.000953070052 XZXIYZZZZZYI\n",
      " 0.001916704642 XZXIXZZZZZXI\n",
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      "-0.088116509340 IIIZIIIIIIII\n",
      " 0.125385319233 ZIIZIIIIIIII\n",
      "-0.004032807702 YZYZIIIIIIII\n",
      "-0.004032807702 XZXZIIIIIIII\n",
      " 0.007052422293 YZZIYIIIIIII\n",
      " 0.007052422293 XZZIXIIIIIII\n",
      " 0.002246332574 YZZIZZZZZZYI\n",
      " 0.002246332574 XZZIZZZZZZXI\n",
      "-0.007946496516 IIIYZYIIIIII\n",
      " 0.000686671990 ZIIYZYIIIIII\n",
      "-0.007946496516 IIIXZXIIIIII\n",
      " 0.000686671990 ZIIXZXIIIIII\n",
      "-0.001873306718 YZYYZYIIIIII\n",
      "-0.001873306718 YZYXZXIIIIII\n",
      "-0.001873306718 XZXYZYIIIIII\n",
      "-0.001873306718 XZXXZXIIIIII\n",
      " 0.000243794074 YZZXXYIIIIII\n",
      "-0.000243794074 YZZYXXIIIIII\n",
      "-0.000243794074 XZZXYYIIIIII\n",
      " 0.000243794074 XZZYYXIIIIII\n",
      "-0.001681536281 YZZXIXZZZZYI\n",
      "-0.001681536281 YZZYIYZZZZYI\n",
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      " 0.000032903147 IIIYZYZIIIII\n",
      " 0.000032903147 IIIXZXZIIIII\n",
      " 0.008335376900 IIIYZZIZZZZY\n",
      " 0.008335376900 IIIXZZIZZZZX\n",
      " 0.003452142425 IIIYZZXXZZYI\n",
      "-0.003452142425 IIIYZZYXZZXI\n",
      "-0.003452142425 IIIXZZXYZZYI\n",
      " 0.003452142425 IIIXZZYYZZXI\n",
      " 0.069572816506 IIIZIIIZIIII\n",
      " 0.005035448451 IIIYZYIZIIII\n",
      " 0.005035448451 IIIXZXIZIIII\n",
      " 0.011787519324 IIIYZZZIZZZY\n",
      " 0.011787519324 IIIXZZZIZZZX\n",
      " 0.076692175902 IIIZIIIIZIII\n",
      " 0.000032903147 IIIYZYIIZIII\n",
      " 0.000032903147 IIIXZXIIZIII\n",
      " 0.008335376900 IIIYZZZZIZZY\n",
      " 0.008335376900 IIIXZZZZIZZX\n",
      " 0.003452142425 IIIYZZZZXXYI\n",
      "-0.003452142425 IIIYZZZZYXXI\n",
      "-0.003452142425 IIIXZZZZXYYI\n",
      " 0.003452142425 IIIXZZZZYYXI\n",
      " 0.069572816506 IIIZIIIIIZII\n",
      " 0.005035448451 IIIYZYIIIZII\n",
      " 0.005035448451 IIIXZXIIIZII\n",
      " 0.011787519324 IIIYZZZZZIZY\n",
      " 0.011787519324 IIIXZZZZZIZX\n",
      " 0.114189677103 IIIZIIIIIIZI\n",
      " 0.008626469742 IIIYZYIIIIZI\n",
      " 0.008626469742 IIIXZXIIIIZI\n",
      " 0.038996566444 IIIYZZZZZZIY\n",
      " 0.038996566444 IIIXZZZZZZIX\n",
      " 0.083458581545 IIIZIIIIIIIZ\n",
      " 0.001563930323 IIIYZYIIIIIZ\n",
      " 0.001563930323 IIIXZXIIIIIZ\n",
      " 0.084330230457 IIIIZZIIIIII\n",
      " 0.009033626871 IIIIYIZZZZYI\n",
      " 0.009033626871 IIIIXIZZZZXI\n",
      " 0.010732385661 IIIIYXXYIIII\n",
      "-0.010732385661 IIIIYYXXIIII\n",
      "-0.010732385661 IIIIXXYYIIII\n",
      " 0.010732385661 IIIIXYYXIIII\n",
      " 0.010732385661 IIIIYXIIXYII\n",
      "-0.010732385661 IIIIYYIIXXII\n",
      "-0.010732385661 IIIIXXIIYYII\n",
      " 0.010732385661 IIIIXYIIYXII\n",
      " 0.009033626871 IIIIZYZZZZZY\n",
      " 0.009033626871 IIIIZXZZZZZX\n",
      " 0.006793524421 IIIIYXIIIIXY\n",
      "-0.006793524421 IIIIYYIIIIXX\n",
      "-0.006793524421 IIIIXXIIIIYY\n",
      " 0.006793524421 IIIIXYIIIIYX\n",
      " 0.059928531983 IIIIZIZIIIII\n",
      " 0.002667106846 IIIIYZIZZZYI\n",
      " 0.002667106846 IIIIXZIZZZXI\n",
      " 0.070660917644 IIIIZIIZIIII\n",
      " 0.000079361247 IIIIYZZIZZYI\n",
      " 0.000079361247 IIIIXZZIZZXI\n",
      " 0.002587745598 IIIIYZYYZZZY\n",
      " 0.002587745598 IIIIYZYXZZZX\n",
      " 0.002587745598 IIIIXZXYZZZY\n",
      " 0.002587745598 IIIIXZXXZZZX\n",
      " 0.059928531983 IIIIZIIIZIII\n",
      " 0.002667106846 IIIIYZZZIZYI\n",
      " 0.002667106846 IIIIXZZZIZXI\n",
      " 0.070660917644 IIIIZIIIIZII\n",
      " 0.000079361247 IIIIYZZZZIYI\n",
      " 0.000079361247 IIIIXZZZZIXI\n",
      " 0.002587745598 IIIIYZZZYYZY\n",
      " 0.002587745598 IIIIYZZZYXZX\n",
      " 0.002587745598 IIIIXZZZXYZY\n",
      " 0.002587745598 IIIIXZZZXXZX\n",
      " 0.055164433440 IIIIZIIIIIZI\n",
      " 0.061957957861 IIIIZIIIIIIZ\n",
      "-0.009731378415 IIIIYZZZZZYZ\n",
      "-0.009731378415 IIIIXZZZZZXZ\n",
      " 0.070660917644 IIIIIZZIIIII\n",
      " 0.000079361247 IIIIIYIZZZZY\n",
      " 0.000079361247 IIIIIXIZZZZX\n",
      " 0.002587745598 IIIIIYXXZZYI\n",
      "-0.002587745598 IIIIIYYXZZXI\n",
      "-0.002587745598 IIIIIXXYZZYI\n",
      " 0.002587745598 IIIIIXYYZZXI\n",
      " 0.059928531983 IIIIIZIZIIII\n",
      " 0.002667106846 IIIIIYZIZZZY\n",
      " 0.002667106846 IIIIIXZIZZZX\n",
      " 0.070660917644 IIIIIZIIZIII\n",
      " 0.000079361247 IIIIIYZZIZZY\n",
      " 0.000079361247 IIIIIXZZIZZX\n",
      " 0.002587745598 IIIIIYZZXXYI\n",
      "-0.002587745598 IIIIIYZZYXXI\n",
      "-0.002587745598 IIIIIXZZXYYI\n",
      " 0.002587745598 IIIIIXZZYYXI\n",
      " 0.059928531983 IIIIIZIIIZII\n",
      " 0.002667106846 IIIIIYZZZIZY\n",
      " 0.002667106846 IIIIIXZZZIZX\n",
      " 0.061957957861 IIIIIZIIIIZI\n",
      "-0.009731378415 IIIIIYZZZZIY\n",
      "-0.009731378415 IIIIIXZZZZIX\n",
      " 0.055164433440 IIIIIZIIIIIZ\n",
      " 0.078236363521 IIIIIIZZIIII\n",
      " 0.004217283943 IIIIIIYXXYII\n",
      "-0.004217283943 IIIIIIYYXXII\n",
      "-0.004217283943 IIIIIIXXYYII\n",
      " 0.004217283943 IIIIIIXYYXII\n",
      " 0.003329640393 IIIIIIYXIIXY\n",
      "-0.003329640393 IIIIIIYYIIXX\n",
      "-0.003329640393 IIIIIIXXIIYY\n",
      " 0.003329640393 IIIIIIXYIIYX\n",
      " 0.065584511691 IIIIIIZIZIII\n",
      " 0.069801795635 IIIIIIZIIZII\n",
      " 0.065648623858 IIIIIIZIIIZI\n",
      " 0.068978264251 IIIIIIZIIIIZ\n",
      " 0.069801795635 IIIIIIIZZIII\n",
      " 0.065584511691 IIIIIIIZIZII\n",
      " 0.068978264251 IIIIIIIZIIZI\n",
      " 0.065648623858 IIIIIIIZIIIZ\n",
      " 0.078236363521 IIIIIIIIZZII\n",
      " 0.003329640393 IIIIIIIIYXXY\n",
      "-0.003329640393 IIIIIIIIYYXX\n",
      "-0.003329640393 IIIIIIIIXXYY\n",
      " 0.003329640393 IIIIIIIIXYYX\n",
      " 0.065648623858 IIIIIIIIZIZI\n",
      " 0.068978264251 IIIIIIIIZIIZ\n",
      " 0.068978264251 IIIIIIIIIZZI\n",
      " 0.065648623858 IIIIIIIIIZIZ\n",
      " 0.109141895865 IIIIIIIIIIZZ\n"
     ]
    }
   ],
   "source": [
    "Hami_ori = create_pauliwords_from_hamilton(H, qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "59c30a28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 1.7066140174865723\n",
      "Number of qubit after tapering = 8\n",
      "The tapered Hamiltonian is \n",
      " -3.68762286+0.00000000j IIIIIIII\n",
      "1.06576939+0.00000000j ZIIIIIII\n",
      "1.06576939+0.00000000j IZIIIIII\n",
      "0.40820127+0.00000000j ZZIIIIII\n",
      "0.02724732+0.00000000j YZYIIIII\n",
      "0.04515773+0.00000000j YIYIIIII\n",
      "0.02724732+0.00000000j XZXIIIII\n",
      "0.04515773+0.00000000j XIXIIIII\n",
      "0.02424001+0.00000000j YZZZYIII\n",
      "0.02899729+0.00000000j YIZZYIII\n",
      "0.02424001+0.00000000j XZZZXIII\n",
      "0.02899729+0.00000000j XIZZXIII\n",
      "0.02583661+0.00000000j XZIZIZZZ\n",
      "0.03096314+0.00000000j XIIZIZZZ\n",
      "-0.02583661+0.00000000j XZZZZZII\n",
      "-0.03096314+0.00000000j XIZZZZII\n",
      "0.02724732+0.00000000j IYZYIIII\n",
      "0.04515773+0.00000000j ZYZYIIII\n",
      "0.02724732+0.00000000j IXZXIIII\n",
      "0.04515773+0.00000000j ZXZXIIII\n",
      "0.01043403+0.00000000j YXXYIIII\n",
      "-0.01043403+0.00000000j YYXXIIII\n",
      "-0.01043403+0.00000000j XXYYIIII\n",
      "0.01043403+0.00000000j XYYXIIII\n",
      "-0.00329930+0.00000000j YXIXYIII\n",
      "-0.00329930+0.00000000j YYIYYIII\n",
      "-0.00329930+0.00000000j XXIXXIII\n",
      "-0.00329930+0.00000000j XYIYXIII\n",
      "-0.00661758+0.00000000j XXZXIZZZ\n",
      "-0.00661758+0.00000000j XYZYIZZZ\n",
      "0.00661758+0.00000000j XXIXZZII\n",
      "0.00661758+0.00000000j XYIYZZII\n",
      "0.02424001+0.00000000j IYZZZYII\n",
      "0.02899729+0.00000000j ZYZZZYII\n",
      "0.02424001+0.00000000j IXZZZXII\n",
      "0.02899729+0.00000000j ZXZZZXII\n",
      "0.00329930+0.00000000j YXXZZYII\n",
      "-0.00329930+0.00000000j YYXZZXII\n",
      "-0.00329930+0.00000000j XXYZZYII\n",
      "0.00329930+0.00000000j XYYZZXII\n",
      "0.00444707+0.00000000j YXIIXYII\n",
      "-0.00444707+0.00000000j YYIIXXII\n",
      "-0.00444707+0.00000000j XXIIYYII\n",
      "0.00444707+0.00000000j XYIIYXII\n",
      "-0.00315417+0.00000000j XXZIZXZZ\n",
      "-0.00315417+0.00000000j XYZIZYZZ\n",
      "0.00315417+0.00000000j XXIIIXII\n",
      "0.00315417+0.00000000j XYIIIYII\n",
      "0.00249166+0.00000000j YXIIIIYI\n",
      "-0.00249166+0.00000000j YYIIIIXI\n",
      "0.00249166+0.00000000j XXIIIIXI\n",
      "0.00249166+0.00000000j XYIIIIYI\n",
      "0.00249166+0.00000000j YXIIIIIY\n",
      "-0.00249166+0.00000000j YYIIIIIX\n",
      "0.00249166+0.00000000j XXIIIIIX\n",
      "0.00249166+0.00000000j XYIIIIIY\n",
      "0.02583661+0.00000000j ZXIIIIII\n",
      "0.03096314+0.00000000j IXIIIIII\n",
      "-0.02583661+0.00000000j ZXIZIZZZ\n",
      "-0.03096314+0.00000000j IXIZIZZZ\n",
      "-0.00661758+0.00000000j XYYIIIII\n",
      "0.00661758+0.00000000j XYYZIZZZ\n",
      "0.00661758+0.00000000j YYXIIIII\n",
      "-0.00661758+0.00000000j YYXZIZZZ\n",
      "-0.00315417+0.00000000j XYZZYIII\n",
      "0.00315417+0.00000000j XYZIYZZZ\n",
      "0.00315417+0.00000000j YYZZXIII\n",
      "-0.00315417+0.00000000j YYZIXZZZ\n",
      "0.00505253+0.00000000j YYIZIZZZ\n",
      "-0.00505253+0.00000000j YYIIIIII\n",
      "-0.00505253+0.00000000j YYZZZZII\n",
      "0.00505253+0.00000000j YYZIZIZZ\n",
      "-0.08811651+0.00000000j IIZIIIII\n",
      "0.11495129+0.00000000j ZIZIIIII\n",
      "-0.00794650+0.00000000j IIYZYIII\n",
      "0.00398597+0.00000000j ZIYZYIII\n",
      "-0.00794650+0.00000000j IIXZXIII\n",
      "0.00398597+0.00000000j ZIXZXIII\n",
      "-0.01453821+0.00000000j ZIXZIZZZ\n",
      "-0.02923834+0.00000000j IIXZIZZZ\n",
      "0.01453821+0.00000000j IIXZZZII\n",
      "0.02923834+0.00000000j ZIXZZZII\n",
      "0.00517912+0.00000000j YZIZYIII\n",
      "0.00517912+0.00000000j XZIZXIII\n",
      "0.00081119+0.00000000j XZZZIZZZ\n",
      "-0.00081119+0.00000000j XZIZZZII\n",
      "0.00286977+0.00000000j XZYIYZZZ\n",
      "0.00191670+0.00000000j XZXIXZZZ\n",
      "-0.00095307+0.00000000j YZYIXZII\n",
      "-0.00095307+0.00000000j YZYIXZZZ\n",
      "0.00191670+0.00000000j XZXIXZII\n",
      "0.00286977+0.00000000j XZYIYZII\n",
      "-0.08811651+0.00000000j IIIZIIII\n",
      "0.12538532+0.00000000j ZIIZIIII\n",
      "-0.00403281+0.00000000j YZYZIIII\n",
      "-0.00403281+0.00000000j XZXZIIII\n",
      "0.00705242+0.00000000j YZZIYIII\n",
      "0.00705242+0.00000000j XZZIXIII\n",
      "-0.00224633+0.00000000j XZIIIZZZ\n",
      "0.00224633+0.00000000j XZZIZZII\n",
      "-0.00794650+0.00000000j IIIYZYII\n",
      "0.00068667+0.00000000j ZIIYZYII\n",
      "-0.00794650+0.00000000j IIIXZXII\n",
      "0.00068667+0.00000000j ZIIXZXII\n",
      "-0.00187331+0.00000000j YZYYZYII\n",
      "-0.00187331+0.00000000j YZYXZXII\n",
      "-0.00187331+0.00000000j XZXYZYII\n",
      "-0.00187331+0.00000000j XZXXZXII\n",
      "0.00024379+0.00000000j YZZXXYII\n",
      "-0.00024379+0.00000000j YZZYXXII\n",
      "-0.00024379+0.00000000j XZZXYYII\n",
      "0.00024379+0.00000000j XZZYYXII\n",
      "0.00168154+0.00000000j XZIXZXZZ\n",
      "0.00168154+0.00000000j XZIYZYZZ\n",
      "-0.00168154+0.00000000j XZZXIXII\n",
      "-0.00168154+0.00000000j XZZYIYII\n",
      "0.00216943+0.00000000j YZZXIIYI\n",
      "-0.00216943+0.00000000j YZZYIIXI\n",
      "0.00216943+0.00000000j XZZXIIXI\n",
      "0.00216943+0.00000000j XZZYIIYI\n",
      "0.00216943+0.00000000j YZZXIIIY\n",
      "-0.00216943+0.00000000j YZZYIIIX\n",
      "0.00216943+0.00000000j XZZXIIIX\n",
      "0.00216943+0.00000000j XZZYIIIY\n",
      "-0.01453821+0.00000000j ZZZXIIII\n",
      "-0.03585592+0.00000000j IZZXIIII\n",
      "0.01453821+0.00000000j ZIZXIZZZ\n",
      "0.03585592+0.00000000j IIZXIZZZ\n",
      "-0.00305752+0.00000000j XIXXIIII\n",
      "0.00305752+0.00000000j XZXXIZZZ\n",
      "-0.00305752+0.00000000j YIYXIIII\n",
      "0.00305752+0.00000000j YZYXIZZZ\n",
      "0.00455131+0.00000000j XIIYYIII\n",
      "-0.00455131+0.00000000j XZIYYZZZ\n",
      "-0.00455131+0.00000000j YIIYXIII\n",
      "0.00455131+0.00000000j YZIYXZZZ\n",
      "0.00265547+0.00000000j YIZYIZZZ\n",
      "-0.00265547+0.00000000j YZZYIIII\n",
      "-0.00265547+0.00000000j YIIYZZII\n",
      "0.00265547+0.00000000j YZIYZIZZ\n",
      "-0.18269688+0.00000000j IIIIZIII\n",
      "0.09340913+0.00000000j ZIIIZIII\n",
      "0.01287107+0.00000000j ZIZIXZZZ\n",
      "-0.00250316+0.00000000j IIZIXZZZ\n",
      "-0.01287107+0.00000000j IIIIXZII\n",
      "0.00250316+0.00000000j ZIIIXZII\n",
      "0.00463360+0.00000000j YZYIZIII\n",
      "0.00463360+0.00000000j XZXIZIII\n",
      "0.00261047+0.00000000j XZIZZZZZ\n",
      "-0.00261047+0.00000000j XZZZIZII\n",
      "-0.18269688+0.00000000j IIIIIZII\n",
      "0.09785620+0.00000000j ZIIIIZII\n",
      "0.00438981+0.00000000j YZYIIZII\n",
      "0.00438981+0.00000000j XZXIIZII\n",
      "-0.00100143+0.00000000j YZZZYZII\n",
      "-0.00100143+0.00000000j XZZZXZII\n",
      "0.00118570+0.00000000j XZIZIIZZ\n",
      "-0.00118570+0.00000000j XZZZZIII\n",
      "0.00255379+0.00000000j YZZZZXYI\n",
      "-0.00255379+0.00000000j YZZZZYXI\n",
      "0.00255379+0.00000000j XZZZZXXI\n",
      "0.00255379+0.00000000j XZZZZYYI\n",
      "0.00255379+0.00000000j YZZZZXIY\n",
      "-0.00255379+0.00000000j YZZZZYIX\n",
      "0.00255379+0.00000000j XZZZZXIX\n",
      "0.00255379+0.00000000j XZZZZYIY\n",
      "0.01287107+0.00000000j ZZZZZXII\n",
      "-0.00565733+0.00000000j IZZZZXII\n",
      "-0.01287107+0.00000000j ZIZIZXZZ\n",
      "0.00565733+0.00000000j IIZIZXZZ\n",
      "0.00359824+0.00000000j XIXZZXII\n",
      "-0.00359824+0.00000000j XZXIZXZZ\n",
      "0.00359824+0.00000000j YIYZZXII\n",
      "-0.00359824+0.00000000j YZYIZXZZ\n",
      "-0.00142477+0.00000000j XIIIXXII\n",
      "0.00142477+0.00000000j XZIZXXZZ\n",
      "-0.00142477+0.00000000j YIIIYXII\n",
      "0.00142477+0.00000000j YZIZYXZZ\n",
      "-0.00164444+0.00000000j YIZIZYZZ\n",
      "0.00164444+0.00000000j YZZZZYII\n",
      "0.00164444+0.00000000j YIIIIYII\n",
      "-0.00164444+0.00000000j YZIZIYZZ\n",
      "-0.42674159+0.00000000j IIIIIIZI\n",
      "0.19547356+0.00000000j ZIIIIIZI\n",
      "0.00526869+0.00000000j YZYIIIZI\n",
      "0.00526869+0.00000000j XZXIIIZI\n",
      "0.00447309+0.00000000j YZZZYIZI\n",
      "0.00447309+0.00000000j XZZZXIZI\n",
      "0.00175884+0.00000000j XZIZIZIZ\n",
      "-0.00175884+0.00000000j XZZZZZZI\n",
      "0.00054488+0.00000000j XIIIIIXI\n",
      "-0.00054488+0.00000000j XZIZIZXZ\n",
      "0.00054488+0.00000000j YIIIIIYI\n",
      "-0.00054488+0.00000000j YZIZIZYZ\n",
      "-0.42674159+0.00000000j IIIIIIIZ\n",
      "0.19547356+0.00000000j ZIIIIIIZ\n",
      "0.00526869+0.00000000j YZYIIIIZ\n",
      "0.00526869+0.00000000j XZXIIIIZ\n",
      "0.00447309+0.00000000j YZZZYIIZ\n",
      "0.00447309+0.00000000j XZZZXIIZ\n",
      "0.00175884+0.00000000j XZIZIZZI\n",
      "-0.00175884+0.00000000j XZZZZZIZ\n",
      "0.00054488+0.00000000j XIIIIIIX\n",
      "-0.00054488+0.00000000j XZIZIZZX\n",
      "0.00054488+0.00000000j YIIIIIIY\n",
      "-0.00054488+0.00000000j YZIZIZZY\n",
      "-0.38874433+0.00000000j ZIZIZIZZ\n",
      "0.10115186+0.00000000j IIZIZIZZ\n",
      "0.00151386+0.00000000j XZXIZIZZ\n",
      "0.00151386+0.00000000j YZYIZIZZ\n",
      "-0.00369981+0.00000000j XZIZXIZZ\n",
      "-0.00369981+0.00000000j YZIZYIZZ\n",
      "-0.38874433+0.00000000j IZIZIZZZ\n",
      "0.10620439+0.00000000j ZZIZIZZZ\n",
      "-0.00416933+0.00000000j YIYZIZZZ\n",
      "-0.00416933+0.00000000j XIXZIZZZ\n",
      "0.00534425+0.00000000j YIZIYZZZ\n",
      "0.00534425+0.00000000j XIZIXZZZ\n",
      "-0.00362247+0.00000000j XIIIIIII\n",
      "0.00362247+0.00000000j XIZIZIZZ\n",
      "0.12538532+0.00000000j IZZIIIII\n",
      "-0.00403281+0.00000000j IYIYIIII\n",
      "-0.00403281+0.00000000j IXIXIIII\n",
      "0.00705242+0.00000000j IYIZZYII\n",
      "0.00705242+0.00000000j IXIZZXII\n",
      "-0.00224633+0.00000000j ZXZIIIII\n",
      "0.00224633+0.00000000j ZXZZIZZZ\n",
      "0.00068667+0.00000000j IZYZYIII\n",
      "0.00068667+0.00000000j IZXZXIII\n",
      "-0.00187331+0.00000000j IYXXYIII\n",
      "0.00187331+0.00000000j IYYXXIII\n",
      "0.00187331+0.00000000j IXXYYIII\n",
      "-0.00187331+0.00000000j IXYYXIII\n",
      "-0.00024379+0.00000000j IYXIXYII\n",
      "-0.00024379+0.00000000j IYYIYYII\n",
      "-0.00024379+0.00000000j IXXIXXII\n",
      "-0.00024379+0.00000000j IXYIYXII\n",
      "-0.00168154+0.00000000j ZXYZYIII\n",
      "-0.00168154+0.00000000j ZXXZXIII\n",
      "0.00168154+0.00000000j ZXYIYZZZ\n",
      "0.00168154+0.00000000j ZXXIXZZZ\n",
      "-0.00216943+0.00000000j IYXIIIYI\n",
      "0.00216943+0.00000000j IYYIIIXI\n",
      "-0.00216943+0.00000000j IXXIIIXI\n",
      "-0.00216943+0.00000000j IXYIIIYI\n",
      "-0.00216943+0.00000000j IYXIIIIY\n",
      "0.00216943+0.00000000j IYYIIIIX\n",
      "-0.00216943+0.00000000j IXXIIIIX\n",
      "-0.00216943+0.00000000j IXYIIIIY\n",
      "-0.03585592+0.00000000j ZZXZIZZZ\n",
      "0.03585592+0.00000000j IZXZZZII\n",
      "-0.00305752+0.00000000j ZYYXIZZZ\n",
      "0.00305752+0.00000000j IYYXZZII\n",
      "0.00305752+0.00000000j ZXYYIZZZ\n",
      "-0.00305752+0.00000000j IXYYZZII\n",
      "0.00455131+0.00000000j ZYYIZXZZ\n",
      "-0.00455131+0.00000000j IYYIIXII\n",
      "-0.00455131+0.00000000j ZXYIZYZZ\n",
      "0.00455131+0.00000000j IXYIIYII\n",
      "0.00265547+0.00000000j IXXZIZZZ\n",
      "-0.00265547+0.00000000j ZXXZZZII\n",
      "-0.00265547+0.00000000j IXXIIIII\n",
      "0.00265547+0.00000000j ZXXIZIZZ\n",
      "0.11495129+0.00000000j IZIZIIII\n",
      "0.00398597+0.00000000j IZIYZYII\n",
      "0.00398597+0.00000000j IZIXZXII\n",
      "-0.02923834+0.00000000j ZIZXIIII\n",
      "0.02923834+0.00000000j ZZZXIZZZ\n",
      "0.00517912+0.00000000j IYZIZYII\n",
      "0.00517912+0.00000000j IXZIZXII\n",
      "0.00081119+0.00000000j ZXIZIIII\n",
      "-0.00081119+0.00000000j ZXIIIZZZ\n",
      "0.00286977+0.00000000j ZXIYZYII\n",
      "0.00191670+0.00000000j ZXIXZXII\n",
      "-0.00095307+0.00000000j ZYIYZXZZ\n",
      "-0.00095307+0.00000000j ZYIYZXII\n",
      "0.00191670+0.00000000j ZXIXZXZZ\n",
      "0.00286977+0.00000000j ZXIYZYZZ\n",
      "0.09785620+0.00000000j IZIIZIII\n",
      "0.00438981+0.00000000j IYZYZIII\n",
      "0.00438981+0.00000000j IXZXZIII\n",
      "-0.00100143+0.00000000j IYZZIYII\n",
      "-0.00100143+0.00000000j IXZZIXII\n",
      "0.00118570+0.00000000j ZXIIZIII\n",
      "-0.00118570+0.00000000j ZXIZZZZZ\n",
      "-0.00255379+0.00000000j IYZZXIYI\n",
      "0.00255379+0.00000000j IYZZYIXI\n",
      "-0.00255379+0.00000000j IXZZXIXI\n",
      "-0.00255379+0.00000000j IXZZYIYI\n",
      "-0.00255379+0.00000000j IYZZXIIY\n",
      "0.00255379+0.00000000j IYZZYIIX\n",
      "-0.00255379+0.00000000j IXZZXIIX\n",
      "-0.00255379+0.00000000j IXZZYIIY\n",
      "-0.00565733+0.00000000j ZZZIXZZZ\n",
      "0.00565733+0.00000000j IZIIXZII\n",
      "-0.00359824+0.00000000j ZYIYXZZZ\n",
      "0.00359824+0.00000000j IYZYXZII\n",
      "-0.00359824+0.00000000j ZXIXXZZZ\n",
      "0.00359824+0.00000000j IXZXXZII\n",
      "-0.00142477+0.00000000j ZYIZYXZZ\n",
      "0.00142477+0.00000000j IYZZYXII\n",
      "0.00142477+0.00000000j ZXIZYYZZ\n",
      "-0.00142477+0.00000000j IXZZYYII\n",
      "-0.00164444+0.00000000j IXZIXZZZ\n",
      "0.00164444+0.00000000j ZXIIXZII\n",
      "0.00164444+0.00000000j IXZZXIII\n",
      "-0.00164444+0.00000000j ZXIZXIZZ\n",
      "0.09340913+0.00000000j IZIIIZII\n",
      "-0.00250316+0.00000000j ZIZZZXII\n",
      "0.00250316+0.00000000j ZZZIZXZZ\n",
      "0.00463360+0.00000000j IYZYIZII\n",
      "0.00463360+0.00000000j IXZXIZII\n",
      "0.00261047+0.00000000j ZXIIIZII\n",
      "-0.00261047+0.00000000j ZXIZIIZZ\n",
      "0.19547356+0.00000000j IZIIIIZI\n",
      "0.00526869+0.00000000j IYZYIIZI\n",
      "0.00526869+0.00000000j IXZXIIZI\n",
      "0.00447309+0.00000000j IYZZZYZI\n",
      "0.00447309+0.00000000j IXZZZXZI\n",
      "0.00175884+0.00000000j ZXIIIIZI\n",
      "-0.00175884+0.00000000j ZXIZIZIZ\n",
      "0.00054488+0.00000000j ZYIZIZYZ\n",
      "-0.00054488+0.00000000j IYZZZZYI\n",
      "0.00054488+0.00000000j ZXIZIZXZ\n",
      "-0.00054488+0.00000000j IXZZZZXI\n",
      "0.19547356+0.00000000j IZIIIIIZ\n",
      "0.00526869+0.00000000j IYZYIIIZ\n",
      "0.00526869+0.00000000j IXZXIIIZ\n",
      "0.00447309+0.00000000j IYZZZYIZ\n",
      "0.00447309+0.00000000j IXZZZXIZ\n",
      "0.00175884+0.00000000j ZXIIIIIZ\n",
      "-0.00175884+0.00000000j ZXIZIZZI\n",
      "0.00054488+0.00000000j ZYIZIZZY\n",
      "-0.00054488+0.00000000j IYZZZZIY\n",
      "0.00054488+0.00000000j ZXIZIZZX\n",
      "-0.00054488+0.00000000j IXZZZZIX\n",
      "0.10620439+0.00000000j ZZZIZIZZ\n",
      "-0.00416933+0.00000000j ZYIYZIZZ\n",
      "-0.00416933+0.00000000j ZXIXZIZZ\n",
      "0.00534425+0.00000000j ZYIZIYZZ\n",
      "0.00534425+0.00000000j ZXIZIXZZ\n",
      "-0.00362247+0.00000000j IXZIZIZZ\n",
      "0.00362247+0.00000000j IXZZZZII\n",
      "0.10115186+0.00000000j IIIZIZZZ\n",
      "0.00151386+0.00000000j IXZXIZZZ\n",
      "0.00151386+0.00000000j IYZYIZZZ\n",
      "-0.00369981+0.00000000j IXZIZXZZ\n",
      "-0.00369981+0.00000000j IYZIZYZZ\n",
      "0.13040595+0.00000000j IIZZIIII\n",
      "0.00882986+0.00000000j IIYIYIII\n",
      "0.00882986+0.00000000j IIXIXIII\n",
      "-0.04024531+0.00000000j ZIXIIZZZ\n",
      "0.04024531+0.00000000j IIXIZZII\n",
      "0.00882986+0.00000000j IIZYZYII\n",
      "0.00882986+0.00000000j IIZXZXII\n",
      "0.00231319+0.00000000j IIYXXYII\n",
      "-0.00231319+0.00000000j IIYYXXII\n",
      "-0.00231319+0.00000000j IIXXYYII\n",
      "0.00231319+0.00000000j IIXYYXII\n",
      "0.00679491+0.00000000j ZIXXZXZZ\n",
      "0.00679491+0.00000000j ZIXYZYZZ\n",
      "-0.00679491+0.00000000j IIXXIXII\n",
      "-0.00679491+0.00000000j IIXYIYII\n",
      "0.00711936+0.00000000j IIYXIIYI\n",
      "-0.00711936+0.00000000j IIYYIIXI\n",
      "0.00711936+0.00000000j IIXXIIXI\n",
      "0.00711936+0.00000000j IIXYIIYI\n",
      "0.00711936+0.00000000j IIYXIIIY\n",
      "-0.00711936+0.00000000j IIYYIIIX\n",
      "0.00711936+0.00000000j IIXXIIIX\n",
      "0.00711936+0.00000000j IIXYIIIY\n",
      "-0.04024531+0.00000000j ZZIXIIII\n",
      "0.04024531+0.00000000j ZIIXIZZZ\n",
      "0.00679491+0.00000000j ZZXYYIII\n",
      "-0.00679491+0.00000000j ZIXYYZZZ\n",
      "-0.00679491+0.00000000j ZZYYXIII\n",
      "0.00679491+0.00000000j ZIYYXZZZ\n",
      "0.03073110+0.00000000j IZYYIZZZ\n",
      "-0.03073110+0.00000000j IIYYIIII\n",
      "-0.03073110+0.00000000j ZZYYZZII\n",
      "0.03073110+0.00000000j ZIYYZIZZ\n",
      "0.06101038+0.00000000j IIZIZIII\n",
      "0.00472073+0.00000000j ZIIIXZZZ\n",
      "-0.00472073+0.00000000j IIZIXZII\n",
      "-0.00528740+0.00000000j ZIXZZZZZ\n",
      "0.00528740+0.00000000j IIXZIZII\n",
      "0.06332357+0.00000000j IIZIIZII\n",
      "0.00112190+0.00000000j IIYZYZII\n",
      "0.00112190+0.00000000j IIXZXZII\n",
      "-0.00627161+0.00000000j ZIXZIIZZ\n",
      "0.00627161+0.00000000j IIXZZIII\n",
      "0.00500255+0.00000000j IIYZZXYI\n",
      "-0.00500255+0.00000000j IIYZZYXI\n",
      "0.00500255+0.00000000j IIXZZXXI\n",
      "0.00500255+0.00000000j IIXZZYYI\n",
      "0.00500255+0.00000000j IIYZZXIY\n",
      "-0.00500255+0.00000000j IIYZZYIX\n",
      "0.00500255+0.00000000j IIXZZXIX\n",
      "0.00500255+0.00000000j IIXZZYIY\n",
      "0.01151564+0.00000000j ZZIZZXII\n",
      "-0.01151564+0.00000000j ZIIIZXZZ\n",
      "-0.00098421+0.00000000j ZZXIXXII\n",
      "0.00098421+0.00000000j ZIXZXXZZ\n",
      "-0.00098421+0.00000000j ZZYIYXII\n",
      "0.00098421+0.00000000j ZIYZYXZZ\n",
      "-0.00706254+0.00000000j IZYIZYZZ\n",
      "0.00706254+0.00000000j IIYZZYII\n",
      "0.00706254+0.00000000j ZZYIIYII\n",
      "-0.00706254+0.00000000j ZIYZIYZZ\n",
      "0.14626499+0.00000000j IIZIIIZI\n",
      "0.00506835+0.00000000j IIYZYIZI\n",
      "0.00506835+0.00000000j IIXZXIZI\n",
      "-0.02012290+0.00000000j ZIXZIZIZ\n",
      "0.02012290+0.00000000j IIXZZZZI\n",
      "0.00345214+0.00000000j ZZXIIIXI\n",
      "-0.00345214+0.00000000j ZIXZIZXZ\n",
      "0.00345214+0.00000000j ZZYIIIYI\n",
      "-0.00345214+0.00000000j ZIYZIZYZ\n",
      "0.14626499+0.00000000j IIZIIIIZ\n",
      "0.00506835+0.00000000j IIYZYIIZ\n",
      "0.00506835+0.00000000j IIXZXIIZ\n",
      "-0.02012290+0.00000000j ZIXZIZZI\n",
      "0.02012290+0.00000000j IIXZZZIZ\n",
      "0.00345214+0.00000000j ZZXIIIIX\n",
      "-0.00345214+0.00000000j ZIXZIZZX\n",
      "0.00345214+0.00000000j ZZYIIIIY\n",
      "-0.00345214+0.00000000j ZIYZIZZY\n",
      "0.08345858+0.00000000j ZIIIZIZZ\n",
      "-0.00156393+0.00000000j ZIXZXIZZ\n",
      "-0.00156393+0.00000000j ZIYZYIZZ\n",
      "0.11418968+0.00000000j IZZZIZZZ\n",
      "0.00862647+0.00000000j IZYIYZZZ\n",
      "0.00862647+0.00000000j IZXIXZZZ\n",
      "-0.03899657+0.00000000j ZZXIIIII\n",
      "0.03899657+0.00000000j IZXIZIZZ\n",
      "0.06332357+0.00000000j IIIZZIII\n",
      "0.00112190+0.00000000j IIIYIYII\n",
      "0.00112190+0.00000000j IIIXIXII\n",
      "-0.00627161+0.00000000j ZZZXZIII\n",
      "0.00627161+0.00000000j ZIZXZZZZ\n",
      "-0.00500255+0.00000000j IIIYXIYI\n",
      "0.00500255+0.00000000j IIIYYIXI\n",
      "-0.00500255+0.00000000j IIIXXIXI\n",
      "-0.00500255+0.00000000j IIIXYIYI\n",
      "-0.00500255+0.00000000j IIIYXIIY\n",
      "0.00500255+0.00000000j IIIYYIIX\n",
      "-0.00500255+0.00000000j IIIXXIIX\n",
      "-0.00500255+0.00000000j IIIXYIIY\n",
      "0.01151564+0.00000000j ZIZZXZZZ\n",
      "-0.01151564+0.00000000j IIIZXZII\n",
      "-0.00098421+0.00000000j ZIZYYXZZ\n",
      "0.00098421+0.00000000j IIIYYXII\n",
      "0.00098421+0.00000000j ZIZXYYZZ\n",
      "-0.00098421+0.00000000j IIIXYYII\n",
      "-0.00706254+0.00000000j IZIXXZZZ\n",
      "0.00706254+0.00000000j ZZZXXZII\n",
      "0.00706254+0.00000000j IIIXXIII\n",
      "-0.00706254+0.00000000j ZIZXXIZZ\n",
      "0.06101038+0.00000000j IIIZIZII\n",
      "0.00472073+0.00000000j ZZZIZXII\n",
      "-0.00472073+0.00000000j ZIZZZXZZ\n",
      "-0.00528740+0.00000000j ZZZXIZII\n",
      "0.00528740+0.00000000j ZIZXIIZZ\n",
      "0.14626499+0.00000000j IIIZIIZI\n",
      "0.00506835+0.00000000j IIIYZYZI\n",
      "0.00506835+0.00000000j IIIXZXZI\n",
      "-0.02012290+0.00000000j ZZZXIIZI\n",
      "0.02012290+0.00000000j ZIZXIZIZ\n",
      "0.00345214+0.00000000j ZIZYIZYZ\n",
      "-0.00345214+0.00000000j IIIYZZYI\n",
      "0.00345214+0.00000000j ZIZXIZXZ\n",
      "-0.00345214+0.00000000j IIIXZZXI\n",
      "0.14626499+0.00000000j IIIZIIIZ\n",
      "0.00506835+0.00000000j IIIYZYIZ\n",
      "0.00506835+0.00000000j IIIXZXIZ\n",
      "-0.02012290+0.00000000j ZZZXIIIZ\n",
      "0.02012290+0.00000000j ZIZXIZZI\n",
      "0.00345214+0.00000000j ZIZYIZZY\n",
      "-0.00345214+0.00000000j IIIYZZIY\n",
      "0.00345214+0.00000000j ZIZXIZZX\n",
      "-0.00345214+0.00000000j IIIXZZIX\n",
      "0.11418968+0.00000000j ZIZZZIZZ\n",
      "0.00862647+0.00000000j ZIZYIYZZ\n",
      "0.00862647+0.00000000j ZIZXIXZZ\n",
      "-0.03899657+0.00000000j IZIXZIZZ\n",
      "0.03899657+0.00000000j IIIXZZII\n",
      "0.08345858+0.00000000j IZIIIZZZ\n",
      "-0.00156393+0.00000000j IZIXZXZZ\n",
      "-0.00156393+0.00000000j IZIYZYZZ\n",
      "0.08433023+0.00000000j IIIIZZII\n",
      "-0.00903363+0.00000000j ZIZIXIZZ\n",
      "0.00903363+0.00000000j IIIIXIII\n",
      "0.01073239+0.00000000j IIIIYXYI\n",
      "-0.01073239+0.00000000j IIIIYYXI\n",
      "0.01073239+0.00000000j IIIIXXXI\n",
      "0.01073239+0.00000000j IIIIXYYI\n",
      "0.01073239+0.00000000j IIIIYXIY\n",
      "-0.01073239+0.00000000j IIIIYYIX\n",
      "0.01073239+0.00000000j IIIIXXIX\n",
      "0.01073239+0.00000000j IIIIXYIY\n",
      "-0.00903363+0.00000000j ZZZZIXII\n",
      "0.00903363+0.00000000j ZIZIIXZZ\n",
      "0.00679352+0.00000000j IZIZYYZZ\n",
      "-0.00679352+0.00000000j IIIIYYII\n",
      "-0.00679352+0.00000000j ZZZZYYII\n",
      "0.00679352+0.00000000j ZIZIYYZZ\n",
      "0.13058945+0.00000000j IIIIZIZI\n",
      "-0.00274647+0.00000000j ZIZIXZIZ\n",
      "0.00274647+0.00000000j IIIIXZZI\n",
      "0.00258775+0.00000000j ZZZZXIXI\n",
      "-0.00258775+0.00000000j ZIZIXZXZ\n",
      "0.00258775+0.00000000j ZZZZYIYI\n",
      "-0.00258775+0.00000000j ZIZIYZYZ\n",
      "0.13058945+0.00000000j IIIIZIIZ\n",
      "-0.00274647+0.00000000j ZIZIXZZI\n",
      "0.00274647+0.00000000j IIIIXZIZ\n",
      "0.00258775+0.00000000j ZZZZXIIX\n",
      "-0.00258775+0.00000000j ZIZIXZZX\n",
      "0.00258775+0.00000000j ZZZZYIIY\n",
      "-0.00258775+0.00000000j ZIZIYZZY\n",
      "0.05516443+0.00000000j ZIZIIIZZ\n",
      "0.06195796+0.00000000j IZIZZZZZ\n",
      "0.00973138+0.00000000j ZZZZXIII\n",
      "-0.00973138+0.00000000j IZIZXIZZ\n",
      "0.13058945+0.00000000j IIIIIZZI\n",
      "-0.00274647+0.00000000j ZZZZZXZI\n",
      "0.00274647+0.00000000j ZIZIZXIZ\n",
      "0.00258775+0.00000000j ZIZIZYYZ\n",
      "-0.00258775+0.00000000j IIIIIYYI\n",
      "0.00258775+0.00000000j ZIZIZXXZ\n",
      "-0.00258775+0.00000000j IIIIIXXI\n",
      "0.13058945+0.00000000j IIIIIZIZ\n",
      "-0.00274647+0.00000000j ZZZZZXIZ\n",
      "0.00274647+0.00000000j ZIZIZXZI\n",
      "0.00258775+0.00000000j ZIZIZYZY\n",
      "-0.00258775+0.00000000j IIIIIYIY\n",
      "0.00258775+0.00000000j ZIZIZXZX\n",
      "-0.00258775+0.00000000j IIIIIXIX\n",
      "0.06195796+0.00000000j ZIZIZZZZ\n",
      "0.00973138+0.00000000j IZIZIXZZ\n",
      "-0.00973138+0.00000000j IIIIIXII\n",
      "0.05516443+0.00000000j IZIZIIZZ\n",
      "0.00843457+0.00000000j IIIIIIYY\n",
      "0.00843457+0.00000000j IIIIIIXX\n",
      "-0.00332964+0.00000000j IZIZIZXZ\n",
      "0.00332964+0.00000000j IIIIIIXI\n",
      "0.00332964+0.00000000j ZZZZZZXI\n",
      "-0.00332964+0.00000000j ZIZIZIXZ\n",
      "0.27077261+0.00000000j IIIIIIZZ\n",
      "0.13462689+0.00000000j ZIZIZIIZ\n",
      "0.13462689+0.00000000j IZIZIZIZ\n",
      "-0.00332964+0.00000000j IZIZIZZX\n",
      "0.00332964+0.00000000j IIIIIIIX\n",
      "0.00332964+0.00000000j ZZZZZZIX\n",
      "-0.00332964+0.00000000j ZIZIZIZX\n",
      "0.13462689+0.00000000j ZIZIZIZI\n",
      "0.13462689+0.00000000j IZIZIZZI\n",
      "0.10914190+0.00000000j ZZZZZZII\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "Hami_reduced_by_tapering = tapering(Hami_ori, n_electrons)\n",
    "print(f'time cost: {time() - begin}')\n",
    "print(\"Number of qubit after tapering =\", Hami_reduced_by_tapering.num_qubits)\n",
    "print(\"The tapered Hamiltonian is \\n\", Hami_reduced_by_tapering)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4665134",
   "metadata": {},
   "source": [
    "## 2.3 compare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1caae99",
   "metadata": {},
   "source": [
    "### 2.3.1 generators and paulixops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b4d457a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1:   (1.0) [Z6 Z7], paulix_op: PauliX(wires=[7])\n",
      "generator 2:   (1.0) [Z8 Z9], paulix_op: PauliX(wires=[9])\n",
      "generator 3:   (1.0) [Z0 Z2 Z4 Z6 Z8 Z10], paulix_op: PauliX(wires=[10])\n",
      "generator 4:   (1.0) [Z1 Z3 Z5 Z6 Z8 Z11], paulix_op: PauliX(wires=[11])\n"
     ]
    }
   ],
   "source": [
    "for idx, generator in enumerate(generators_by_qml):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulixops_by_qml[idx]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b1f2e41e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1: 1.00000000 IIIIIIZZIIII, paulix_op: 1.00000000 IIIIIIIXIIII\n",
      "generator 2: 1.00000000 IIIIIIIIZZII, paulix_op: 1.00000000 IIIIIIIIIXII\n",
      "generator 3: 1.00000000 ZIZIZIZIZIZI, paulix_op: 1.00000000 IIIIIIIIIIXI\n",
      "generator 4: 1.00000000 IZIZIZZIZIIZ, paulix_op: 1.00000000 IIIIIIIIIIIX\n"
     ]
    }
   ],
   "source": [
    "generators_by_tapering_ = get_generators_from_kernel(\n",
    "    kernel_of_E(create_parity_check_matrix_E(*create_binary_matrix_G(Hami_ori)))\n",
    ")\n",
    "generators_by_tapering, paulix_ops_by_tapering = get_paulix_ops_from_generators(generators_by_tapering_)\n",
    "\n",
    "for idx, generator in enumerate(generators_by_tapering.terms):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulix_ops_by_tapering.terms[idx]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b04f509",
   "metadata": {},
   "source": [
    "### 2.3.2 optimal sectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "b0b2e30c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sectors by qml: [1, 1, 1, 1]\n",
      "sectors by tapering: [1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "print(f'sectors by qml: {paulix_sector_by_qml}')\n",
    "print(f'sectors by tapering: {optimal_sector(Hami_ori, generators_by_tapering, n_electrons)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d81f933",
   "metadata": {},
   "source": [
    "### 2.3.3 final eigen values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f65a4bd1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: Hami_reduced_by_qml\n",
      "\n",
      "min eigenvalue:  (-7.686812902258399+2.958247109450349e-30j)\n"
     ]
    }
   ],
   "source": [
    "print('Test: Hami_reduced_by_qml\\n')\n",
    "eigvals_reduced_by_qml = np.linalg.eigvals(Hami_reduced_by_qml.matrix)\n",
    "print('min eigenvalue: ', min(eigvals_reduced_by_qml))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "db6f2abb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: Hami_reduced_by_tapering\n",
      "\n",
      "min eigenvalue:  (-7.686812902258386+0j)\n"
     ]
    }
   ],
   "source": [
    "print('Test: Hami_reduced_by_tapering\\n')\n",
    "eigvals_reduced_by_tapering = np.linalg.eigvals(Hami_reduced_by_tapering.matrix)\n",
    "print('min eigenvalue: ', min(eigvals_reduced_by_tapering))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a20cf01b",
   "metadata": {},
   "source": [
    "# 3. Example: H2O"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d2660323",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://github.com/aoterodelaroza/refdata/blob/master/20_g3/lih.xyz\n",
    "symbols = [\"O\", \"H\", \"H\"]\n",
    "coordinates = np.array([0.0, 0.0, 0.118882, 0.0, 0.756653, -0.475529, 0.0, -0.756653, -0.475529])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "04b1d960",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of qubits =  14\n",
      "The Hamiltonian is \n",
      "   (-41.7155299387761) [I0]\n",
      "+ (0.5850622252195492) [Z10]\n",
      "+ (0.5850622252195492) [Z11]\n",
      "+ (0.61931339074801) [Z12]\n",
      "+ (0.6193133907480104) [Z13]\n",
      "+ (1.5317896296077471) [Z8]\n",
      "+ (1.5317896296077482) [Z9]\n",
      "+ (1.5557964873210017) [Z6]\n",
      "+ (1.5557964873210017) [Z7]\n",
      "+ (1.610860163302403) [Z4]\n",
      "+ (1.610860163302403) [Z5]\n",
      "+ (2.004283632934837) [Z2]\n",
      "+ (2.0042836329348384) [Z3]\n",
      "+ (12.684194370490733) [Z0]\n",
      "+ (12.684194370490733) [Z1]\n",
      "+ (-0.10769798653007104) [Y0 Y2]\n",
      "+ (-0.10769798653007104) [X0 X2]\n",
      "+ (-0.0017547076881392477) [Y1 Y3]\n",
      "+ (-0.0017547076881392477) [X1 X3]\n",
      "+ (0.11466433091423167) [Z10 Z12]\n",
      "+ (0.11466433091423167) [Z11 Z13]\n",
      "+ (0.1247842526916471) [Z6 Z10]\n",
      "+ (0.1247842526916471) [Z7 Z11]\n",
      "+ (0.12849290220939635) [Z10 Z11]\n",
      "+ (0.1290238247351076) [Z6 Z11]\n",
      "+ (0.1290238247351076) [Z7 Z10]\n",
      "+ (0.13065731403782913) [Z8 Z10]\n",
      "+ (0.13065731403782913) [Z9 Z11]\n",
      "+ (0.1319073137762945) [Z4 Z10]\n",
      "+ (0.1319073137762945) [Z5 Z11]\n",
      "+ (0.13268317826520623) [Z2 Z10]\n",
      "+ (0.13268317826520623) [Z3 Z11]\n",
      "+ (0.13649056313154917) [Z10 Z13]\n",
      "+ (0.13649056313154917) [Z11 Z12]\n",
      "+ (0.14201966254208623) [Z4 Z11]\n",
      "+ (0.14201966254208623) [Z5 Z10]\n",
      "+ (0.14252935041492276) [Z8 Z11]\n",
      "+ (0.14252935041492276) [Z9 Z10]\n",
      "+ (0.14256640054495978) [Z4 Z12]\n",
      "+ (0.14256640054495978) [Z5 Z13]\n",
      "+ (0.15221925917810897) [Z2 Z4]\n",
      "+ (0.15221925917810897) [Z3 Z5]\n",
      "+ (0.1535396642099675) [Z6 Z12]\n",
      "+ (0.1535396642099675) [Z7 Z13]\n",
      "+ (0.1558992547284585) [Z2 Z11]\n",
      "+ (0.1558992547284585) [Z3 Z10]\n",
      "+ (0.15590746045488063) [Z2 Z6]\n",
      "+ (0.15590746045488063) [Z3 Z7]\n",
      "+ (0.16069615808550403) [Z2 Z8]\n",
      "+ (0.16069615808550403) [Z3 Z9]\n",
      "+ (0.16243990216716953) [Z8 Z12]\n",
      "+ (0.16243990216716953) [Z9 Z13]\n",
      "+ (0.1624924024665317) [Z2 Z12]\n",
      "+ (0.1624924024665317) [Z3 Z13]\n",
      "+ (0.16703650747322088) [Z4 Z6]\n",
      "+ (0.16703650747322088) [Z5 Z7]\n",
      "+ (0.16756153000491153) [Z8 Z13]\n",
      "+ (0.16756153000491153) [Z9 Z12]\n",
      "+ (0.16986681048440655) [Z12 Z13]\n",
      "+ (0.170563533325121) [Z6 Z13]\n",
      "+ (0.170563533325121) [Z7 Z12]\n",
      "+ (0.17302242289597325) [Z4 Z8]\n",
      "+ (0.17302242289597325) [Z5 Z9]\n",
      "+ (0.17396917512754373) [Z2 Z13]\n",
      "+ (0.17396917512754373) [Z3 Z12]\n",
      "+ (0.17612902332562408) [Z4 Z13]\n",
      "+ (0.17612902332562408) [Z5 Z12]\n",
      "+ (0.17745376722567013) [Z2 Z7]\n",
      "+ (0.17745376722567013) [Z3 Z6]\n",
      "+ (0.17953531074171336) [Z4 Z7]\n",
      "+ (0.17953531074171336) [Z5 Z6]\n",
      "+ (0.17986610523076396) [Z6 Z8]\n",
      "+ (0.17986610523076396) [Z7 Z9]\n",
      "+ (0.18074775560201112) [Z0 Z10]\n",
      "+ (0.18074775560201112) [Z1 Z11]\n",
      "+ (0.18315914040026393) [Z4 Z9]\n",
      "+ (0.18315914040026393) [Z5 Z8]\n",
      "+ (0.1899351276455576) [Z0 Z11]\n",
      "+ (0.1899351276455576) [Z1 Z10]\n",
      "+ (0.1924349305398947) [Z2 Z5]\n",
      "+ (0.1924349305398947) [Z3 Z4]\n",
      "+ (0.19695255601362005) [Z4 Z5]\n",
      "+ (0.19695669883940664) [Z6 Z9]\n",
      "+ (0.19695669883940664) [Z7 Z8]\n",
      "+ (0.19755741800141086) [Z2 Z9]\n",
      "+ (0.19755741800141086) [Z3 Z8]\n",
      "+ (0.2182149658460584) [Z2 Z3]\n",
      "+ (0.2200397724026298) [Z8 Z9]\n",
      "+ (0.23508802822003658) [Z0 Z12]\n",
      "+ (0.23508802822003658) [Z1 Z13]\n",
      "+ (0.23748626761124247) [Z6 Z7]\n",
      "+ (0.24256883004516888) [Z0 Z4]\n",
      "+ (0.24256883004516888) [Z1 Z5]\n",
      "+ (0.24266982149785044) [Z0 Z13]\n",
      "+ (0.24266982149785044) [Z1 Z12]\n",
      "+ (0.24680926546332085) [Z0 Z5]\n",
      "+ (0.24680926546332085) [Z1 Z4]\n",
      "+ (0.2573652325853251) [Z0 Z2]\n",
      "+ (0.2573652325853251) [Z1 Z3]\n",
      "+ (0.26973471357551315) [Z0 Z6]\n",
      "+ (0.26973471357551315) [Z1 Z7]\n",
      "+ (0.2722191117825801) [Z0 Z8]\n",
      "+ (0.2722191117825801) [Z1 Z9]\n",
      "+ (0.2738007905256303) [Z0 Z3]\n",
      "+ (0.2738007905256303) [Z1 Z2]\n",
      "+ (0.27798007389224927) [Z0 Z7]\n",
      "+ (0.27798007389224927) [Z1 Z6]\n",
      "+ (0.2788171411300905) [Z0 Z9]\n",
      "+ (0.2788171411300905) [Z1 Z8]\n",
      "+ (1.1840639567913724) [Z0 Z1]\n",
      "+ (-0.13840506431292243) [Y1 Z2 Y3]\n",
      "+ (-0.13840506431292243) [X1 Z2 X3]\n",
      "+ (-0.1384050643129224) [Y0 Z1 Y2]\n",
      "+ (-0.1384050643129224) [X0 Z1 X2]\n",
      "+ (-0.10769798653007104) [Z0 Y1 Z2 Y3]\n",
      "+ (-0.10769798653007104) [Z0 X1 Z2 X3]\n",
      "+ (-0.04021567136178576) [Y2 Y3 X4 X5]\n",
      "+ (-0.04021567136178576) [X2 X3 Y4 Y5]\n",
      "+ (-0.0368612599159068) [Y2 Y3 X8 X9]\n",
      "+ (-0.0368612599159068) [X2 X3 Y8 Y9]\n",
      "+ (-0.033562622780664304) [Y4 Y5 X12 X13]\n",
      "+ (-0.033562622780664304) [X4 X5 Y12 Y13]\n",
      "+ (-0.023216076463252293) [Y2 Y3 X10 X11]\n",
      "+ (-0.023216076463252293) [X2 X3 Y10 Y11]\n",
      "+ (-0.02226823790292089) [Y2 Z4 Z5 Y6]\n",
      "+ (-0.02226823790292089) [X2 Z4 Z5 X6]\n",
      "+ (-0.021826232217317276) [Y10 Y11 X12 X13]\n",
      "+ (-0.021826232217317276) [X10 X11 Y12 Y13]\n",
      "+ (-0.02154630677078951) [Y2 Y3 X6 X7]\n",
      "+ (-0.02154630677078951) [X2 X3 Y6 Y7]\n",
      "+ (-0.01709059360864266) [Y6 Y7 X8 X9]\n",
      "+ (-0.01709059360864266) [X6 X7 Y8 Y9]\n",
      "+ (-0.01702386911515346) [Y6 Y7 X12 X13]\n",
      "+ (-0.01702386911515346) [X6 X7 Y12 Y13]\n",
      "+ (-0.016720217023471276) [Y3 Y4 X11 X12]\n",
      "+ (-0.016720217023471276) [X3 X4 Y11 Y12]\n",
      "+ (-0.016435557940305164) [Y0 Y1 X2 X3]\n",
      "+ (-0.016435557940305164) [X0 X1 Y2 Y3]\n",
      "+ (-0.012498803268492486) [Y4 Y5 X6 X7]\n",
      "+ (-0.012498803268492486) [X4 X5 Y6 Y7]\n",
      "+ (-0.01187203637709363) [Y8 Y9 X10 X11]\n",
      "+ (-0.01187203637709363) [X8 X9 Y10 Y11]\n",
      "+ (-0.011476772661011995) [Y2 Y3 X12 X13]\n",
      "+ (-0.011476772661011995) [X2 X3 Y12 Y13]\n",
      "+ (-0.011272904389529482) [Y0 Z1 Y2 Z8]\n",
      "+ (-0.011272904389529482) [X0 Z1 X2 Z8]\n",
      "+ (-0.011272904389529482) [Y1 Z2 Y3 Z9]\n",
      "+ (-0.011272904389529482) [X1 Z2 X3 Z9]\n",
      "+ (-0.011132845511868541) [Y0 Z1 Y2 Z6]\n",
      "+ (-0.011132845511868541) [X0 Z1 X2 Z6]\n",
      "+ (-0.011132845511868541) [Y1 Z2 Y3 Z7]\n",
      "+ (-0.011132845511868541) [X1 Z2 X3 Z7]\n",
      "+ (-0.01013671750429068) [Y4 Y5 X8 X9]\n",
      "+ (-0.01013671750429068) [X4 X5 Y8 Y9]\n",
      "+ (-0.010112348765791698) [Y4 Y5 X10 X11]\n",
      "+ (-0.010112348765791698) [X4 X5 Y10 Y11]\n",
      "+ (-0.010086815837273154) [Y2 Z3 Z5 Y6]\n",
      "+ (-0.010086815837273154) [X2 Z3 Z5 X6]\n",
      "+ (-0.010086815837273154) [Y3 Z4 Z6 Y7]\n",
      "+ (-0.010086815837273154) [X3 Z4 Z6 X7]\n",
      "+ (-0.00918737204354651) [Y0 Y1 X10 X11]\n",
      "+ (-0.00918737204354651) [X0 X1 Y10 Y11]\n",
      "+ (-0.00824536031673612) [Y0 Y1 X6 X7]\n",
      "+ (-0.00824536031673612) [X0 X1 Y6 Y7]\n",
      "+ (-0.008144301016007773) [Y0 Z1 Y2 Z4]\n",
      "+ (-0.008144301016007773) [X0 Z1 X2 Z4]\n",
      "+ (-0.008144301016007773) [Y1 Z2 Y3 Z5]\n",
      "+ (-0.008144301016007773) [X1 Z2 X3 Z5]\n",
      "+ (-0.007581793277813864) [Y0 Y1 X12 X13]\n",
      "+ (-0.007581793277813864) [X0 X1 Y12 Y13]\n",
      "+ (-0.0066058628470217476) [Y0 Z1 Y2 Z12]\n",
      "+ (-0.0066058628470217476) [X0 Z1 X2 Z12]\n",
      "+ (-0.0066058628470217476) [Y1 Z2 Y3 Z13]\n",
      "+ (-0.0066058628470217476) [X1 Z2 X3 Z13]\n",
      "+ (-0.006601884395863032) [Y3 X4 X5 Y6]\n",
      "+ (-0.006601884395863032) [X3 Y4 Y5 X6]\n",
      "+ (-0.006598029347510367) [Y0 Y1 X8 X9]\n",
      "+ (-0.006598029347510367) [X0 X1 Y8 Y9]\n",
      "+ (-0.005985081336705124) [Y0 Z1 Y2 Z7]\n",
      "+ (-0.005985081336705124) [X0 Z1 X2 Z7]\n",
      "+ (-0.005985081336705124) [Y1 Z2 Y3 Z6]\n",
      "+ (-0.005985081336705124) [X1 Z2 X3 Z6]\n",
      "+ (-0.00540905111489334) [Y7 Y8 X9 X10]\n",
      "+ (-0.00540905111489334) [X7 X8 Y9 Y10]\n",
      "+ (-0.0051216278377419835) [Y8 Y9 X12 X13]\n",
      "+ (-0.0051216278377419835) [X8 X9 Y12 Y13]\n",
      "+ (-0.004240435418151988) [Y0 Y1 X4 X5]\n",
      "+ (-0.004240435418151988) [X0 X1 Y4 Y5]\n",
      "+ (-0.004239572043460486) [Y6 Y7 X10 X11]\n",
      "+ (-0.004239572043460486) [X6 X7 Y10 Y11]\n",
      "+ (-0.0037240516097137156) [Y0 Z1 Y2 Z13]\n",
      "+ (-0.0037240516097137156) [X0 Z1 X2 Z13]\n",
      "+ (-0.0037240516097137156) [Y1 Z2 Y3 Z12]\n",
      "+ (-0.0037240516097137156) [X1 Z2 X3 Z12]\n",
      "+ (-0.0034849314414101226) [Y2 Z3 Z4 Y6]\n",
      "+ (-0.0034849314414101226) [X2 Z3 Z4 X6]\n",
      "+ (-0.0034849314414101226) [Y3 Z5 Z6 Y7]\n",
      "+ (-0.0034849314414101226) [X3 Z5 Z6 X7]\n",
      "+ (-0.0029839454751721096) [Y0 Z1 Y2 Z9]\n",
      "+ (-0.0029839454751721096) [X0 Z1 X2 Z9]\n",
      "+ (-0.0029839454751721096) [Y1 Z2 Y3 Z8]\n",
      "+ (-0.0029839454751721096) [X1 Z2 X3 Z8]\n",
      "+ (-0.002667951562967844) [Y5 Y6 X11 X12]\n",
      "+ (-0.002667951562967844) [X5 X6 Y11 Y12]\n",
      "+ (-0.0017547076881392477) [Y0 Z1 Y2 Z3]\n",
      "+ (-0.0017547076881392477) [X0 Z1 X2 Z3]\n",
      "+ (-0.0015439165209360987) [Y0 Z1 Y2 Z5]\n",
      "+ (-0.0015439165209360987) [X0 Z1 X2 Z5]\n",
      "+ (-0.0015439165209360987) [Y1 Z2 Y3 Z4]\n",
      "+ (-0.0015439165209360987) [X1 Z2 X3 Z4]\n",
      "+ (-0.0010789850798320162) [Y0 Z1 Y2 Z11]\n",
      "+ (-0.0010789850798320162) [X0 Z1 X2 Z11]\n",
      "+ (-0.0010789850798320162) [Y1 Z2 Y3 Z10]\n",
      "+ (-0.0010789850798320162) [X1 Z2 X3 Z10]\n",
      "+ (-0.0007017246291736842) [Y0 Z1 Y2 Z10]\n",
      "+ (-0.0007017246291736842) [X0 Z1 X2 Z10]\n",
      "+ (-0.0007017246291736842) [Y1 Z2 Y3 Z11]\n",
      "+ (-0.0007017246291736842) [X1 Z2 X3 Z11]\n",
      "+ (-0.0003772604506583473) [Y1 X2 X10 Y11]\n",
      "+ (-0.0003772604506583473) [Y1 Y2 Y10 Y11]\n",
      "+ (-0.0003772604506583473) [X1 X2 X10 X11]\n",
      "+ (-0.0003772604506583473) [X1 Y2 Y10 X11]\n",
      "+ (0.002667951562967844) [Y5 X6 X11 Y12]\n",
      "+ (0.002667951562967844) [X5 Y6 Y11 X12]\n",
      "+ (0.002881811237308026) [Y1 X2 X12 Y13]\n",
      "+ (0.002881811237308026) [Y1 Y2 Y12 Y13]\n",
      "+ (0.002881811237308026) [X1 X2 X12 X13]\n",
      "+ (0.002881811237308026) [X1 Y2 Y12 X13]\n",
      "+ (0.003173605106256773) [Y7 Z8 Z9 Y11]\n",
      "+ (0.003173605106256773) [X7 Z8 Z9 X11]\n",
      "+ (0.003354024465367893) [Y6 Z7 Z8 Y10]\n",
      "+ (0.003354024465367893) [X6 Z7 Z8 X10]\n",
      "+ (0.003354024465367893) [Y7 Z9 Z10 Y11]\n",
      "+ (0.003354024465367893) [X7 Z9 Z10 X11]\n",
      "+ (0.003969463373475351) [Y6 Z8 Z9 Y10]\n",
      "+ (0.003969463373475351) [X6 Z8 Z9 X10]\n",
      "+ (0.004239572043460486) [Y6 X7 X10 Y11]\n",
      "+ (0.004239572043460486) [X6 Y7 Y10 X11]\n",
      "+ (0.004240435418151988) [Y0 X1 X4 Y5]\n",
      "+ (0.004240435418151988) [X0 Y1 Y4 X5]\n",
      "+ (0.0051216278377419835) [Y8 X9 X12 Y13]\n",
      "+ (0.0051216278377419835) [X8 Y9 Y12 X13]\n",
      "+ (0.005147764175163418) [Y1 X2 X6 Y7]\n",
      "+ (0.005147764175163418) [Y1 Y2 Y6 Y7]\n",
      "+ (0.005147764175163418) [X1 X2 X6 X7]\n",
      "+ (0.005147764175163418) [X1 Y2 Y6 X7]\n",
      "+ (0.00540905111489334) [Y7 X8 X9 Y10]\n",
      "+ (0.00540905111489334) [X7 Y8 Y9 X10]\n",
      "+ (0.006598029347510367) [Y0 X1 X8 Y9]\n",
      "+ (0.006598029347510367) [X0 Y1 Y8 X9]\n",
      "+ (0.006600384495071672) [Y1 X2 X4 Y5]\n",
      "+ (0.006600384495071672) [Y1 Y2 Y4 Y5]\n",
      "+ (0.006600384495071672) [X1 X2 X4 X5]\n",
      "+ (0.006600384495071672) [X1 Y2 Y4 X5]\n",
      "+ (0.006601884395863032) [Y3 Y4 X5 X6]\n",
      "+ (0.006601884395863032) [X3 X4 Y5 Y6]\n",
      "+ (0.007581793277813864) [Y0 X1 X12 Y13]\n",
      "+ (0.007581793277813864) [X0 Y1 Y12 X13]\n",
      "+ (0.00824536031673612) [Y0 X1 X6 Y7]\n",
      "+ (0.00824536031673612) [X0 Y1 Y6 X7]\n",
      "+ (0.008288958914357374) [Y1 X2 X8 Y9]\n",
      "+ (0.008288958914357374) [Y1 Y2 Y8 Y9]\n",
      "+ (0.008288958914357374) [X1 X2 X8 X9]\n",
      "+ (0.008288958914357374) [X1 Y2 Y8 X9]\n",
      "+ (0.008763075580261232) [Y6 Z7 Z9 Y10]\n",
      "+ (0.008763075580261232) [X6 Z7 Z9 X10]\n",
      "+ (0.008763075580261232) [Y7 Z8 Z10 Y11]\n",
      "+ (0.008763075580261232) [X7 Z8 Z10 X11]\n",
      "+ (0.00918737204354651) [Y0 X1 X10 Y11]\n",
      "+ (0.00918737204354651) [X0 Y1 Y10 X11]\n",
      "+ (0.010112348765791698) [Y4 X5 X10 Y11]\n",
      "+ (0.010112348765791698) [X4 Y5 Y10 X11]\n",
      "+ (0.01013671750429068) [Y4 X5 X8 Y9]\n",
      "+ (0.01013671750429068) [X4 Y5 Y8 X9]\n",
      "+ (0.011476772661011995) [Y2 X3 X12 Y13]\n",
      "+ (0.011476772661011995) [X2 Y3 Y12 X13]\n",
      "+ (0.01187203637709363) [Y8 X9 X10 Y11]\n",
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      "+ (-0.011854651772572389) [Y0 X1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.011854651772572389) [X0 Y1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.010666985833076646) [Y0 Z1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.010666985833076646) [X0 Z1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.010666985833076646) [Y1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.010666985833076646) [X1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.006985881285674787) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 X12 X13]\n",
      "+ (-0.006985881285674787) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 Y12 Y13]\n",
      "+ (-0.006970757809070147) [Y0 Z1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.006970757809070147) [Y0 Z1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.006970757809070147) [X0 Z1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.006970757809070147) [X0 Z1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.006970757809070147) [Y1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.006970757809070147) [Y1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.006970757809070147) [X1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.006970757809070147) [X1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.005798612375201525) [Y0 Z1 Y2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.005798612375201525) [X0 Z1 X2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.005798612375201525) [Y1 Z2 Y3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.005798612375201525) [X1 Z2 X3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.005592085321336598) [Y0 X1 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.005592085321336598) [X0 Y1 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.00486837345787512) [Y0 Z1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.00486837345787512) [X0 Z1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.00486837345787512) [Y1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.00486837345787512) [X1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.003995391361439507) [Y0 Z1 Z2 Z3 Y4 Y7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.003995391361439507) [Y0 Z1 Z2 Z3 Y4 X7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.003995391361439507) [X0 Z1 Z2 Z3 X4 Y7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.003995391361439507) [X0 Z1 Z2 Z3 X4 X7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.003995391361439507) [Y1 Z2 Z3 Z4 Y5 Y6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.003995391361439507) [Y1 Z2 Z3 Z4 Y5 X6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.003995391361439507) [X1 Z2 Z3 Z4 X5 Y6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.003995391361439507) [X1 Z2 Z3 Z4 X5 X6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.0036962280240064997) [Y0 Z1 Y2 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0036962280240064997) [Y0 Z1 Y2 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0036962280240064997) [X0 Z1 X2 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0036962280240064997) [X0 Z1 X2 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0036962280240064997) [Y1 Z2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.0036962280240064997) [Y1 Z2 Y3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.0036962280240064997) [X1 Z2 X3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.0036962280240064997) [X1 Z2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.0032894817809553975) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 X12 Y13]\n",
      "+ (-0.0032894817809553975) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Y12 Y13]\n",
      "+ (-0.0032894817809553975) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 X12 X13]\n",
      "+ (-0.0032894817809553975) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Y12 X13]\n",
      "+ (-0.0026484029904838237) [Y2 Y3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0026484029904838237) [X2 X3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.002091504489226331) [Y0 Z1 Y2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.002091504489226331) [Y0 Z1 Y2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.002091504489226331) [X0 Z1 X2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.002091504489226331) [X0 Z1 X2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.002060735792436379) [Y0 Z1 Z2 Z3 Y4 X6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.002060735792436379) [X0 Z1 Z2 Z3 X4 Y6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.002060735792436379) [Y1 Z2 Z3 Z4 Y5 X7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.002060735792436379) [X1 Z2 Z3 Z4 X5 Y7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.000900443517820118) [Y0 Z1 Z2 Z3 Y4 Y6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.000900443517820118) [X0 Z1 Z2 Z3 X4 X6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.000900443517820118) [Y1 Z2 Z3 Z4 Y5 Y7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.000900443517820118) [X1 Z2 Z3 Z4 X5 X7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.00036825323672738707) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z11]\n",
      "+ (-0.00036825323672738707) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z11]\n",
      "+ (0.0009826061355412991) [Y0 Z1 Z2 Z3 Y4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0009826061355412991) [Y0 Z1 Z2 Z3 Y4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0009826061355412991) [X0 Z1 Z2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0009826061355412991) [X0 Z1 Z2 Z3 X4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0011602922746162601) [Y0 Z1 Z2 Z3 X4 X6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.0011602922746162601) [X0 Z1 Z2 Z3 Y4 Y6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.0011602922746162601) [Y1 Z2 Z3 Z4 X5 X7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.0011602922746162601) [X1 Z2 Z3 Z4 Y5 Y7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0019781119622813985) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0019781119622813985) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X7 Z8 Z9 Z10 X11]\n",
      "+ (0.0019781119622813985) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0019781119622813985) [X0 Z1 Z2 Z3 Z4 Z5 X6 X7 Z8 Z9 Z10 X11]\n",
      "+ (0.0026484029904838237) [Y2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.0026484029904838237) [X2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.00289410660445888) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z13]\n",
      "+ (0.00289410660445888) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z13]\n",
      "+ (0.00289410660445888) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Z12]\n",
      "+ (0.00289410660445888) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 Z12]\n",
      "+ (0.0030949478436193894) [Y0 Z1 Z2 Z3 Z4 X5 X7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.0030949478436193894) [Y0 Z1 Z2 Z3 Z4 Y5 Y7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.0030949478436193894) [X0 Z1 Z2 Z3 Z4 X5 X7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.0030949478436193894) [X0 Z1 Z2 Z3 Z4 Y5 Y7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.0030949478436193894) [Y1 Z2 Z3 X4 X6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.0030949478436193894) [Y1 Z2 Z3 Y4 Y6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.0030949478436193894) [X1 Z2 Z3 X4 X6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0030949478436193894) [X1 Z2 Z3 Y4 Y6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.005337955092756546) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y9 Z10 Y11]\n",
      "+ (0.005337955092756546) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 X9 Z10 X11]\n",
      "+ (0.005337955092756546) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Y9 Z10 Y11]\n",
      "+ (0.005337955092756546) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 X9 Z10 X11]\n",
      "+ (0.005592085321336598) [Y0 Y1 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.005592085321336598) [X0 X1 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.006183588385414275) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z12]\n",
      "+ (0.006183588385414275) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z12]\n",
      "+ (0.006183588385414275) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Z13]\n",
      "+ (0.006183588385414275) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 Z13]\n",
      "+ (0.006985881285674787) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 X12 Y13]\n",
      "+ (0.006985881285674787) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Y12 X13]\n",
      "+ (0.011854651772572389) [Y0 Y1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.011854651772572389) [X0 X1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.01472330102610801) [Y2 Z3 Z4 X5 X6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.01472330102610801) [X2 Z3 Z4 Y5 Y6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.07189520638731398) [Z0 Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.07189520638731398) [Z0 X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0032894817809553975) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 X12 X13]\n",
      "+ (-0.0032894817809553975) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 Y12 Y13]\n",
      "+ (-0.0021023843511950276) [Y0 Z1 Z2 Y3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0021023843511950276) [X0 Z1 Z2 X3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0019346555690031287) [Y0 Z1 Z2 Z3 Z4 X5 X6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0019346555690031287) [X0 Z1 Z2 Z3 Z4 Y5 Y6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0019346555690031287) [Y0 Z1 Z2 Z3 Z4 Y5 X6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0019346555690031287) [X0 Z1 Z2 Z3 Z4 X5 Y6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.0021023843511950276) [Y0 Z1 Z2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.0021023843511950276) [X0 Z1 Z2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0032894817809553975) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 X12 Y13]\n",
      "+ (0.0032894817809553975) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Y12 X13]\n",
      "--------------------\n",
      "Number of terms:  1090\n"
     ]
    }
   ],
   "source": [
    "# 基于JW变换构建的H2哈密顿量\n",
    "H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)\n",
    "print(\"Number of qubits = \", qubits)\n",
    "print(\"The Hamiltonian is \\n\", H)\n",
    "print(\"-\" * 20)\n",
    "print(\"Number of terms: \", len(H.ops))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3401acab",
   "metadata": {},
   "source": [
    "## 3.1 Tapering using QML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "3b119d65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 80.01912212371826\n",
      "Number of qubit after tapering = 11\n",
      "The tapered Hamiltonian is \n",
      "   ((-41.49549016637345+0j)) [I0]\n",
      "+ ((0.005121627837741981+0j)) [X8]\n",
      "+ ((0.5850622252195489+0j)) [Z10]\n",
      "+ ((0.5850622252195489+0j)) [Z11]\n",
      "+ ((1.5557964873210008+0j)) [Z6]\n",
      "+ ((1.5557964873210008+0j)) [Z7]\n",
      "+ ((1.610860163302402+0j)) [Z4]\n",
      "+ ((1.610860163302402+0j)) [Z5]\n",
      "+ ((2.004283632934836+0j)) [Z2]\n",
      "+ ((2.0042836329348375+0j)) [Z3]\n",
      "+ ((3.0635792592154942+0j)) [Z8]\n",
      "+ ((12.684194370490728+0j)) [Z0]\n",
      "+ ((12.684194370490728+0j)) [Z1]\n",
      "+ ((-0.107697986530071+0j)) [Y0 Y2]\n",
      "+ ((-0.107697986530071+0j)) [X0 X2]\n",
      "+ ((-0.03356262278066429+0j)) [Y4 Y5]\n",
      "+ ((-0.02182623221731727+0j)) [Y10 Y11]\n",
      "+ ((-0.017023869115153453+0j)) [Y6 Y7]\n",
      "+ ((-0.01147677266101199+0j)) [Y2 Y3]\n",
      "+ ((-0.010604076936661527+0j)) [X7 X10]\n",
      "+ ((-0.0075817932778138595+0j)) [Y0 Y1]\n",
      "+ ((-0.0032894817809553953+0j)) [Y0 Y11]\n",
      "+ ((-0.0017547076881392469+0j)) [Y1 Y3]\n",
      "+ ((-0.0017547076881392469+0j)) [X1 X3]\n",
      "+ ((0.0028818112373080245+0j)) [X1 X2]\n",
      "+ ((0.003173605106256771+0j)) [Y7 Y11]\n",
      "+ ((0.003173605106256771+0j)) [X7 X11]\n",
      "+ ((0.003969463373475348+0j)) [Y6 Y10]\n",
      "+ ((0.003969463373475348+0j)) [X6 X10]\n",
      "+ ((0.12478425269164704+0j)) [Z6 Z10]\n",
      "+ ((0.12478425269164704+0j)) [Z7 Z11]\n",
      "+ ((0.12849290220939627+0j)) [Z10 Z11]\n",
      "+ ((0.12902382473510754+0j)) [Z6 Z11]\n",
      "+ ((0.12902382473510754+0j)) [Z7 Z10]\n",
      "+ ((0.13190731377629447+0j)) [Z4 Z10]\n",
      "+ ((0.13190731377629447+0j)) [Z5 Z11]\n",
      "+ ((0.13268317826520618+0j)) [Z2 Z10]\n",
      "+ ((0.13268317826520618+0j)) [Z3 Z11]\n",
      "+ ((0.14201966254208617+0j)) [Z4 Z11]\n",
      "+ ((0.14201966254208617+0j)) [Z5 Z10]\n",
      "+ ((0.15221925917810888+0j)) [Z2 Z4]\n",
      "+ ((0.15221925917810888+0j)) [Z3 Z5]\n",
      "+ ((0.15589925472845842+0j)) [Z2 Z11]\n",
      "+ ((0.15589925472845842+0j)) [Z3 Z10]\n",
      "+ ((0.15590746045488055+0j)) [Z2 Z6]\n",
      "+ ((0.15590746045488055+0j)) [Z3 Z7]\n",
      "+ ((0.16703650747322077+0j)) [Z4 Z6]\n",
      "+ ((0.16703650747322077+0j)) [Z5 Z7]\n",
      "+ ((0.17745376722567002+0j)) [Z2 Z7]\n",
      "+ ((0.17745376722567002+0j)) [Z3 Z6]\n",
      "+ ((0.17953531074171328+0j)) [Z4 Z7]\n",
      "+ ((0.17953531074171328+0j)) [Z5 Z6]\n",
      "+ ((0.180747755602011+0j)) [Z0 Z10]\n",
      "+ ((0.180747755602011+0j)) [Z1 Z11]\n",
      "+ ((0.18993512764555745+0j)) [Z0 Z11]\n",
      "+ ((0.18993512764555745+0j)) [Z1 Z10]\n",
      "+ ((0.19243493053989458+0j)) [Z2 Z5]\n",
      "+ ((0.19243493053989458+0j)) [Z3 Z4]\n",
      "+ ((0.19695255601362+0j)) [Z4 Z5]\n",
      "+ ((0.21821496584605832+0j)) [Z2 Z3]\n",
      "+ ((0.23748626761124236+0j)) [Z6 Z7]\n",
      "+ ((0.24256883004516874+0j)) [Z0 Z4]\n",
      "+ ((0.24256883004516874+0j)) [Z1 Z5]\n",
      "+ ((0.24680926546332074+0j)) [Z0 Z5]\n",
      "+ ((0.24680926546332074+0j)) [Z1 Z4]\n",
      "+ ((0.257365232585325+0j)) [Z0 Z2]\n",
      "+ ((0.257365232585325+0j)) [Z1 Z3]\n",
      "+ ((0.269734713575513+0j)) [Z0 Z6]\n",
      "+ ((0.269734713575513+0j)) [Z1 Z7]\n",
      "+ ((0.27318666445275175+0j)) [Z8 Z10]\n",
      "+ ((0.27318666445275175+0j)) [Z8 Z11]\n",
      "+ ((0.2738007905256301+0j)) [Z0 Z3]\n",
      "+ ((0.2738007905256301+0j)) [Z1 Z2]\n",
      "+ ((0.2779800738922491+0j)) [Z0 Z7]\n",
      "+ ((0.2779800738922491+0j)) [Z1 Z6]\n",
      "+ ((0.35618156329623707+0j)) [Z4 Z8]\n",
      "+ ((0.35618156329623707+0j)) [Z5 Z8]\n",
      "+ ((0.3582535760869147+0j)) [Z2 Z8]\n",
      "+ ((0.3582535760869147+0j)) [Z3 Z8]\n",
      "+ ((0.37682280407017044+0j)) [Z6 Z8]\n",
      "+ ((0.37682280407017044+0j)) [Z7 Z8]\n",
      "+ ((0.5510362529126704+0j)) [Z0 Z8]\n",
      "+ ((0.5510362529126704+0j)) [Z1 Z8]\n",
      "+ ((1.1840639567913718+0j)) [Z0 Z1]\n",
      "+ ((-0.13840506431292235+0j)) [Y0 Z1 Y2]\n",
      "+ ((-0.13840506431292235+0j)) [X0 Z1 X2]\n",
      "+ ((-0.13840506431292235+0j)) [Y1 Z2 Y3]\n",
      "+ ((-0.13840506431292235+0j)) [X1 Z2 X3]\n",
      "+ ((-0.03686125991590678+0j)) [Y2 Y3 X8]\n",
      "+ ((-0.017090593608642655+0j)) [Y6 Y7 X8]\n",
      "+ ((-0.016720217023471266+0j)) [X3 Y4 Y11]\n",
      "+ ((-0.011872036377093624+0j)) [X8 Y10 Y11]\n",
      "+ ((-0.010136717504290675+0j)) [Y4 Y5 X8]\n",
      "+ ((-0.008288958914357368+0j)) [Y1 Y2 X8]\n",
      "+ ((-0.006598029347510364+0j)) [Y0 Y1 X8]\n",
      "+ ((-0.005409051114893337+0j)) [Y7 Y8 X10]\n",
      "+ ((-0.005409051114893337+0j)) [X7 Y8 Y10]\n",
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      "+ ((-0.0009703144619385066+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Y7 Y10 X11]\n",
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      "+ ((0.0019781119622813976+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z10 Y11]\n",
      "+ ((0.0019781119622813976+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X7 Z10 X11]\n",
      "+ ((0.0019781119622813976+0j)) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y7 Z10 Y11]\n",
      "+ ((0.0019781119622813976+0j)) [X0 Z1 Z2 Z3 Z4 Z5 X6 X7 Z10 X11]\n",
      "+ ((0.0028818112373080245+0j)) [Z0 X1 X2 Z3 Z4 Z5 Z6 Z7 Z10 Z11]\n",
      "+ ((0.008394629447298978+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y10]\n",
      "+ ((0.008394629447298978+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X10]\n",
      "+ ((0.008394629447298978+0j)) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z10 Y11]\n",
      "+ ((0.008394629447298978+0j)) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z10 X11]\n",
      "+ ((0.011854651772572382+0j)) [Y0 Y1 X2 Z3 Z4 Z5 Z6 Z7 Z10 X11]\n",
      "+ ((0.011854651772572382+0j)) [X0 X1 Y2 Z3 Z4 Z5 Z6 Z7 Z10 Y11]\n",
      "+ ((0.07189520638731393+0j)) [Z0 Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z10 Y11]\n",
      "+ ((0.07189520638731393+0j)) [Z0 X1 Z2 Z3 Z4 Z5 Z6 Z7 Z10 X11]\n",
      "+ ((0.1698668104844065+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z10 Z11]\n",
      "+ ((-0.005337955092756543+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Z10 Y11]\n",
      "+ ((0.005121627837741981+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Z10 Z11]\n",
      "+ ((0.005337955092756543+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Z10 X11]\n",
      "+ ((0.005337955092756543+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Z10 Y11]\n",
      "+ ((0.005337955092756543+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Z10 X11]\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "generators_by_qml = qml.symmetry_generators(H)\n",
    "paulixops_by_qml = qml.paulix_ops(generators_by_qml, qubits)\n",
    "\n",
    "n_electrons = 10\n",
    "paulix_sector_by_qml = qml.qchem.optimal_sector(H, generators_by_qml, n_electrons)\n",
    "\n",
    "H_tapered = qml.taper(H, generators_by_qml, paulixops_by_qml, paulix_sector_by_qml)\n",
    "print(f'time cost: {time() - begin}')\n",
    "\n",
    "print(\"Number of qubit after tapering =\", len(H_tapered.wires))\n",
    "print(\"The tapered Hamiltonian is \\n\", H_tapered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "99b0e3d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      " 0.155899254728 IIZIIIIIIIIZ\n",
      "-0.014206967165 IIYZZZYIIIIZ\n",
      "-0.014206967165 IIXZZZXIIIIZ\n",
      " 0.017456195751 IIYZZZZZIIYZ\n",
      " 0.017456195751 IIXZZZZZIIXZ\n",
      "-0.023151540977 ZZXIXZZZIIZX\n",
      "-0.023151540977 ZIXZXIZIZIZX\n",
      "-0.023151540977 ZZYIYZZZIIZX\n",
      "-0.023151540977 ZIYZYIZIZIZX\n",
      "-0.006985881286 IZYIZIZIZIZY\n",
      "-0.006985881286 IIYZZZZZIIZY\n",
      "-0.006985881286 ZZYIIIIIIIIY\n",
      "-0.006985881286 ZIYZIZIZZIIY\n",
      "-0.162492402467 ZIIIZIZIZIZI\n",
      "-0.005140392414 ZIXZIZXIZIZI\n",
      "-0.005140392414 ZIYZIZYIZIZI\n",
      " 0.026418894697 ZIXZIZIZZIXI\n",
      " 0.026418894697 ZIYZIZIZZIYI\n",
      "-0.173969175128 IZZZIZIZZIIZ\n",
      " 0.002648943735 IZYIZIYZZIIZ\n",
      " 0.002648943735 IZXIZIXZZIIZ\n",
      "-0.019433013411 IZYIZIZIZIYZ\n",
      "-0.019433013411 IZXIZIZIZIXZ\n",
      " 0.192434930540 IIIZZIIIIIII\n",
      "-0.003484931441 IIIYIZZYIIII\n",
      "-0.003484931441 IIIXIZZXIIII\n",
      " 0.025464432384 IIIYIZZZIIZY\n",
      " 0.025464432384 IIIXIZZZIIZX\n",
      "-0.006601884396 IIIYXXYIIIII\n",
      " 0.006601884396 IIIYYXXIIIII\n",
      " 0.006601884396 IIIXXYYIIIII\n",
      "-0.006601884396 IIIXYYXIIIII\n",
      " 0.007468806981 ZZZXYZYIIIII\n",
      " 0.007468806981 ZZZXXZXIIIII\n",
      " 0.007468806981 ZIZXYIYZZIIZ\n",
      " 0.007468806981 ZIZXXIXZZIIZ\n",
      " 0.007090645615 IIIYXXZZIIYI\n",
      "-0.007090645615 IIIYYXZZIIXI\n",
      "-0.007090645615 IIIXXYZZIIYI\n",
      " 0.007090645615 IIIXYYZZIIXI\n",
      " 0.008163577408 ZZZXYZZZIIYI\n",
      " 0.008163577408 ZZZXXZZZIIXI\n",
      " 0.008163577408 ZIZXYIZIZIYZ\n",
      " 0.008163577408 ZIZXXIZIZIXZ\n",
      "-0.016681247896 ZIZZXZIZZIIZ\n",
      "-0.016681247896 IIIZXZZZIIZZ\n",
      " 0.014723301026 ZIZYYIZXZIIZ\n",
      " 0.014723301026 IIIYYIIXIIZZ\n",
      "-0.014723301026 ZIZXYIZYZIIZ\n",
      "-0.014723301026 IIIXYIIYIIZZ\n",
      " 0.016720217023 ZIZYYIZIZIZX\n",
      " 0.016720217023 IIIYYIIIIIIX\n",
      "-0.016720217023 ZIZXYIZIZIZY\n",
      "-0.016720217023 IIIXYIIIIIIY\n",
      " 0.152219259178 IIIZIZIIIIII\n",
      " 0.019329650887 ZZZIZXIIIIII\n",
      " 0.019329650887 ZIZZZXIZZIIZ\n",
      "-0.010086815837 IIIYZIZYIIII\n",
      "-0.010086815837 IIIXZIZXIIII\n",
      " 0.032555077998 IIIYZIZZIIZY\n",
      " 0.032555077998 IIIXZIZZIIZX\n",
      "-0.007254494046 ZZZXIYZYIIII\n",
      "-0.011062261808 ZZZXIXZXIIII\n",
      " 0.003807767762 ZIZYIYZXZIIZ\n",
      "-0.003807767762 ZZZYIYZXIIII\n",
      " 0.011062261808 ZIZXIXZXZIIZ\n",
      " 0.007254494046 ZIZXIYZYZIIZ\n",
      "-0.008556639616 ZZZXIYZZIIZY\n",
      "-0.014987963570 ZZZXIXZZIIZX\n",
      " 0.006431323954 ZIZYIYZIZIZX\n",
      "-0.006431323954 ZZZYIYZZIIZX\n",
      " 0.014987963570 ZIZXIXZIZIZX\n",
      " 0.008556639616 ZIZXIYZIZIZY\n",
      " 0.177453767226 IIIZIIZIIIII\n",
      " 0.016116344065 IIIYZZIYIIII\n",
      " 0.016116344065 IIIXZZIXIIII\n",
      " 0.032705833820 IIIYZZIZIIZY\n",
      " 0.032705833820 IIIXZZIZIIZX\n",
      " 0.011601687992 IIIYZZXIYIII\n",
      "-0.011601687992 IIIYZZYIXIII\n",
      " 0.011601687992 IIIXZZXIXIII\n",
      " 0.011601687992 IIIXZZYIYIII\n",
      " 0.007930378651 IIIZIIYZIIYI\n",
      " 0.007930378651 IIIZIIXZIIXI\n",
      "-0.004194096036 IIIYZZXXIIYI\n",
      " 0.004194096036 IIIYZZYXIIXI\n",
      " 0.004194096036 IIIXZZXYIIYI\n",
      "-0.004194096036 IIIXZZYYIIXI\n",
      "-0.006300011531 IIIYZZXIIIXY\n",
      "-0.006300011531 IIIYZZYIIIYY\n",
      "-0.006300011531 IIIXZZXIIIXX\n",
      "-0.006300011531 IIIXZZYIIIYX\n",
      "-0.018531068788 ZIZYIYXZZIIZ\n",
      "-0.018531068788 IIIYZYXZIIZZ\n",
      "-0.018531068788 ZIZXIXXZZIIZ\n",
      "-0.018531068788 IIIXZXXZIIZZ\n",
      " 0.002491448679 IZIXZIXZZIIZ\n",
      " 0.002491448679 ZZZXIIXZIIZZ\n",
      " 0.002491448679 IIIXZZXIIIII\n",
      " 0.002491448679 ZIZXIZXIZIZI\n",
      " 0.155907460455 IIIZIIIZIIII\n",
      " 0.004012096409 IIIZIIIYIIZY\n",
      " 0.004012096409 IIIZIIIXIIZX\n",
      " 0.028511737784 IIIYZZZIIIZY\n",
      " 0.028511737784 IIIXZZZIIIZX\n",
      " 0.358253576087 IIIZIIIIZIII\n",
      "-0.006867210574 IIIYZZZYZIII\n",
      "-0.006867210574 IIIXZZZXZIII\n",
      " 0.064357086876 IIIYZZZZZIZY\n",
      " 0.064357086876 IIIXZZZZZIZX\n",
      "-0.017732312189 IIIYZZZZXIYI\n",
      " 0.017732312189 IIIYZZZZYIXI\n",
      " 0.017732312189 IIIXZZZZYIYI\n",
      " 0.017732312189 IIIXZZZZXIXI\n",
      " 0.155899254728 IIIZIIIIIIZI\n",
      "-0.014206967165 IIIYZZZYIIZI\n",
      "-0.014206967165 IIIXZZZXIIZI\n",
      " 0.017456195751 IIIYZZZZIIIY\n",
      " 0.017456195751 IIIXZZZZIIIX\n",
      "-0.023151540977 ZIZYIYZIZIXZ\n",
      "-0.023151540977 IIIYZYIIIIXZ\n",
      "-0.023151540977 ZIZXIXZIZIXZ\n",
      "-0.023151540977 IIIXZXIIIIXZ\n",
      "-0.006985881286 IZIXZIZIZIXZ\n",
      "-0.006985881286 ZZZXIIIIIIXZ\n",
      "-0.006985881286 IIIXZZZZIIXI\n",
      "-0.006985881286 ZIZXIZIZZIXI\n",
      " 0.132683178265 IIIZIIIIIIIZ\n",
      "-0.007906955634 IIIYZZZYIIIZ\n",
      "-0.007906955634 IIIXZZZXIIIZ\n",
      "-0.173969175128 ZIZZZIZIZIZI\n",
      " 0.002648943735 ZIZYIZIYZIZI\n",
      " 0.002648943735 ZIZXIZIXZIZI\n",
      "-0.019433013411 ZIZYIZIZZIIY\n",
      "-0.019433013411 ZIZXIZIZZIIX\n",
      "-0.162492402467 IZIIIZIZZIIZ\n",
      "-0.005140392414 IZIXZIZXZIIZ\n",
      "-0.005140392414 IZIYZIZYZIIZ\n",
      " 0.026418894697 IZIXZIZIZIZX\n",
      " 0.026418894697 IZIYZIZIZIZY\n",
      " 0.196952556014 IIIIZZIIIIII\n",
      "-0.025643603422 ZIZIXIIZZIIZ\n",
      "-0.025643603422 IIIIXIZZIIZZ\n",
      " 0.012498803268 IIIIYXXYIIII\n",
      "-0.012498803268 IIIIYYXXIIII\n",
      "-0.012498803268 IIIIXXYYIIII\n",
      " 0.012498803268 IIIIXYYXIIII\n",
      "-0.000663890475 IIIIYXIXIIYI\n",
      "-0.000663890475 IIIIYYIYIIYI\n",
      "-0.000663890475 IIIIXXIXIIXI\n",
      "-0.000663890475 IIIIXYIYIIXI\n",
      " 0.010136717504 IIIIYXIIYIII\n",
      "-0.010136717504 IIIIYYIIXIII\n",
      " 0.010136717504 IIIIXXIIXIII\n",
      " 0.010136717504 IIIIXYIIYIII\n",
      " 0.000663890475 IIIIYXXZIIZY\n",
      "-0.000663890475 IIIIYYXZIIZX\n",
      "-0.000663890475 IIIIXXYZIIZY\n",
      " 0.000663890475 IIIIXYYZIIZX\n",
      " 0.010112348766 IIIIYXIIIIXY\n",
      "-0.010112348766 IIIIYYIIIIXX\n",
      "-0.010112348766 IIIIXXIIIIYY\n",
      " 0.010112348766 IIIIXYIIIIYX\n",
      " 0.025643603422 ZZZZIXIIIIII\n",
      " 0.025643603422 ZIZIIXIZZIIZ\n",
      "-0.033562622781 IZIZYYIZZIIZ\n",
      "-0.033562622781 IIIIYYIIIIII\n",
      "-0.033562622781 ZZZZYYZZIIZZ\n",
      "-0.033562622781 ZIZIYYZIZIZI\n",
      " 0.167036507473 IIIIZIZIIIII\n",
      " 0.003610912198 IIIIZIYZIIYI\n",
      " 0.003610912198 IIIIZIXZIIXI\n",
      "-0.034909617700 ZIZIXZZZZIIZ\n",
      "-0.034909617700 IIIIXZIZIIZZ\n",
      " 0.000829438698 ZIZIXZYIZIYZ\n",
      "-0.003707903422 ZIZIXZXIZIXZ\n",
      " 0.004537342120 IIIIYZYIIIXZ\n",
      "-0.004537342120 ZIZIYZYIZIXZ\n",
      " 0.003707903422 IIIIXZXIIIXZ\n",
      "-0.000829438698 IIIIXZYIIIYZ\n",
      " 0.179535310742 IIIIZIIZIIII\n",
      "-0.045997379252 ZIZIXZIIZIIZ\n",
      "-0.045997379252 IIIIXZZIIIZZ\n",
      " 0.002947021723 IIIIZIIYIIZY\n",
      " 0.002947021723 IIIIZIIXIIZX\n",
      " 0.001838512865 ZIZIXZIXZIZX\n",
      " 0.001838512865 ZIZIXZIYZIZY\n",
      " 0.001838512865 IIIIXZZXIIIX\n",
      " 0.001838512865 IIIIXZZYIIIY\n",
      " 0.011087761553 ZZZZXIXXIIII\n",
      " 0.011087761553 ZIZIXZXXZIIZ\n",
      " 0.011087761553 ZZZZYIYXIIII\n",
      " 0.011087761553 ZIZIYZYXZIIZ\n",
      "-0.002667951563 ZZZZXIIYIIYI\n",
      "-0.002667951563 ZIZIXZIYZIYZ\n",
      " 0.002667951563 ZZZZYIIYIIXI\n",
      " 0.002667951563 ZIZIYZIYZIXZ\n",
      " 0.356181563296 IIIIZIIIZIII\n",
      "-0.066310652759 ZIZIXZIZIIIZ\n",
      "-0.066310652759 IIIIXZZZZIZZ\n",
      " 0.004968968849 ZZZZXIIIXIII\n",
      " 0.004968968849 ZIZIXZIZXIIZ\n",
      " 0.004968968849 ZZZZYIIIYIII\n",
      " 0.004968968849 ZIZIYZIZYIIZ\n",
      " 0.131907313776 IIIIZIIIIIZI\n",
      "-0.013756686288 ZIZIXZIZZIZZ\n",
      "-0.013756686288 IIIIXZZZIIIZ\n",
      " 0.142019662542 IIIIZIIIIIIZ\n",
      "-0.003296173013 ZIZIXZIZZIII\n",
      "-0.003296173013 IIIIXZZZIIZI\n",
      " 0.001869390557 ZZZZXIXZIIZX\n",
      " 0.001869390557 ZIZIXZXIZIZX\n",
      " 0.001869390557 ZZZZYIYZIIZX\n",
      " 0.001869390557 ZIZIYZYIZIZX\n",
      "-0.010460513275 ZZZZXIIIIIXX\n",
      "-0.010460513275 ZIZIXZIZZIXX\n",
      "-0.010460513275 ZZZZYIIIIIYX\n",
      "-0.010460513275 ZIZIYZIZZIYX\n",
      "-0.142566400545 ZIZIIIZIZIZI\n",
      "-0.176129023326 IZIZZZIZZIIZ\n",
      " 0.021277705504 ZZZZXIIIIIII\n",
      " 0.021277705504 IZIZXIZIZIZI\n",
      " 0.179535310742 IIIIIZZIIIII\n",
      " 0.045997379252 ZZZZZXZIIIII\n",
      " 0.045997379252 ZIZIZXZZZIIZ\n",
      " 0.002947021723 IIIIIZYZIIYI\n",
      " 0.002947021723 IIIIIZXZIIXI\n",
      " 0.001838512865 ZZZZZXYZIIYI\n",
      " 0.001838512865 ZZZZZXXZIIXI\n",
      " 0.001838512865 ZIZIZXYIZIYZ\n",
      " 0.001838512865 ZIZIZXXIZIXZ\n",
      "-0.011087761553 ZIZIZYYXZIIZ\n",
      "-0.011087761553 IIIIIYYXIIZZ\n",
      " 0.011087761553 ZIZIZXYYZIIZ\n",
      " 0.011087761553 IIIIIXYYIIZZ\n",
      " 0.002667951563 ZIZIZYYIZIZX\n",
      " 0.002667951563 IIIIIYYIIIIX\n",
      "-0.002667951563 ZIZIZXYIZIZY\n",
      "-0.002667951563 IIIIIXYIIIIY\n",
      " 0.167036507473 IIIIIZIZIIII\n",
      " 0.003610912198 IIIIIZIYIIZY\n",
      " 0.003610912198 IIIIIZIXIIZX\n",
      " 0.034909617700 ZZZZZXIZIIII\n",
      " 0.034909617700 ZIZIZXIIZIIZ\n",
      "-0.000829438698 ZZZZZXIYIIZY\n",
      " 0.003707903422 ZZZZZXIXIIZX\n",
      "-0.004537342120 ZIZIZYIYZIZX\n",
      " 0.004537342120 ZZZZZYIYIIZX\n",
      "-0.003707903422 ZIZIZXIXZIZX\n",
      " 0.000829438698 ZIZIZXIYZIZY\n",
      " 0.356181563296 IIIIIZIIZIII\n",
      " 0.066310652759 ZZZZZXIIZIII\n",
      " 0.066310652759 ZIZIZXIZIIIZ\n",
      "-0.004968968849 ZIZIZYIZYIIZ\n",
      "-0.004968968849 IIIIIYZZYIZZ\n",
      "-0.004968968849 ZIZIZXIZXIIZ\n",
      "-0.004968968849 IIIIIXZZXIZZ\n",
      " 0.142019662542 IIIIIZIIIIZI\n",
      " 0.003296173013 ZZZZZXIIIIZI\n",
      " 0.003296173013 ZIZIZXIZZIZZ\n",
      " 0.001869390557 ZIZIZYIYZIXZ\n",
      " 0.001869390557 IIIIIYZYIIXZ\n",
      " 0.001869390557 ZIZIZXIXZIXZ\n",
      " 0.001869390557 IIIIIXZXIIXZ\n",
      " 0.010460513275 ZIZIZYIZZIYX\n",
      " 0.010460513275 IIIIIYZZIIYX\n",
      "-0.010460513275 ZIZIZXIZZIYY\n",
      "-0.010460513275 IIIIIXZZIIYY\n",
      " 0.131907313776 IIIIIZIIIIIZ\n",
      " 0.013756686288 ZZZZZXIIIIIZ\n",
      " 0.013756686288 ZIZIZXIZZIII\n",
      "-0.176129023326 ZIZIZZZIZIZI\n",
      "-0.021277705504 IZIZIXZIZIZI\n",
      "-0.021277705504 IIIIIXZZIIZZ\n",
      "-0.142566400545 IZIZIIIZZIIZ\n",
      " 0.237486267611 IIIIIIZZIIII\n",
      " 0.003969463373 IIIIIIYIIIYI\n",
      " 0.003969463373 IIIIIIXIIIXI\n",
      " 0.017090593609 IIIIIIYXYIII\n",
      "-0.017090593609 IIIIIIYYXIII\n",
      " 0.017090593609 IIIIIIXXXIII\n",
      " 0.017090593609 IIIIIIXYYIII\n",
      " 0.003969463373 IIIIIIZYIIZY\n",
      " 0.003969463373 IIIIIIZXIIZX\n",
      " 0.004239572043 IIIIIIYXIIXY\n",
      "-0.004239572043 IIIIIIYYIIXX\n",
      "-0.004239572043 IIIIIIXXIIYY\n",
      " 0.004239572043 IIIIIIXYIIYX\n",
      "-0.017023869115 IZIZIZYYZIIZ\n",
      "-0.017023869115 IIIIIIYYIIII\n",
      "-0.017023869115 ZZZZZZYYIIZZ\n",
      "-0.017023869115 ZIZIZIYYZIZI\n",
      " 0.376822804070 IIIIIIZIZIII\n",
      " 0.012117100046 IIIIIIYZZIYI\n",
      " 0.012117100046 IIIIIIXZZIXI\n",
      "-0.005409051115 IIIIIIYZXIZY\n",
      " 0.005409051115 IIIIIIYZYIZX\n",
      " 0.005409051115 IIIIIIXZYIZY\n",
      " 0.005409051115 IIIIIIXZXIZX\n",
      " 0.124784252692 IIIIIIZIIIZI\n",
      " 0.129023824735 IIIIIIZIIIIZ\n",
      " 0.003173605106 IIIIIIYZIIYZ\n",
      " 0.003173605106 IIIIIIXZIIXZ\n",
      "-0.010604076937 IZIZIZYIZIZY\n",
      "-0.010604076937 IIIIIIYZIIZY\n",
      "-0.010604076937 ZZZZZZYIIIIY\n",
      "-0.010604076937 ZIZIZIYZZIIY\n",
      "-0.153539664210 ZIZIZIIIZIZI\n",
      " 0.010848088259 ZIZIZIXZZIXI\n",
      " 0.010848088259 ZIZIZIYZZIYI\n",
      "-0.170563533325 IZIZIZZZZIIZ\n",
      "-0.000244011322 IZIZIZYIZIYZ\n",
      "-0.000244011322 IZIZIZXIZIXZ\n",
      " 0.376822804070 IIIIIIIZZIII\n",
      " 0.012117100046 IIIIIIIYZIZY\n",
      " 0.012117100046 IIIIIIIXZIZX\n",
      " 0.005409051115 IIIIIIIYXIYI\n",
      "-0.005409051115 IIIIIIIYYIXI\n",
      "-0.005409051115 IIIIIIIXYIYI\n",
      "-0.005409051115 IIIIIIIXXIXI\n",
      " 0.129023824735 IIIIIIIZIIZI\n",
      " 0.003173605106 IIIIIIIYIIIY\n",
      " 0.003173605106 IIIIIIIXIIIX\n",
      "-0.010604076937 IZIZIZIXZIXZ\n",
      "-0.010604076937 ZZZZZZZXIIXZ\n",
      "-0.010604076937 IIIIIIIXIIXI\n",
      "-0.010604076937 ZIZIZIZXZIXI\n",
      " 0.124784252692 IIIIIIIZIIIZ\n",
      "-0.170563533325 ZIZIZIZZZIZI\n",
      "-0.000244011322 ZIZIZIZYZIIY\n",
      "-0.000244011322 ZIZIZIZXZIIX\n",
      "-0.153539664210 IZIZIZIIZIIZ\n",
      " 0.010848088259 IZIZIZIXZIZX\n",
      " 0.010848088259 IZIZIZIYZIZY\n",
      " 0.011872036377 IIIIIIIIYIXY\n",
      " 0.011872036377 IIIIIIIIXIXX\n",
      "-0.011872036377 IIIIIIIIXIYY\n",
      " 0.011872036377 IIIIIIIIYIYX\n",
      " 0.005121627838 IZIZIZIZXIIZ\n",
      " 0.005121627838 IIIIIIIIXIII\n",
      " 0.005121627838 ZZZZZZZZXIZZ\n",
      " 0.005121627838 ZIZIZIZIXIZI\n",
      " 0.273186664453 IIIIIIIIZIZI\n",
      " 0.273186664453 IIIIIIIIZIIZ\n",
      "-0.330001432172 ZIZIZIZIIIZI\n",
      "-0.330001432172 IZIZIZIZIIIZ\n",
      " 0.128492902209 IIIIIIIIIIZZ\n",
      "-0.021826232217 IZIZIZIZZIYY\n",
      "-0.021826232217 IIIIIIIIIIYY\n",
      "-0.021826232217 ZZZZZZZZIIYY\n",
      "-0.021826232217 ZIZIZIZIZIYY\n",
      "-0.114664330914 ZIZIZIZIZIII\n",
      "-0.136490563132 IZIZIZIZZIZZ\n",
      "-0.136490563132 ZIZIZIZIZIZZ\n",
      "-0.114664330914 IZIZIZIZZIII\n",
      " 0.169866810484 ZZZZZZZZIIZZ\n"
     ]
    }
   ],
   "source": [
    "Hami_reduced_by_qml = create_pauliwords_from_hamilton(H_tapered, 12)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d50aad7f",
   "metadata": {},
   "source": [
    "## 3.2 Tapering using mytarpering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c9482877",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-41.715529938776 IIIIIIIIIIIIII\n",
      " 12.684194370491 ZIIIIIIIIIIIII\n",
      " 12.684194370491 IZIIIIIIIIIIII\n",
      " 1.184063956791 ZZIIIIIIIIIIII\n",
      "-0.138405064313 YZYIIIIIIIIIII\n",
      "-0.107697986530 YIYIIIIIIIIIII\n",
      "-0.138405064313 XZXIIIIIIIIIII\n",
      "-0.107697986530 XIXIIIIIIIIIII\n",
      " 0.051575032412 YZZZZZYIIIIIII\n",
      " 0.046386627497 YIZZZZYIIIIIII\n",
      " 0.051575032412 XZZZZZXIIIIIII\n",
      " 0.046386627497 XIZZZZXIIIIIII\n",
      " 0.084661213761 YZZZZZZZZZYIII\n",
      " 0.071895206387 YIZZZZZZZZYIII\n",
      " 0.084661213761 XZZZZZZZZZXIII\n",
      " 0.071895206387 XIZZZZZZZZXIII\n",
      "-0.138405064313 IYZYIIIIIIIIII\n",
      "-0.107697986530 ZYZYIIIIIIIIII\n",
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      " 0.014723301026 IIIYXIIXZZZZYI\n",
      "-0.014723301026 IIIYYIIXZZZZXI\n",
      "-0.014723301026 IIIXXIIYZZZZYI\n",
      " 0.014723301026 IIIXYIIYZZZZXI\n",
      " 0.016720217023 IIIYXIIIIIIXYI\n",
      "-0.016720217023 IIIYYIIIIIIXXI\n",
      "-0.016720217023 IIIXXIIIIIIYYI\n",
      " 0.016720217023 IIIXYIIIIIIYXI\n",
      " 0.152219259178 IIIZIZIIIIIIII\n",
      " 0.019329650887 IIIZIYZZZZZZZY\n",
      " 0.019329650887 IIIZIXZZZZZZZX\n",
      "-0.010086815837 IIIYZIZYIIIIII\n",
      "-0.010086815837 IIIXZIZXIIIIII\n",
      " 0.032555077998 IIIYZIZZZZZYII\n",
      " 0.032555077998 IIIXZIZZZZZXII\n",
      " 0.007254494046 IIIYZXIXZZZZZY\n",
      " 0.011062261808 IIIYZYIYZZZZZY\n",
      " 0.003807767762 IIIYZYIXZZZZZX\n",
      " 0.003807767762 IIIXZXIYZZZZZY\n",
      " 0.011062261808 IIIXZXIXZZZZZX\n",
      " 0.007254494046 IIIXZYIYZZZZZX\n",
      " 0.008556639616 IIIYZXIIIIIXZY\n",
      " 0.014987963570 IIIYZYIIIIIYZY\n",
      " 0.006431323954 IIIYZYIIIIIXZX\n",
      " 0.006431323954 IIIXZXIIIIIYZY\n",
      " 0.014987963570 IIIXZXIIIIIXZX\n",
      " 0.008556639616 IIIXZYIIIIIYZX\n",
      " 0.177453767226 IIIZIIZIIIIIII\n",
      " 0.016116344065 IIIYZZIYIIIIII\n",
      " 0.016116344065 IIIXZZIXIIIIII\n",
      " 0.032705833820 IIIYZZIZZZZYII\n",
      " 0.032705833820 IIIXZZIZZZZXII\n",
      " 0.011601687992 IIIYZZXIXYIIII\n",
      " 0.011601687992 IIIYZZYIYYIIII\n",
      " 0.011601687992 IIIXZZXIXXIIII\n",
      " 0.011601687992 IIIXZZYIYXIIII\n",
      " 0.007930378651 IIIZIIYZZZYIII\n",
      " 0.007930378651 IIIZIIXZZZXIII\n",
      "-0.004194096036 IIIYZZXXZZYIII\n",
      " 0.004194096036 IIIYZZYXZZXIII\n",
      " 0.004194096036 IIIXZZXYZZYIII\n",
      "-0.004194096036 IIIXZZYYZZXIII\n",
      "-0.006300011531 IIIYZZXIIIXYII\n",
      "-0.006300011531 IIIYZZYIIIYYII\n",
      "-0.006300011531 IIIXZZXIIIXXII\n",
      "-0.006300011531 IIIXZZYIIIYXII\n",
      " 0.018531068788 IIIYZYYZZZZZYI\n",
      " 0.018531068788 IIIYZYXZZZZZXI\n",
      " 0.018531068788 IIIXZXYZZZZZYI\n",
      " 0.018531068788 IIIXZXXZZZZZXI\n",
      " 0.002491448679 IIIYZZXIIIIIXY\n",
      " 0.002491448679 IIIYZZYIIIIIYY\n",
      " 0.002491448679 IIIXZZXIIIIIXX\n",
      " 0.002491448679 IIIXZZYIIIIIYX\n",
      " 0.155907460455 IIIZIIIZIIIIII\n",
      " 0.004012096409 IIIZIIIYZZZYII\n",
      " 0.004012096409 IIIZIIIXZZZXII\n",
      " 0.028511737784 IIIYZZZIZZZYII\n",
      " 0.028511737784 IIIXZZZIZZZXII\n",
      " 0.197557418001 IIIZIIIIZIIIII\n",
      " 0.002367238709 IIIYZZZYZIIIII\n",
      " 0.002367238709 IIIXZZZXZIIIII\n",
      " 0.041044699532 IIIYZZZZIZZYII\n",
      " 0.041044699532 IIIXZZZZIZZXII\n",
      "-0.017732312189 IIIYZZZZXXYIII\n",
      " 0.017732312189 IIIYZZZZYXXIII\n",
      " 0.017732312189 IIIXZZZZXYYIII\n",
      "-0.017732312189 IIIXZZZZYYXIII\n",
      " 0.160696158086 IIIZIIIIIZIIII\n",
      "-0.009234449283 IIIYZZZYIZIIII\n",
      "-0.009234449283 IIIXZZZXIZIIII\n",
      " 0.023312387343 IIIYZZZZZIZYII\n",
      " 0.023312387343 IIIXZZZZZIZXII\n",
      " 0.155899254728 IIIZIIIIIIZIII\n",
      "-0.014206967165 IIIYZZZYIIZIII\n",
      "-0.014206967165 IIIXZZZXIIZIII\n",
      " 0.017456195751 IIIYZZZZZZIYII\n",
      " 0.017456195751 IIIXZZZZZZIXII\n",
      " 0.023151540977 IIIYZYIIIIYZYI\n",
      " 0.023151540977 IIIYZYIIIIXZXI\n",
      " 0.023151540977 IIIXZXIIIIYZYI\n",
      " 0.023151540977 IIIXZXIIIIXZXI\n",
      "-0.006985881286 IIIYZZZZZZXIXY\n",
      "-0.006985881286 IIIYZZZZZZYIYY\n",
      "-0.006985881286 IIIXZZZZZZXIXX\n",
      "-0.006985881286 IIIXZZZZZZYIYX\n",
      " 0.132683178265 IIIZIIIIIIIZII\n",
      "-0.007906955634 IIIYZZZYIIIZII\n",
      "-0.007906955634 IIIXZZZXIIIZII\n",
      " 0.173969175128 IIIZIIIIIIIIZI\n",
      "-0.002648943735 IIIYZZZYIIIIZI\n",
      "-0.002648943735 IIIXZZZXIIIIZI\n",
      " 0.019433013411 IIIYZZZZZZZYZI\n",
      " 0.019433013411 IIIXZZZZZZZXZI\n",
      " 0.000000000001 IIIYZZZZZZZZZY\n",
      " 0.000000000001 IIIXZZZZZZZZZX\n",
      " 0.162492402467 IIIZIIIIIIIIIZ\n",
      "-0.005140392414 IIIYZZZYIIIIIZ\n",
      "-0.005140392414 IIIXZZZXIIIIIZ\n",
      " 0.026418894697 IIIYZZZZZZZYIZ\n",
      " 0.026418894697 IIIXZZZZZZZXIZ\n",
      " 0.196952556014 IIIIZZIIIIIIII\n",
      " 0.025643603422 IIIIYIZZZZZZYI\n",
      " 0.025643603422 IIIIXIZZZZZZXI\n",
      " 0.012498803268 IIIIYXXYIIIIII\n",
      "-0.012498803268 IIIIYYXXIIIIII\n",
      "-0.012498803268 IIIIXXYYIIIIII\n",
      " 0.012498803268 IIIIXYYXIIIIII\n",
      "-0.000663890475 IIIIYXIXZZYIII\n",
      "-0.000663890475 IIIIYYIYZZYIII\n",
      "-0.000663890475 IIIIXXIXZZXIII\n",
      "-0.000663890475 IIIIXYIYZZXIII\n",
      " 0.010136717504 IIIIYXIIXYIIII\n",
      "-0.010136717504 IIIIYYIIXXIIII\n",
      "-0.010136717504 IIIIXXIIYYIIII\n",
      " 0.010136717504 IIIIXYIIYXIIII\n",
      " 0.000663890475 IIIIYXXZZZZYII\n",
      "-0.000663890475 IIIIYYXZZZZXII\n",
      "-0.000663890475 IIIIXXYZZZZYII\n",
      " 0.000663890475 IIIIXYYZZZZXII\n",
      " 0.010112348766 IIIIYXIIIIXYII\n",
      "-0.010112348766 IIIIYYIIIIXXII\n",
      "-0.010112348766 IIIIXXIIIIYYII\n",
      " 0.010112348766 IIIIXYIIIIYXII\n",
      " 0.025643603422 IIIIZYZZZZZZZY\n",
      " 0.025643603422 IIIIZXZZZZZZZX\n",
      " 0.033562622781 IIIIYXIIIIIIXY\n",
      "-0.033562622781 IIIIYYIIIIIIXX\n",
      "-0.033562622781 IIIIXXIIIIIIYY\n",
      " 0.033562622781 IIIIXYIIIIIIYX\n",
      " 0.167036507473 IIIIZIZIIIIIII\n",
      " 0.003610912198 IIIIZIYZZZYIII\n",
      " 0.003610912198 IIIIZIXZZZXIII\n",
      " 0.034909617700 IIIIYZIZZZZZYI\n",
      " 0.034909617700 IIIIXZIZZZZZXI\n",
      " 0.000829438698 IIIIYZXIIIXZYI\n",
      "-0.003707903422 IIIIYZYIIIYZYI\n",
      "-0.004537342120 IIIIYZYIIIXZXI\n",
      "-0.004537342120 IIIIXZXIIIYZYI\n",
      "-0.003707903422 IIIIXZXIIIXZXI\n",
      " 0.000829438698 IIIIXZYIIIYZXI\n",
      " 0.179535310742 IIIIZIIZIIIIII\n",
      " 0.045997379252 IIIIYZZIZZZZYI\n",
      " 0.045997379252 IIIIXZZIZZZZXI\n",
      " 0.002947021723 IIIIZIIYZZZYII\n",
      " 0.002947021723 IIIIZIIXZZZXII\n",
      "-0.001838512865 IIIIYZZXIIIXYI\n",
      "-0.001838512865 IIIIYZZYIIIYYI\n",
      "-0.001838512865 IIIIXZZXIIIXXI\n",
      "-0.001838512865 IIIIXZZYIIIYXI\n",
      "-0.011087761553 IIIIYZYYZZZZZY\n",
      "-0.011087761553 IIIIYZYXZZZZZX\n",
      "-0.011087761553 IIIIXZXYZZZZZY\n",
      "-0.011087761553 IIIIXZXXZZZZZX\n",
      " 0.002667951563 IIIIYZZXIIXZZY\n",
      "-0.002667951563 IIIIYZZYIIXZZX\n",
      "-0.002667951563 IIIIXZZXIIYZZY\n",
      " 0.002667951563 IIIIXZZYIIYZZX\n",
      " 0.173022422896 IIIIZIIIZIIIII\n",
      " 0.030670841955 IIIIYZZZIZZZYI\n",
      " 0.030670841955 IIIIXZZZIZZZXI\n",
      " 0.183159140400 IIIIZIIIIZIIII\n",
      " 0.035639810804 IIIIYZZZZIZZYI\n",
      " 0.035639810804 IIIIXZZZZIZZXI\n",
      "-0.004968968849 IIIIYZZZYYZZZY\n",
      "-0.004968968849 IIIIYZZZYXZZZX\n",
      "-0.004968968849 IIIIXZZZXYZZZY\n",
      "-0.004968968849 IIIIXZZZXXZZZX\n",
      " 0.131907313776 IIIIZIIIIIZIII\n",
      " 0.013756686288 IIIIYZZZZZIZYI\n",
      " 0.013756686288 IIIIXZZZZZIZXI\n",
      " 0.142019662542 IIIIZIIIIIIZII\n",
      " 0.003296173013 IIIIYZZZZZZIYI\n",
      " 0.003296173013 IIIIXZZZZZZIXI\n",
      "-0.001869390557 IIIIYZYIIIIYZY\n",
      "-0.001869390557 IIIIYZYIIIIXZX\n",
      "-0.001869390557 IIIIXZXIIIIYZY\n",
      "-0.001869390557 IIIIXZXIIIIXZX\n",
      " 0.010460513275 IIIIYZZZZZYYZY\n",
      " 0.010460513275 IIIIYZZZZZYXZX\n",
      " 0.010460513275 IIIIXZZZZZXYZY\n",
      " 0.010460513275 IIIIXZZZZZXXZX\n",
      " 0.142566400545 IIIIZIIIIIIIZI\n",
      " 0.176129023326 IIIIZIIIIIIIIZ\n",
      " 0.021277705504 IIIIYZZZZZZZYZ\n",
      " 0.021277705504 IIIIXZZZZZZZXZ\n",
      " 0.179535310742 IIIIIZZIIIIIII\n",
      " 0.045997379252 IIIIIYIZZZZZZY\n",
      " 0.045997379252 IIIIIXIZZZZZZX\n",
      " 0.002947021723 IIIIIZYZZZYIII\n",
      " 0.002947021723 IIIIIZXZZZXIII\n",
      "-0.001838512865 IIIIIYXIIIXZZY\n",
      "-0.001838512865 IIIIIYYIIIYZZY\n",
      "-0.001838512865 IIIIIXXIIIXZZX\n",
      "-0.001838512865 IIIIIXYIIIYZZX\n",
      "-0.011087761553 IIIIIYXXZZZZYI\n",
      " 0.011087761553 IIIIIYYXZZZZXI\n",
      " 0.011087761553 IIIIIXXYZZZZYI\n",
      "-0.011087761553 IIIIIXYYZZZZXI\n",
      " 0.002667951563 IIIIIYXIIIIXYI\n",
      "-0.002667951563 IIIIIYYIIIIXXI\n",
      "-0.002667951563 IIIIIXXIIIIYYI\n",
      " 0.002667951563 IIIIIXYIIIIYXI\n",
      " 0.167036507473 IIIIIZIZIIIIII\n",
      " 0.003610912198 IIIIIZIYZZZYII\n",
      " 0.003610912198 IIIIIZIXZZZXII\n",
      " 0.034909617700 IIIIIYZIZZZZZY\n",
      " 0.034909617700 IIIIIXZIZZZZZX\n",
      " 0.000829438698 IIIIIYZXIIIXZY\n",
      "-0.003707903422 IIIIIYZYIIIYZY\n",
      "-0.004537342120 IIIIIYZYIIIXZX\n",
      "-0.004537342120 IIIIIXZXIIIYZY\n",
      "-0.003707903422 IIIIIXZXIIIXZX\n",
      " 0.000829438698 IIIIIXZYIIIYZX\n",
      " 0.183159140400 IIIIIZIIZIIIII\n",
      " 0.035639810804 IIIIIYZZIZZZZY\n",
      " 0.035639810804 IIIIIXZZIZZZZX\n",
      "-0.004968968849 IIIIIYZZXXZZYI\n",
      " 0.004968968849 IIIIIYZZYXZZXI\n",
      " 0.004968968849 IIIIIXZZXYZZYI\n",
      "-0.004968968849 IIIIIXZZYYZZXI\n",
      " 0.173022422896 IIIIIZIIIZIIII\n",
      " 0.030670841955 IIIIIYZZZIZZZY\n",
      " 0.030670841955 IIIIIXZZZIZZZX\n",
      " 0.142019662542 IIIIIZIIIIZIII\n",
      " 0.003296173013 IIIIIYZZZZIZZY\n",
      " 0.003296173013 IIIIIXZZZZIZZX\n",
      "-0.001869390557 IIIIIYZYIIYZYI\n",
      "-0.001869390557 IIIIIYZYIIXZXI\n",
      "-0.001869390557 IIIIIXZXIIYZYI\n",
      "-0.001869390557 IIIIIXZXIIXZXI\n",
      " 0.010460513275 IIIIIYZZZZXXYI\n",
      "-0.010460513275 IIIIIYZZZZYXXI\n",
      "-0.010460513275 IIIIIXZZZZXYYI\n",
      " 0.010460513275 IIIIIXZZZZYYXI\n",
      " 0.131907313776 IIIIIZIIIIIZII\n",
      " 0.013756686288 IIIIIYZZZZZIZY\n",
      " 0.013756686288 IIIIIXZZZZZIZX\n",
      " 0.176129023326 IIIIIZIIIIIIZI\n",
      " 0.021277705504 IIIIIYZZZZZZIY\n",
      " 0.021277705504 IIIIIXZZZZZZIX\n",
      " 0.142566400545 IIIIIZIIIIIIIZ\n",
      " 0.237486267611 IIIIIIZZIIIIII\n",
      " 0.003969463373 IIIIIIYIZZYIII\n",
      " 0.003969463373 IIIIIIXIZZXIII\n",
      " 0.017090593609 IIIIIIYXXYIIII\n",
      "-0.017090593609 IIIIIIYYXXIIII\n",
      "-0.017090593609 IIIIIIXXYYIIII\n",
      " 0.017090593609 IIIIIIXYYXIIII\n",
      " 0.003969463373 IIIIIIZYZZZYII\n",
      " 0.003969463373 IIIIIIZXZZZXII\n",
      " 0.004239572043 IIIIIIYXIIXYII\n",
      "-0.004239572043 IIIIIIYYIIXXII\n",
      "-0.004239572043 IIIIIIXXIIYYII\n",
      " 0.004239572043 IIIIIIXYIIYXII\n",
      " 0.017023869115 IIIIIIYXIIIIXY\n",
      "-0.017023869115 IIIIIIYYIIIIXX\n",
      "-0.017023869115 IIIIIIXXIIIIYY\n",
      " 0.017023869115 IIIIIIXYIIIIYX\n",
      " 0.179866105231 IIIIIIZIZIIIII\n",
      " 0.008763075580 IIIIIIYZIZYIII\n",
      " 0.008763075580 IIIIIIXZIZXIII\n",
      " 0.196956698839 IIIIIIZIIZIIII\n",
      " 0.003354024465 IIIIIIYZZIYIII\n",
      " 0.003354024465 IIIIIIXZZIXIII\n",
      " 0.005409051115 IIIIIIYZYYZYII\n",
      " 0.005409051115 IIIIIIYZYXZXII\n",
      " 0.005409051115 IIIIIIXZXYZYII\n",
      " 0.005409051115 IIIIIIXZXXZXII\n",
      " 0.124784252692 IIIIIIZIIIZIII\n",
      " 0.129023824735 IIIIIIZIIIIZII\n",
      " 0.003173605106 IIIIIIYZZZYZII\n",
      " 0.003173605106 IIIIIIXZZZXZII\n",
      " 0.010604076937 IIIIIIYZZZZXXY\n",
      "-0.010604076937 IIIIIIYZZZZYXX\n",
      "-0.010604076937 IIIIIIXZZZZXYY\n",
      " 0.010604076937 IIIIIIXZZZZYYX\n",
      " 0.153539664210 IIIIIIZIIIIIZI\n",
      " 0.010848088259 IIIIIIYZZZYIZI\n",
      " 0.010848088259 IIIIIIXZZZXIZI\n",
      " 0.170563533325 IIIIIIZIIIIIIZ\n",
      " 0.000244011322 IIIIIIYZZZYIIZ\n",
      " 0.000244011322 IIIIIIXZZZXIIZ\n",
      " 0.196956698839 IIIIIIIZZIIIII\n",
      " 0.003354024465 IIIIIIIYIZZYII\n",
      " 0.003354024465 IIIIIIIXIZZXII\n",
      " 0.005409051115 IIIIIIIYXXYIII\n",
      "-0.005409051115 IIIIIIIYYXXIII\n",
      "-0.005409051115 IIIIIIIXXYYIII\n",
      " 0.005409051115 IIIIIIIXYYXIII\n",
      " 0.179866105231 IIIIIIIZIZIIII\n",
      " 0.008763075580 IIIIIIIYZIZYII\n",
      " 0.008763075580 IIIIIIIXZIZXII\n",
      " 0.129023824735 IIIIIIIZIIZIII\n",
      " 0.003173605106 IIIIIIIYZZIYII\n",
      " 0.003173605106 IIIIIIIXZZIXII\n",
      "-0.010604076937 IIIIIIIYZZXIXY\n",
      "-0.010604076937 IIIIIIIYZZYIYY\n",
      "-0.010604076937 IIIIIIIXZZXIXX\n",
      "-0.010604076937 IIIIIIIXZZYIYX\n",
      " 0.124784252692 IIIIIIIZIIIZII\n",
      " 0.170563533325 IIIIIIIZIIIIZI\n",
      " 0.000244011322 IIIIIIIYZZZYZI\n",
      " 0.000244011322 IIIIIIIXZZZXZI\n",
      " 0.153539664210 IIIIIIIZIIIIIZ\n",
      " 0.010848088259 IIIIIIIYZZZYIZ\n",
      " 0.010848088259 IIIIIIIXZZZXIZ\n",
      " 0.220039772403 IIIIIIIIZZIIII\n",
      " 0.011872036377 IIIIIIIIYXXYII\n",
      "-0.011872036377 IIIIIIIIYYXXII\n",
      "-0.011872036377 IIIIIIIIXXYYII\n",
      " 0.011872036377 IIIIIIIIXYYXII\n",
      " 0.005121627838 IIIIIIIIYXIIXY\n",
      "-0.005121627838 IIIIIIIIYYIIXX\n",
      "-0.005121627838 IIIIIIIIXXIIYY\n",
      " 0.005121627838 IIIIIIIIXYIIYX\n",
      " 0.130657314038 IIIIIIIIZIZIII\n",
      " 0.142529350415 IIIIIIIIZIIZII\n",
      " 0.162439902167 IIIIIIIIZIIIZI\n",
      " 0.167561530005 IIIIIIIIZIIIIZ\n",
      " 0.142529350415 IIIIIIIIIZZIII\n",
      " 0.130657314038 IIIIIIIIIZIZII\n",
      " 0.167561530005 IIIIIIIIIZIIZI\n",
      " 0.162439902167 IIIIIIIIIZIIIZ\n",
      " 0.128492902209 IIIIIIIIIIZZII\n",
      " 0.021826232217 IIIIIIIIIIYXXY\n",
      "-0.021826232217 IIIIIIIIIIYYXX\n",
      "-0.021826232217 IIIIIIIIIIXXYY\n",
      " 0.021826232217 IIIIIIIIIIXYYX\n",
      " 0.114664330914 IIIIIIIIIIZIZI\n",
      " 0.136490563132 IIIIIIIIIIZIIZ\n",
      " 0.136490563132 IIIIIIIIIIIZZI\n",
      " 0.114664330914 IIIIIIIIIIIZIZ\n",
      " 0.169866810484 IIIIIIIIIIIIZZ\n"
     ]
    }
   ],
   "source": [
    "Hami_ori = create_pauliwords_from_hamilton(H, qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "fc25c2eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 3.968219518661499\n",
      "Number of qubit after tapering = 11\n",
      "The tapered Hamiltonian is \n",
      " -41.49549017+0.00000000j IIIIIIIIIII\n",
      "12.68419437+0.00000000j ZIIIIIIIIII\n",
      "12.68419437+0.00000000j IZIIIIIIIII\n",
      "1.18406396+0.00000000j ZZIIIIIIIII\n",
      "-0.13840506+0.00000000j YZYIIIIIIII\n",
      "-0.10769799+0.00000000j YIYIIIIIIII\n",
      "-0.13840506+0.00000000j XZXIIIIIIII\n",
      "-0.10769799+0.00000000j XIXIIIIIIII\n",
      "0.05157503+0.00000000j YZZZZZYIIII\n",
      "0.04638663+0.00000000j YIZZZZYIIII\n",
      "0.05157503+0.00000000j XZZZZZXIIII\n",
      "0.04638663+0.00000000j XIZZZZXIIII\n",
      "0.08466121+0.00000000j YZZZZZZZIYI\n",
      "0.07189521+0.00000000j YIZZZZZZIYI\n",
      "0.08466121+0.00000000j XZZZZZZZIXI\n",
      "0.07189521+0.00000000j XIZZZZZZIXI\n",
      "-0.13840506+0.00000000j IYZYIIIIIII\n",
      "-0.10769799+0.00000000j ZYZYIIIIIII\n",
      "-0.13840506+0.00000000j IXZXIIIIIII\n",
      "-0.10769799+0.00000000j ZXZXIIIIIII\n",
      "0.01643556+0.00000000j YXXYIIIIIII\n",
      "-0.01643556+0.00000000j YYXXIIIIIII\n",
      "-0.01643556+0.00000000j XXYYIIIIIII\n",
      "0.01643556+0.00000000j XYYXIIIIIII\n",
      "0.00435517+0.00000000j YXIXZZYIIII\n",
      "0.00435517+0.00000000j YYIYZZYIIII\n",
      "0.00435517+0.00000000j XXIXZZXIIII\n",
      "0.00435517+0.00000000j XYIYZZXIIII\n",
      "0.01185465+0.00000000j YXIXZZZZIYI\n",
      "0.01185465+0.00000000j YYIYZZZZIYI\n",
      "0.01185465+0.00000000j XXIXZZZZIXI\n",
      "0.01185465+0.00000000j XYIYZZZZIXI\n",
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      "0.00264894+0.00000000j IZYIZIYZZIZ\n",
      "0.00264894+0.00000000j IZXIZIXZZIZ\n",
      "-0.01943301+0.00000000j IZYIZIZIZYZ\n",
      "-0.01943301+0.00000000j IZXIZIZIZXZ\n",
      "0.19243493+0.00000000j IIIZZIIIIII\n",
      "-0.00348493+0.00000000j IIIYIZZYIII\n",
      "-0.00348493+0.00000000j IIIXIZZXIII\n",
      "0.02546443+0.00000000j IIIYIZZZIZY\n",
      "0.02546443+0.00000000j IIIXIZZZIZX\n",
      "-0.00660188+0.00000000j IIIYXXYIIII\n",
      "0.00660188+0.00000000j IIIYYXXIIII\n",
      "0.00660188+0.00000000j IIIXXYYIIII\n",
      "-0.00660188+0.00000000j IIIXYYXIIII\n",
      "-0.00746881+0.00000000j ZZZXYZYIIII\n",
      "-0.00746881+0.00000000j ZZZXXZXIIII\n",
      "-0.00746881+0.00000000j ZIZXYIYZZIZ\n",
      "-0.00746881+0.00000000j ZIZXXIXZZIZ\n",
      "0.00709065+0.00000000j IIIYXXZZIYI\n",
      "-0.00709065+0.00000000j IIIYYXZZIXI\n",
      "-0.00709065+0.00000000j IIIXXYZZIYI\n",
      "0.00709065+0.00000000j IIIXYYZZIXI\n",
      "-0.00816358+0.00000000j ZZZXYZZZIYI\n",
      "-0.00816358+0.00000000j ZZZXXZZZIXI\n",
      "-0.00816358+0.00000000j ZIZXYIZIZYZ\n",
      "-0.00816358+0.00000000j ZIZXXIZIZXZ\n",
      "0.01668125+0.00000000j ZIZZXZIZZIZ\n",
      "0.01668125+0.00000000j IIIZXZZZIZZ\n",
      "-0.01472330+0.00000000j ZIZYYIZXZIZ\n",
      "-0.01472330+0.00000000j IIIYYIIXIZZ\n",
      "0.01472330+0.00000000j ZIZXYIZYZIZ\n",
      "0.01472330+0.00000000j IIIXYIIYIZZ\n",
      "-0.01672022+0.00000000j ZIZYYIZIZZX\n",
      "-0.01672022+0.00000000j IIIYYIIIIIX\n",
      "0.01672022+0.00000000j ZIZXYIZIZZY\n",
      "0.01672022+0.00000000j IIIXYIIIIIY\n",
      "0.15221926+0.00000000j IIIZIZIIIII\n",
      "-0.01932965+0.00000000j ZZZIZXIIIII\n",
      "-0.01932965+0.00000000j ZIZZZXIZZIZ\n",
      "-0.01008682+0.00000000j IIIYZIZYIII\n",
      "-0.01008682+0.00000000j IIIXZIZXIII\n",
      "0.03255508+0.00000000j IIIYZIZZIZY\n",
      "0.03255508+0.00000000j IIIXZIZZIZX\n",
      "0.00725449+0.00000000j ZZZXIYZYIII\n",
      "0.01106226+0.00000000j ZZZXIXZXIII\n",
      "-0.00380777+0.00000000j ZIZYIYZXZIZ\n",
      "0.00380777+0.00000000j ZZZYIYZXIII\n",
      "-0.01106226+0.00000000j ZIZXIXZXZIZ\n",
      "-0.00725449+0.00000000j ZIZXIYZYZIZ\n",
      "0.00855664+0.00000000j ZZZXIYZZIZY\n",
      "0.01498796+0.00000000j ZZZXIXZZIZX\n",
      "-0.00643132+0.00000000j ZIZYIYZIZZX\n",
      "0.00643132+0.00000000j ZZZYIYZZIZX\n",
      "-0.01498796+0.00000000j ZIZXIXZIZZX\n",
      "-0.00855664+0.00000000j ZIZXIYZIZZY\n",
      "0.17745377+0.00000000j IIIZIIZIIII\n",
      "0.01611634+0.00000000j IIIYZZIYIII\n",
      "0.01611634+0.00000000j IIIXZZIXIII\n",
      "0.03270583+0.00000000j IIIYZZIZIZY\n",
      "0.03270583+0.00000000j IIIXZZIZIZX\n",
      "0.01160169+0.00000000j IIIYZZXIYII\n",
      "-0.01160169+0.00000000j IIIYZZYIXII\n",
      "0.01160169+0.00000000j IIIXZZXIXII\n",
      "0.01160169+0.00000000j IIIXZZYIYII\n",
      "0.00793038+0.00000000j IIIZIIYZIYI\n",
      "0.00793038+0.00000000j IIIZIIXZIXI\n",
      "-0.00419410+0.00000000j IIIYZZXXIYI\n",
      "0.00419410+0.00000000j IIIYZZYXIXI\n",
      "0.00419410+0.00000000j IIIXZZXYIYI\n",
      "-0.00419410+0.00000000j IIIXZZYYIXI\n",
      "-0.00630001+0.00000000j IIIYZZXIIXY\n",
      "-0.00630001+0.00000000j IIIYZZYIIYY\n",
      "-0.00630001+0.00000000j IIIXZZXIIXX\n",
      "-0.00630001+0.00000000j IIIXZZYIIYX\n",
      "0.01853107+0.00000000j ZIZYIYXZZIZ\n",
      "0.01853107+0.00000000j IIIYZYXZIZZ\n",
      "0.01853107+0.00000000j ZIZXIXXZZIZ\n",
      "0.01853107+0.00000000j IIIXZXXZIZZ\n",
      "0.00249145+0.00000000j IZIXZIXZZIZ\n",
      "0.00249145+0.00000000j ZZZXIIXZIZZ\n",
      "0.00249145+0.00000000j IIIXZZXIIII\n",
      "0.00249145+0.00000000j ZIZXIZXIZZI\n",
      "0.15590746+0.00000000j IIIZIIIZIII\n",
      "0.00401210+0.00000000j IIIZIIIYIZY\n",
      "0.00401210+0.00000000j IIIZIIIXIZX\n",
      "0.02851174+0.00000000j IIIYZZZIIZY\n",
      "0.02851174+0.00000000j IIIXZZZIIZX\n",
      "0.35825358+0.00000000j IIIZIIIIZII\n",
      "-0.00686721+0.00000000j IIIYZZZYZII\n",
      "-0.00686721+0.00000000j IIIXZZZXZII\n",
      "0.06435709+0.00000000j IIIYZZZZZZY\n",
      "0.06435709+0.00000000j IIIXZZZZZZX\n",
      "-0.01773231+0.00000000j IIIYZZZZXYI\n",
      "0.01773231+0.00000000j IIIYZZZZYXI\n",
      "0.01773231+0.00000000j IIIXZZZZYYI\n",
      "0.01773231+0.00000000j IIIXZZZZXXI\n",
      "0.15589925+0.00000000j IIIZIIIIIZI\n",
      "-0.01420697+0.00000000j IIIYZZZYIZI\n",
      "-0.01420697+0.00000000j IIIXZZZXIZI\n",
      "0.01745620+0.00000000j IIIYZZZZIIY\n",
      "0.01745620+0.00000000j IIIXZZZZIIX\n",
      "0.02315154+0.00000000j ZIZYIYZIZXZ\n",
      "0.02315154+0.00000000j IIIYZYIIIXZ\n",
      "0.02315154+0.00000000j ZIZXIXZIZXZ\n",
      "0.02315154+0.00000000j IIIXZXIIIXZ\n",
      "-0.00698588+0.00000000j IZIXZIZIZXZ\n",
      "-0.00698588+0.00000000j ZZZXIIIIIXZ\n",
      "-0.00698588+0.00000000j IIIXZZZZIXI\n",
      "-0.00698588+0.00000000j ZIZXIZIZZXI\n",
      "0.13268318+0.00000000j IIIZIIIIIIZ\n",
      "-0.00790696+0.00000000j IIIYZZZYIIZ\n",
      "-0.00790696+0.00000000j IIIXZZZXIIZ\n",
      "-0.17396918+0.00000000j ZIZZZIZIZZI\n",
      "0.00264894+0.00000000j ZIZYIZIYZZI\n",
      "0.00264894+0.00000000j ZIZXIZIXZZI\n",
      "-0.01943301+0.00000000j ZIZYIZIZZIY\n",
      "-0.01943301+0.00000000j ZIZXIZIZZIX\n",
      "-0.16249240+0.00000000j IZIIIZIZZIZ\n",
      "-0.00514039+0.00000000j IZIXZIZXZIZ\n",
      "-0.00514039+0.00000000j IZIYZIZYZIZ\n",
      "0.02641889+0.00000000j IZIXZIZIZZX\n",
      "0.02641889+0.00000000j IZIYZIZIZZY\n",
      "0.19695256+0.00000000j IIIIZZIIIII\n",
      "0.02564360+0.00000000j ZIZIXIIZZIZ\n",
      "0.02564360+0.00000000j IIIIXIZZIZZ\n",
      "0.01249880+0.00000000j IIIIYXXYIII\n",
      "-0.01249880+0.00000000j IIIIYYXXIII\n",
      "-0.01249880+0.00000000j IIIIXXYYIII\n",
      "0.01249880+0.00000000j IIIIXYYXIII\n",
      "-0.00066389+0.00000000j IIIIYXIXIYI\n",
      "-0.00066389+0.00000000j IIIIYYIYIYI\n",
      "-0.00066389+0.00000000j IIIIXXIXIXI\n",
      "-0.00066389+0.00000000j IIIIXYIYIXI\n",
      "0.01013672+0.00000000j IIIIYXIIYII\n",
      "-0.01013672+0.00000000j IIIIYYIIXII\n",
      "0.01013672+0.00000000j IIIIXXIIXII\n",
      "0.01013672+0.00000000j IIIIXYIIYII\n",
      "0.00066389+0.00000000j IIIIYXXZIZY\n",
      "-0.00066389+0.00000000j IIIIYYXZIZX\n",
      "-0.00066389+0.00000000j IIIIXXYZIZY\n",
      "0.00066389+0.00000000j IIIIXYYZIZX\n",
      "0.01011235+0.00000000j IIIIYXIIIXY\n",
      "-0.01011235+0.00000000j IIIIYYIIIXX\n",
      "-0.01011235+0.00000000j IIIIXXIIIYY\n",
      "0.01011235+0.00000000j IIIIXYIIIYX\n",
      "-0.02564360+0.00000000j ZZZZIXIIIII\n",
      "-0.02564360+0.00000000j ZIZIIXIZZIZ\n",
      "-0.03356262+0.00000000j IZIZYYIZZIZ\n",
      "-0.03356262+0.00000000j IIIIYYIIIII\n",
      "-0.03356262+0.00000000j ZZZZYYZZIZZ\n",
      "-0.03356262+0.00000000j ZIZIYYZIZZI\n",
      "0.16703651+0.00000000j IIIIZIZIIII\n",
      "0.00361091+0.00000000j IIIIZIYZIYI\n",
      "0.00361091+0.00000000j IIIIZIXZIXI\n",
      "0.03490962+0.00000000j ZIZIXZZZZIZ\n",
      "0.03490962+0.00000000j IIIIXZIZIZZ\n",
      "-0.00082944+0.00000000j ZIZIXZYIZYZ\n",
      "0.00370790+0.00000000j ZIZIXZXIZXZ\n",
      "-0.00453734+0.00000000j IIIIYZYIIXZ\n",
      "0.00453734+0.00000000j ZIZIYZYIZXZ\n",
      "-0.00370790+0.00000000j IIIIXZXIIXZ\n",
      "0.00082944+0.00000000j IIIIXZYIIYZ\n",
      "0.17953531+0.00000000j IIIIZIIZIII\n",
      "0.04599738+0.00000000j ZIZIXZIIZIZ\n",
      "0.04599738+0.00000000j IIIIXZZIIZZ\n",
      "0.00294702+0.00000000j IIIIZIIYIZY\n",
      "0.00294702+0.00000000j IIIIZIIXIZX\n",
      "-0.00183851+0.00000000j ZIZIXZIXZZX\n",
      "-0.00183851+0.00000000j ZIZIXZIYZZY\n",
      "-0.00183851+0.00000000j IIIIXZZXIIX\n",
      "-0.00183851+0.00000000j IIIIXZZYIIY\n",
      "-0.01108776+0.00000000j ZZZZXIXXIII\n",
      "-0.01108776+0.00000000j ZIZIXZXXZIZ\n",
      "-0.01108776+0.00000000j ZZZZYIYXIII\n",
      "-0.01108776+0.00000000j ZIZIYZYXZIZ\n",
      "0.00266795+0.00000000j ZZZZXIIYIYI\n",
      "0.00266795+0.00000000j ZIZIXZIYZYZ\n",
      "-0.00266795+0.00000000j ZZZZYIIYIXI\n",
      "-0.00266795+0.00000000j ZIZIYZIYZXZ\n",
      "0.35618156+0.00000000j IIIIZIIIZII\n",
      "0.06631065+0.00000000j ZIZIXZIZIIZ\n",
      "0.06631065+0.00000000j IIIIXZZZZZZ\n",
      "-0.00496897+0.00000000j ZZZZXIIIXII\n",
      "-0.00496897+0.00000000j ZIZIXZIZXIZ\n",
      "-0.00496897+0.00000000j ZZZZYIIIYII\n",
      "-0.00496897+0.00000000j ZIZIYZIZYIZ\n",
      "0.13190731+0.00000000j IIIIZIIIIZI\n",
      "0.01375669+0.00000000j ZIZIXZIZZZZ\n",
      "0.01375669+0.00000000j IIIIXZZZIIZ\n",
      "0.14201966+0.00000000j IIIIZIIIIIZ\n",
      "0.00329617+0.00000000j ZIZIXZIZZII\n",
      "0.00329617+0.00000000j IIIIXZZZIZI\n",
      "-0.00186939+0.00000000j ZZZZXIXZIZX\n",
      "-0.00186939+0.00000000j ZIZIXZXIZZX\n",
      "-0.00186939+0.00000000j ZZZZYIYZIZX\n",
      "-0.00186939+0.00000000j ZIZIYZYIZZX\n",
      "0.01046051+0.00000000j ZZZZXIIIIXX\n",
      "0.01046051+0.00000000j ZIZIXZIZZXX\n",
      "0.01046051+0.00000000j ZZZZYIIIIYX\n",
      "0.01046051+0.00000000j ZIZIYZIZZYX\n",
      "-0.14256640+0.00000000j ZIZIIIZIZZI\n",
      "-0.17612902+0.00000000j IZIZZZIZZIZ\n",
      "-0.02127771+0.00000000j ZZZZXIIIIII\n",
      "-0.02127771+0.00000000j IZIZXIZIZZI\n",
      "0.17953531+0.00000000j IIIIIZZIIII\n",
      "-0.04599738+0.00000000j ZZZZZXZIIII\n",
      "-0.04599738+0.00000000j ZIZIZXZZZIZ\n",
      "0.00294702+0.00000000j IIIIIZYZIYI\n",
      "0.00294702+0.00000000j IIIIIZXZIXI\n",
      "-0.00183851+0.00000000j ZZZZZXYZIYI\n",
      "-0.00183851+0.00000000j ZZZZZXXZIXI\n",
      "-0.00183851+0.00000000j ZIZIZXYIZYZ\n",
      "-0.00183851+0.00000000j ZIZIZXXIZXZ\n",
      "0.01108776+0.00000000j ZIZIZYYXZIZ\n",
      "0.01108776+0.00000000j IIIIIYYXIZZ\n",
      "-0.01108776+0.00000000j ZIZIZXYYZIZ\n",
      "-0.01108776+0.00000000j IIIIIXYYIZZ\n",
      "-0.00266795+0.00000000j ZIZIZYYIZZX\n",
      "-0.00266795+0.00000000j IIIIIYYIIIX\n",
      "0.00266795+0.00000000j ZIZIZXYIZZY\n",
      "0.00266795+0.00000000j IIIIIXYIIIY\n",
      "0.16703651+0.00000000j IIIIIZIZIII\n",
      "0.00361091+0.00000000j IIIIIZIYIZY\n",
      "0.00361091+0.00000000j IIIIIZIXIZX\n",
      "-0.03490962+0.00000000j ZZZZZXIZIII\n",
      "-0.03490962+0.00000000j ZIZIZXIIZIZ\n",
      "0.00082944+0.00000000j ZZZZZXIYIZY\n",
      "-0.00370790+0.00000000j ZZZZZXIXIZX\n",
      "0.00453734+0.00000000j ZIZIZYIYZZX\n",
      "-0.00453734+0.00000000j ZZZZZYIYIZX\n",
      "0.00370790+0.00000000j ZIZIZXIXZZX\n",
      "-0.00082944+0.00000000j ZIZIZXIYZZY\n",
      "0.35618156+0.00000000j IIIIIZIIZII\n",
      "-0.06631065+0.00000000j ZZZZZXIIZII\n",
      "-0.06631065+0.00000000j ZIZIZXIZIIZ\n",
      "0.00496897+0.00000000j ZIZIZYIZYIZ\n",
      "0.00496897+0.00000000j IIIIIYZZYZZ\n",
      "0.00496897+0.00000000j ZIZIZXIZXIZ\n",
      "0.00496897+0.00000000j IIIIIXZZXZZ\n",
      "0.14201966+0.00000000j IIIIIZIIIZI\n",
      "-0.00329617+0.00000000j ZZZZZXIIIZI\n",
      "-0.00329617+0.00000000j ZIZIZXIZZZZ\n",
      "-0.00186939+0.00000000j ZIZIZYIYZXZ\n",
      "-0.00186939+0.00000000j IIIIIYZYIXZ\n",
      "-0.00186939+0.00000000j ZIZIZXIXZXZ\n",
      "-0.00186939+0.00000000j IIIIIXZXIXZ\n",
      "-0.01046051+0.00000000j ZIZIZYIZZYX\n",
      "-0.01046051+0.00000000j IIIIIYZZIYX\n",
      "0.01046051+0.00000000j ZIZIZXIZZYY\n",
      "0.01046051+0.00000000j IIIIIXZZIYY\n",
      "0.13190731+0.00000000j IIIIIZIIIIZ\n",
      "-0.01375669+0.00000000j ZZZZZXIIIIZ\n",
      "-0.01375669+0.00000000j ZIZIZXIZZII\n",
      "-0.17612902+0.00000000j ZIZIZZZIZZI\n",
      "0.02127771+0.00000000j IZIZIXZIZZI\n",
      "0.02127771+0.00000000j IIIIIXZZIZZ\n",
      "-0.14256640+0.00000000j IZIZIIIZZIZ\n",
      "0.23748627+0.00000000j IIIIIIZZIII\n",
      "0.00396946+0.00000000j IIIIIIYIIYI\n",
      "0.00396946+0.00000000j IIIIIIXIIXI\n",
      "0.01709059+0.00000000j IIIIIIYXYII\n",
      "-0.01709059+0.00000000j IIIIIIYYXII\n",
      "0.01709059+0.00000000j IIIIIIXXXII\n",
      "0.01709059+0.00000000j IIIIIIXYYII\n",
      "0.00396946+0.00000000j IIIIIIZYIZY\n",
      "0.00396946+0.00000000j IIIIIIZXIZX\n",
      "0.00423957+0.00000000j IIIIIIYXIXY\n",
      "-0.00423957+0.00000000j IIIIIIYYIXX\n",
      "-0.00423957+0.00000000j IIIIIIXXIYY\n",
      "0.00423957+0.00000000j IIIIIIXYIYX\n",
      "-0.01702387+0.00000000j IZIZIZYYZIZ\n",
      "-0.01702387+0.00000000j IIIIIIYYIII\n",
      "-0.01702387+0.00000000j ZZZZZZYYIZZ\n",
      "-0.01702387+0.00000000j ZIZIZIYYZZI\n",
      "0.37682280+0.00000000j IIIIIIZIZII\n",
      "0.01211710+0.00000000j IIIIIIYZZYI\n",
      "0.01211710+0.00000000j IIIIIIXZZXI\n",
      "-0.00540905+0.00000000j IIIIIIYZXZY\n",
      "0.00540905+0.00000000j IIIIIIYZYZX\n",
      "0.00540905+0.00000000j IIIIIIXZYZY\n",
      "0.00540905+0.00000000j IIIIIIXZXZX\n",
      "0.12478425+0.00000000j IIIIIIZIIZI\n",
      "0.12902382+0.00000000j IIIIIIZIIIZ\n",
      "0.00317361+0.00000000j IIIIIIYZIYZ\n",
      "0.00317361+0.00000000j IIIIIIXZIXZ\n",
      "-0.01060408+0.00000000j IZIZIZYIZZY\n",
      "-0.01060408+0.00000000j IIIIIIYZIZY\n",
      "-0.01060408+0.00000000j ZZZZZZYIIIY\n",
      "-0.01060408+0.00000000j ZIZIZIYZZIY\n",
      "-0.15353966+0.00000000j ZIZIZIIIZZI\n",
      "0.01084809+0.00000000j ZIZIZIXZZXI\n",
      "0.01084809+0.00000000j ZIZIZIYZZYI\n",
      "-0.17056353+0.00000000j IZIZIZZZZIZ\n",
      "-0.00024401+0.00000000j IZIZIZYIZYZ\n",
      "-0.00024401+0.00000000j IZIZIZXIZXZ\n",
      "0.37682280+0.00000000j IIIIIIIZZII\n",
      "0.01211710+0.00000000j IIIIIIIYZZY\n",
      "0.01211710+0.00000000j IIIIIIIXZZX\n",
      "0.00540905+0.00000000j IIIIIIIYXYI\n",
      "-0.00540905+0.00000000j IIIIIIIYYXI\n",
      "-0.00540905+0.00000000j IIIIIIIXYYI\n",
      "-0.00540905+0.00000000j IIIIIIIXXXI\n",
      "0.12902382+0.00000000j IIIIIIIZIZI\n",
      "0.00317361+0.00000000j IIIIIIIYIIY\n",
      "0.00317361+0.00000000j IIIIIIIXIIX\n",
      "-0.01060408+0.00000000j IZIZIZIXZXZ\n",
      "-0.01060408+0.00000000j ZZZZZZZXIXZ\n",
      "-0.01060408+0.00000000j IIIIIIIXIXI\n",
      "-0.01060408+0.00000000j ZIZIZIZXZXI\n",
      "0.12478425+0.00000000j IIIIIIIZIIZ\n",
      "-0.17056353+0.00000000j ZIZIZIZZZZI\n",
      "-0.00024401+0.00000000j ZIZIZIZYZIY\n",
      "-0.00024401+0.00000000j ZIZIZIZXZIX\n",
      "-0.15353966+0.00000000j IZIZIZIIZIZ\n",
      "0.01084809+0.00000000j IZIZIZIXZZX\n",
      "0.01084809+0.00000000j IZIZIZIYZZY\n",
      "0.01187204+0.00000000j IIIIIIIIYXY\n",
      "0.01187204+0.00000000j IIIIIIIIXXX\n",
      "-0.01187204+0.00000000j IIIIIIIIXYY\n",
      "0.01187204+0.00000000j IIIIIIIIYYX\n",
      "0.00512163+0.00000000j IZIZIZIZXIZ\n",
      "0.00512163+0.00000000j IIIIIIIIXII\n",
      "0.00512163+0.00000000j ZZZZZZZZXZZ\n",
      "0.00512163+0.00000000j ZIZIZIZIXZI\n",
      "0.27318666+0.00000000j IIIIIIIIZZI\n",
      "0.27318666+0.00000000j IIIIIIIIZIZ\n",
      "-0.33000143+0.00000000j ZIZIZIZIIZI\n",
      "-0.33000143+0.00000000j IZIZIZIZIIZ\n",
      "0.12849290+0.00000000j IIIIIIIIIZZ\n",
      "-0.02182623+0.00000000j IZIZIZIZZYY\n",
      "-0.02182623+0.00000000j IIIIIIIIIYY\n",
      "-0.02182623+0.00000000j ZZZZZZZZIYY\n",
      "-0.02182623+0.00000000j ZIZIZIZIZYY\n",
      "-0.11466433+0.00000000j ZIZIZIZIZII\n",
      "-0.13649056+0.00000000j IZIZIZIZZZZ\n",
      "-0.13649056+0.00000000j ZIZIZIZIZZZ\n",
      "-0.11466433+0.00000000j IZIZIZIZZII\n",
      "0.16986681+0.00000000j ZZZZZZZZIZZ\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "Hami_reduced_by_tapering = tapering(Hami_ori, n_electrons)\n",
    "print(f'time cost: {time() - begin}')\n",
    "print(\"Number of qubit after tapering =\", Hami_reduced_by_tapering.num_qubits)\n",
    "print(\"The tapered Hamiltonian is \\n\", Hami_reduced_by_tapering)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f78616ce",
   "metadata": {},
   "source": [
    "## 3.3 compare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f83a46df",
   "metadata": {},
   "source": [
    "### 3.3.1 generators and paulixops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1b12352e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1:   (1.0) [Z8 Z9], paulix_op: PauliX(wires=[9])\n",
      "generator 2:   (1.0) [Z0 Z2 Z4 Z6 Z8 Z10 Z12], paulix_op: PauliX(wires=[12])\n",
      "generator 3:   (1.0) [Z1 Z3 Z5 Z7 Z8 Z11 Z13], paulix_op: PauliX(wires=[13])\n"
     ]
    }
   ],
   "source": [
    "for idx, generator in enumerate(generators_by_qml):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulixops_by_qml[idx]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "ab7b51c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1: 1.00000000 IIIIIIIIZZIIII, paulix_op: 1.00000000 IIIIIIIIIXIIII\n",
      "generator 2: 1.00000000 ZIZIZIZIZIZIZI, paulix_op: 1.00000000 IIIIIIIIIIIIXI\n",
      "generator 3: 1.00000000 IZIZIZIZZIIZIZ, paulix_op: 1.00000000 IIIIIIIIIIIIIX\n"
     ]
    }
   ],
   "source": [
    "generators_by_tapering_ = get_generators_from_kernel(\n",
    "    kernel_of_E(create_parity_check_matrix_E(*create_binary_matrix_G(Hami_ori)))\n",
    ")\n",
    "generators_by_tapering, paulix_ops_by_tapering = get_paulix_ops_from_generators(generators_by_tapering_)\n",
    "\n",
    "for idx, generator in enumerate(generators_by_tapering.terms):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulix_ops_by_tapering.terms[idx]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9356446d",
   "metadata": {},
   "source": [
    "### 3.3.2 optimal sectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "6df76d3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sectors by qml: [1, -1, -1]\n",
      "sectors by tapering: [1, -1, -1]\n"
     ]
    }
   ],
   "source": [
    "print(f'sectors by qml: {paulix_sector_by_qml}')\n",
    "print(f'sectors by tapering: {optimal_sector(Hami_ori, generators_by_tapering, n_electrons)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "465a4998",
   "metadata": {},
   "source": [
    "# 4. Example: BeH2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "9a05e556",
   "metadata": {},
   "outputs": [],
   "source": [
    "# http://ursula.chem.yale.edu/~chem220/chem220js/STUDYAIDS/hybridization/mo/beh2.log\n",
    "symbols = [\"Be\", \"H\", \"H\"]\n",
    "coordinates = np.array([-0.49317, 1.16085, 0.0, 0.69683, 1.16085, 0.0, -1.68317, 1.16085, 0.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "6cb9af55",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of qubits =  14\n",
      "The Hamiltonian is \n",
      "   (-6.311794785724469) [I0]\n",
      "+ (-0.8171638849443204) [Z13]\n",
      "+ (-0.8171638849443201) [Z12]\n",
      "+ (-0.3412642728703804) [Z10]\n",
      "+ (-0.3412642728703803) [Z11]\n",
      "+ (-0.07268403369472537) [Z7]\n",
      "+ (-0.07268403369472531) [Z6]\n",
      "+ (-0.07268403369472362) [Z9]\n",
      "+ (-0.07268403369472358) [Z8]\n",
      "+ (0.08400532522364187) [Z3]\n",
      "+ (0.08400532522364221) [Z2]\n",
      "+ (0.09592687719026514) [Z4]\n",
      "+ (0.09592687719026514) [Z5]\n",
      "+ (2.4673468849172937) [Z0]\n",
      "+ (2.4673468849172946) [Z1]\n",
      "+ (0.07717080613357652) [Z10 Z12]\n",
      "+ (0.07717080613357652) [Z11 Z13]\n",
      "+ (0.08687237248084279) [Z2 Z4]\n",
      "+ (0.08687237248084279) [Z3 Z5]\n",
      "+ (0.08998679138300451) [Z4 Z6]\n",
      "+ (0.08998679138300451) [Z5 Z7]\n",
      "+ (0.08998679138302458) [Z4 Z8]\n",
      "+ (0.08998679138302458) [Z5 Z9]\n",
      "+ (0.09124508190558271) [Z6 Z10]\n",
      "+ (0.09124508190558271) [Z7 Z11]\n",
      "+ (0.09124508190560301) [Z8 Z10]\n",
      "+ (0.09124508190560301) [Z9 Z11]\n",
      "+ (0.09150767112431096) [Z6 Z12]\n",
      "+ (0.09150767112431096) [Z7 Z13]\n",
      "+ (0.09150767112433156) [Z8 Z12]\n",
      "+ (0.09150767112433156) [Z9 Z13]\n",
      "+ (0.09390618306219624) [Z6 Z13]\n",
      "+ (0.09390618306219624) [Z7 Z12]\n",
      "+ (0.09390618306221737) [Z8 Z13]\n",
      "+ (0.09390618306221737) [Z9 Z12]\n",
      "+ (0.09421858051502296) [Z2 Z10]\n",
      "+ (0.09421858051502296) [Z3 Z11]\n",
      "+ (0.09427773555506455) [Z6 Z8]\n",
      "+ (0.09427773555506455) [Z7 Z9]\n",
      "+ (0.09480391510390578) [Z4 Z10]\n",
      "+ (0.09480391510390578) [Z5 Z11]\n",
      "+ (0.09913579126417825) [Z6 Z11]\n",
      "+ (0.09913579126417825) [Z7 Z10]\n",
      "+ (0.09913579126420033) [Z8 Z11]\n",
      "+ (0.09913579126420033) [Z9 Z10]\n",
      "+ (0.09975310083117958) [Z4 Z12]\n",
      "+ (0.09975310083117958) [Z5 Z13]\n",
      "+ (0.09986768535861199) [Z2 Z6]\n",
      "+ (0.09986768535861199) [Z3 Z7]\n",
      "+ (0.09986768535863425) [Z2 Z8]\n",
      "+ (0.09986768535863425) [Z3 Z9]\n",
      "+ (0.10034008122331742) [Z6 Z9]\n",
      "+ (0.10034008122331742) [Z7 Z8]\n",
      "+ (0.10100219200777798) [Z2 Z12]\n",
      "+ (0.10100219200777798) [Z3 Z13]\n",
      "+ (0.10510725386453687) [Z2 Z7]\n",
      "+ (0.10510725386453687) [Z3 Z6]\n",
      "+ (0.1051072538645603) [Z2 Z9]\n",
      "+ (0.1051072538645603) [Z3 Z8]\n",
      "+ (0.10764564946398016) [Z4 Z7]\n",
      "+ (0.10764564946398016) [Z5 Z6]\n",
      "+ (0.10764564946400416) [Z4 Z9]\n",
      "+ (0.10764564946400416) [Z5 Z8]\n",
      "+ (0.11150071170476154) [Z4 Z13]\n",
      "+ (0.11150071170476154) [Z5 Z12]\n",
      "+ (0.11246477255979805) [Z6 Z7]\n",
      "+ (0.1124647725598482) [Z8 Z9]\n",
      "+ (0.11318140021203878) [Z4 Z11]\n",
      "+ (0.11318140021203878) [Z5 Z10]\n",
      "+ (0.11514320194023175) [Z10 Z11]\n",
      "+ (0.11581147076482523) [Z10 Z13]\n",
      "+ (0.11581147076482523) [Z11 Z12]\n",
      "+ (0.11989751197370997) [Z4 Z5]\n",
      "+ (0.12078066856326783) [Z2 Z11]\n",
      "+ (0.12078066856326783) [Z3 Z10]\n",
      "+ (0.12123678414246353) [Z12 Z13]\n",
      "+ (0.12285766370291647) [Z2 Z13]\n",
      "+ (0.12285766370291647) [Z3 Z12]\n",
      "+ (0.12374432995635995) [Z2 Z5]\n",
      "+ (0.12374432995635995) [Z3 Z4]\n",
      "+ (0.13085626153011778) [Z0 Z12]\n",
      "+ (0.13085626153011778) [Z1 Z13]\n",
      "+ (0.13172903403410097) [Z0 Z13]\n",
      "+ (0.13172903403410097) [Z1 Z12]\n",
      "+ (0.13470747957293586) [Z2 Z3]\n",
      "+ (0.13818374110220205) [Z0 Z6]\n",
      "+ (0.13818374110220205) [Z1 Z7]\n",
      "+ (0.1381837411022328) [Z0 Z8]\n",
      "+ (0.1381837411022328) [Z1 Z9]\n",
      "+ (0.13887411226970822) [Z0 Z10]\n",
      "+ (0.13887411226970822) [Z1 Z11]\n",
      "+ (0.14214775786741568) [Z0 Z7]\n",
      "+ (0.14214775786741568) [Z1 Z6]\n",
      "+ (0.14214775786744732) [Z0 Z9]\n",
      "+ (0.14214775786744732) [Z1 Z8]\n",
      "+ (0.14594438262440224) [Z0 Z11]\n",
      "+ (0.14594438262440224) [Z1 Z10]\n",
      "+ (0.1505603901110433) [Z0 Z2]\n",
      "+ (0.1505603901110433) [Z1 Z3]\n",
      "+ (0.1505790586135176) [Z0 Z4]\n",
      "+ (0.1505790586135176) [Z1 Z5]\n",
      "+ (0.1552293664340867) [Z0 Z3]\n",
      "+ (0.1552293664340867) [Z1 Z2]\n",
      "+ (0.16860038156280882) [Z0 Z5]\n",
      "+ (0.16860038156280882) [Z1 Z4]\n",
      "+ (0.5594612241246861) [Z0 Z1]\n",
      "+ (-0.0386406646312486) [Y10 Y11 X12 X13]\n",
      "+ (-0.0386406646312486) [X10 X11 Y12 Y13]\n",
      "+ (-0.036871957475517164) [Y2 Y3 X4 X5]\n",
      "+ (-0.036871957475517164) [X2 X3 Y4 Y5]\n",
      "+ (-0.026562088048244847) [Y2 Y3 X10 X11]\n",
      "+ (-0.026562088048244847) [X2 X3 Y10 Y11]\n",
      "+ (-0.021855471695138462) [Y2 Y3 X12 X13]\n",
      "+ (-0.021855471695138462) [X2 X3 Y12 Y13]\n",
      "+ (-0.018377485108133015) [Y4 Y5 X10 X11]\n",
      "+ (-0.018377485108133015) [X4 X5 Y10 Y11]\n",
      "+ (-0.01802132294929119) [Y0 Y1 X4 X5]\n",
      "+ (-0.01802132294929119) [X0 X1 Y4 Y5]\n",
      "+ (-0.01765885808097957) [Y4 Y5 X8 X9]\n",
      "+ (-0.01765885808097957) [X4 X5 Y8 Y9]\n",
      "+ (-0.01765885808097564) [Y4 Y5 X6 X7]\n",
      "+ (-0.01765885808097564) [X4 X5 Y6 Y7]\n",
      "+ (-0.015535884180727152) [Y3 Y4 X11 X12]\n",
      "+ (-0.015535884180727152) [X3 X4 Y11 Y12]\n",
      "+ (-0.011747610873581948) [Y4 Y5 X12 X13]\n",
      "+ (-0.011747610873581948) [X4 X5 Y12 Y13]\n",
      "+ (-0.00926858142544823) [Y1 Y2 X3 X4]\n",
      "+ (-0.00926858142544823) [X1 X2 Y3 Y4]\n",
      "+ (-0.007890709358597321) [Y8 Y9 X10 X11]\n",
      "+ (-0.007890709358597321) [X8 X9 Y10 Y11]\n",
      "+ (-0.007890709358595548) [Y6 Y7 X10 X11]\n",
      "+ (-0.007890709358595548) [X6 X7 Y10 Y11]\n",
      "+ (-0.007070270354694011) [Y0 Y1 X10 X11]\n",
      "+ (-0.007070270354694011) [X0 X1 Y10 Y11]\n",
      "+ (-0.006062345668252867) [Y6 Y7 X8 X9]\n",
      "+ (-0.006062345668252867) [X6 X7 Y8 Y9]\n",
      "+ (-0.005239568505926058) [Y2 Y3 X8 X9]\n",
      "+ (-0.005239568505926058) [X2 X3 Y8 Y9]\n",
      "+ (-0.005239568505924887) [Y2 Y3 X6 X7]\n",
      "+ (-0.005239568505924887) [X2 X3 Y6 Y7]\n",
      "+ (-0.004668976323043365) [Y0 Y1 X2 X3]\n",
      "+ (-0.004668976323043365) [X0 X1 Y2 Y3]\n",
      "+ (-0.003964016765214507) [Y0 Y1 X8 X9]\n",
      "+ (-0.003964016765214507) [X0 X1 Y8 Y9]\n",
      "+ (-0.003964016765213624) [Y0 Y1 X6 X7]\n",
      "+ (-0.003964016765213624) [X0 X1 Y6 Y7]\n",
      "+ (-0.002843650408391835) [Y1 Y2 X11 X12]\n",
      "+ (-0.002843650408391835) [X1 X2 Y11 Y12]\n",
      "+ (-0.0023985119378858305) [Y8 Y9 X12 X13]\n",
      "+ (-0.0023985119378858305) [X8 X9 Y12 Y13]\n",
      "+ (-0.0023985119378852724) [Y6 Y7 X12 X13]\n",
      "+ (-0.0023985119378852724) [X6 X7 Y12 Y13]\n",
      "+ (-0.0008727725039831987) [Y0 Y1 X12 X13]\n",
      "+ (-0.0008727725039831987) [X0 X1 Y12 Y13]\n",
      "+ (0.0008727725039831987) [Y0 X1 X12 Y13]\n",
      "+ (0.0008727725039831987) [X0 Y1 Y12 X13]\n",
      "+ (0.0014518476916988675) [Y0 Z1 Z2 Y4]\n",
      "+ (0.0014518476916988675) [X0 Z1 Z2 X4]\n",
      "+ (0.0014518476916988675) [Y1 Z3 Z4 Y5]\n",
      "+ (0.0014518476916988675) [X1 Z3 Z4 X5]\n",
      "+ (0.0023985119378852724) [Y6 X7 X12 Y13]\n",
      "+ (0.0023985119378852724) [X6 Y7 Y12 X13]\n",
      "+ (0.0023985119378858305) [Y8 X9 X12 Y13]\n",
      "+ (0.0023985119378858305) [X8 Y9 Y12 X13]\n",
      "+ (0.002843650408391835) [Y1 X2 X11 Y12]\n",
      "+ (0.002843650408391835) [X1 Y2 Y11 X12]\n",
      "+ (0.003964016765213624) [Y0 X1 X6 Y7]\n",
      "+ (0.003964016765213624) [X0 Y1 Y6 X7]\n",
      "+ (0.003964016765214507) [Y0 X1 X8 Y9]\n",
      "+ (0.003964016765214507) [X0 Y1 Y8 X9]\n",
      "+ (0.004668976323043365) [Y0 X1 X2 Y3]\n",
      "+ (0.004668976323043365) [X0 Y1 Y2 X3]\n",
      "+ (0.005239568505924887) [Y2 X3 X6 Y7]\n",
      "+ (0.005239568505924887) [X2 Y3 Y6 X7]\n",
      "+ (0.005239568505926058) [Y2 X3 X8 Y9]\n",
      "+ (0.005239568505926058) [X2 Y3 Y8 X9]\n",
      "+ (0.006062345668252867) [Y6 X7 X8 Y9]\n",
      "+ (0.006062345668252867) [X6 Y7 Y8 X9]\n",
      "+ (0.00632988225631909) [Y1 Z2 Z3 Y5]\n",
      "+ (0.00632988225631909) [X1 Z2 Z3 X5]\n",
      "+ (0.007070270354694011) [Y0 X1 X10 Y11]\n",
      "+ (0.007070270354694011) [X0 Y1 Y10 X11]\n",
      "+ (0.007890709358595548) [Y6 X7 X10 Y11]\n",
      "+ (0.007890709358595548) [X6 Y7 Y10 X11]\n",
      "+ (0.007890709358597321) [Y8 X9 X10 Y11]\n",
      "+ (0.007890709358597321) [X8 Y9 Y10 X11]\n",
      "+ (0.00926858142544823) [Y1 X2 X3 Y4]\n",
      "+ (0.00926858142544823) [X1 Y2 Y3 X4]\n",
      "+ (0.010720429117147094) [Y0 Z1 Z3 Y4]\n",
      "+ (0.010720429117147094) [X0 Z1 Z3 X4]\n",
      "+ (0.010720429117147094) [Y1 Z2 Z4 Y5]\n",
      "+ (0.010720429117147094) [X1 Z2 Z4 X5]\n",
      "+ (0.011747610873581948) [Y4 X5 X12 Y13]\n",
      "+ (0.011747610873581948) [X4 Y5 Y12 X13]\n",
      "+ (0.015535884180727152) [Y3 X4 X11 Y12]\n",
      "+ (0.015535884180727152) [X3 Y4 Y11 X12]\n",
      "+ (0.01765885808097564) [Y4 X5 X6 Y7]\n",
      "+ (0.01765885808097564) [X4 Y5 Y6 X7]\n",
      "+ (0.01765885808097957) [Y4 X5 X8 Y9]\n",
      "+ (0.01765885808097957) [X4 Y5 Y8 X9]\n",
      "+ (0.01802132294929119) [Y0 X1 X4 Y5]\n",
      "+ (0.01802132294929119) [X0 Y1 Y4 X5]\n",
      "+ (0.018377485108133015) [Y4 X5 X10 Y11]\n",
      "+ (0.018377485108133015) [X4 Y5 Y10 X11]\n",
      "+ (0.021855471695138462) [Y2 X3 X12 Y13]\n",
      "+ (0.021855471695138462) [X2 Y3 Y12 X13]\n",
      "+ (0.026562088048244847) [Y2 X3 X10 Y11]\n",
      "+ (0.026562088048244847) [X2 Y3 Y10 X11]\n",
      "+ (0.036871957475517164) [Y2 X3 X4 Y5]\n",
      "+ (0.036871957475517164) [X2 Y3 Y4 X5]\n",
      "+ (0.0386406646312486) [Y10 X11 X12 Y13]\n",
      "+ (0.0386406646312486) [X10 Y11 Y12 X13]\n",
      "+ (0.07841586380014585) [Y0 Z2 Z3 Y4]\n",
      "+ (0.07841586380014585) [X0 Z2 Z3 X4]\n",
      "+ (0.06783269320052565) [Y1 Z2 Z3 Z4 Y5]\n",
      "+ (0.06783269320052565) [X1 Z2 Z3 Z4 X5]\n",
      "+ (0.06783269320052566) [Y0 Z1 Z2 Z3 Y4]\n",
      "+ (0.06783269320052566) [X0 Z1 Z2 Z3 X4]\n",
      "+ (-0.02499681205831311) [Y5 Z6 Z7 Z8 Z9 Y11]\n",
      "+ (-0.02499681205831311) [X5 Z6 Z7 Z8 Z9 X11]\n",
      "+ (-0.021980989825478706) [Y4 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (-0.021980989825478706) [X4 Z6 Z7 Z8 Z9 X10]\n",
      "+ (-0.018221796314406815) [Y2 Z3 Z4 X5 X11 Y12]\n",
      "+ (-0.018221796314406815) [Y2 Z3 Z4 Y5 Y11 Y12]\n",
      "+ (-0.018221796314406815) [X2 Z3 Z4 X5 X11 X12]\n",
      "+ (-0.018221796314406815) [X2 Z3 Z4 Y5 Y11 X12]\n",
      "+ (-0.018221796314406815) [Y3 X4 X10 Z11 Z12 Y13]\n",
      "+ (-0.018221796314406815) [Y3 Y4 Y10 Z11 Z12 Y13]\n",
      "+ (-0.018221796314406815) [X3 X4 X10 Z11 Z12 X13]\n",
      "+ (-0.018221796314406815) [X3 Y4 Y10 Z11 Z12 X13]\n",
      "+ (-0.01816772910332353) [Y4 Z5 Z6 Z7 Z9 Y10]\n",
      "+ (-0.01816772910332353) [X4 Z5 Z6 Z7 Z9 X10]\n",
      "+ (-0.01816772910332353) [Y5 Z6 Z7 Z8 Z10 Y11]\n",
      "+ (-0.01816772910332353) [X5 Z6 Z7 Z8 Z10 X11]\n",
      "+ (-0.018167729103319482) [Y4 Z5 Z7 Z8 Z9 Y10]\n",
      "+ (-0.018167729103319482) [X4 Z5 Z7 Z8 Z9 X10]\n",
      "+ (-0.018167729103319482) [Y5 Z6 Z8 Z9 Z10 Y11]\n",
      "+ (-0.018167729103319482) [X5 Z6 Z8 Z9 Z10 X11]\n",
      "+ (-0.009114676966938092) [Y5 Z6 Z7 X8 X9 Y10]\n",
      "+ (-0.009114676966938092) [X5 Z6 Z7 Y8 Y9 X10]\n",
      "+ (-0.009114676966936068) [Y5 X6 X7 Z8 Z9 Y10]\n",
      "+ (-0.009114676966936068) [X5 Y6 Y7 Z8 Z9 X10]\n",
      "+ (-0.00905305213638544) [Y4 Z5 Z6 Z7 Z8 Y10]\n",
      "+ (-0.00905305213638544) [X4 Z5 Z6 Z7 Z8 X10]\n",
      "+ (-0.00905305213638544) [Y5 Z6 Z7 Z9 Z10 Y11]\n",
      "+ (-0.00905305213638544) [X5 Z6 Z7 Z9 Z10 X11]\n",
      "+ (-0.009053052136383414) [Y4 Z5 Z6 Z8 Z9 Y10]\n",
      "+ (-0.009053052136383414) [X4 Z5 Z6 Z8 Z9 X10]\n",
      "+ (-0.009053052136383414) [Y5 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.009053052136383414) [X5 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0048617954058218366) [Y1 Z2 Z3 X4 X8 Y9]\n",
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      "+ (-0.0020403141613172335) [X1 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0015617276684878898) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 X8 X9 Y10]\n",
      "+ (-0.0015617276684878898) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y9 X10]\n",
      "+ (-0.0015617276684875415) [Y1 Z2 Z3 Z4 Z5 X6 X7 Z8 Z9 Y10]\n",
      "+ (-0.0015617276684875415) [X1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Z9 X10]\n",
      "+ (-0.0011429426936436808) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y11]\n",
      "+ (-0.0011429426936436808) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X11]\n",
      "+ (-0.0010031556441050188) [Y0 Z1 Z2 Z3 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (-0.0010031556441050188) [X0 Z1 Z2 Z3 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (-0.0010031556441050188) [Y1 Z2 Z3 Z4 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.0010031556441050188) [X1 Z2 Z3 Z4 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0006690558642047136) [Y1 Y2 X5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.0006690558642047136) [X1 X2 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.00026636258878415725) [Y0 Z1 Z2 Z3 Z4 Z5 Z7 Z8 Z9 Y10]\n",
      "+ (0.00026636258878415725) [X0 Z1 Z2 Z3 Z4 Z5 Z7 Z8 Z9 X10]\n",
      "+ (0.00026636258878415725) [Y1 Z2 Z3 Z4 Z5 Z6 Z8 Z9 Z10 Y11]\n",
      "+ (0.00026636258878415725) [X1 Z2 Z3 Z4 Z5 Z6 Z8 Z9 Z10 X11]\n",
      "+ (0.00026636258878422507) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z9 Y10]\n",
      "+ (0.00026636258878422507) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z9 X10]\n",
      "+ (0.00026636258878422507) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z10 Y11]\n",
      "+ (0.00026636258878422507) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z10 X11]\n",
      "+ (0.0006690558642047136) [Y1 X2 X5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.0006690558642047136) [X1 Y2 Y5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.0007616590206936946) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z11 Y12]\n",
      "+ (0.0007616590206936946) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z11 X12]\n",
      "+ (0.0007616590206936946) [Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z12 Y13]\n",
      "+ (0.0007616590206936946) [X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z12 X13]\n",
      "+ (0.0015617276684875415) [Y1 Z2 Z3 Z4 Z5 Y6 X7 Z8 Z9 X10]\n",
      "+ (0.0015617276684875415) [X1 Z2 Z3 Z4 Z5 X6 Y7 Z8 Z9 Y10]\n",
      "+ (0.0015617276684878898) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 X9 X10]\n",
      "+ (0.0015617276684878898) [X1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Y9 Y10]\n",
      "+ (0.0018280902572716988) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9 Y10]\n",
      "+ (0.0018280902572716988) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9 X10]\n",
      "+ (0.0018280902572716988) [Y1 Z2 Z3 Z4 Z5 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0018280902572716988) [X1 Z2 Z3 Z4 Z5 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0018280902572721143) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y10]\n",
      "+ (0.0018280902572721143) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X10]\n",
      "+ (0.0018280902572721143) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z9 Z10 Y11]\n",
      "+ (0.0018280902572721143) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z9 Z10 X11]\n",
      "+ (0.0023312560067726973) [Y3 Z4 Z5 Y6 X7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.0023312560067726973) [X3 Z4 Z5 X6 Y7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.0023312560067732142) [Y3 Z4 Z5 Z6 Z7 Y8 X9 Z10 Z11 X12]\n",
      "+ (0.0023312560067732142) [X3 Z4 Z5 Z6 Z7 X8 Y9 Z10 Z11 Y12]\n",
      "+ (0.002341106428001799) [Y0 Z1 Z2 Z3 Z4 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.002341106428001799) [X0 Z1 Z2 Z3 Z4 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.002341106428001799) [Y1 Z2 Z3 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.002341106428001799) [X1 Z2 Z3 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0033442620721068177) [Y1 Z2 Z3 Y4 X5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.0033442620721068177) [X1 Z2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.006155118174119318) [Y0 Z1 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.006155118174119318) [X0 Z1 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.006155118174119318) [Y1 Z2 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.006155118174119318) [X1 Z2 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.008195432335436554) [Y1 X2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.008195432335436554) [X1 Y2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.010764826109046383) [Y0 X1 X4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.010764826109046383) [X0 Y1 Y4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.011218370529167474) [Y3 X4 X5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.011218370529167474) [X3 Y4 Y5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.015932894580459253) [Y4 Z5 Z6 Z7 Z8 Z9 Z10 X11 X12 Y13]\n",
      "+ (0.015932894580459253) [X4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Y12 X13]\n",
      "+ (0.02716847847060864) [Y2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.02716847847060864) [X2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.029804138248567855) [Y3 Z4 Z5 Z6 Z7 Z8 Z9 X10 X11 Y12]\n",
      "+ (0.029804138248567855) [X3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Y11 X12]\n",
      "+ (0.04329392228902874) [Y0 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.04329392228902874) [X0 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (-0.014120945784627768) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.014120945784627768) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.014120945784627748) [Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.014120945784627748) [X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.04827706363648314) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.04827706363648314) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.04827706363648315) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.04827706363648315) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (-0.03270435341767386) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12 Z13]\n",
      "+ (-0.03270435341767386) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12 Z13]\n",
      "+ (-0.030551433116473514) [Z2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.030551433116473514) [Z2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.029360657413472945) [Z0 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.029360657413472945) [Z0 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.029360657413472945) [Z1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.029360657413472945) [Z1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.029196719263215983) [Z0 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.029196719263215983) [Z0 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.029196719263215983) [Z1 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.029196719263215983) [Z1 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.003671623118533921) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 X12 Y13]\n",
      "+ (-0.003671623118533921) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Y12 Y13]\n",
      "+ (-0.003671623118533921) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 X12 X13]\n",
      "+ (-0.003671623118533921) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Y12 X13]\n",
      "+ (-0.0033442620721068177) [Y0 Z1 Z2 Z3 Y4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.0033442620721068177) [Y0 Z1 Z2 Z3 Y4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0033442620721068177) [X0 Z1 Z2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.0033442620721068177) [X0 Z1 Z2 Z3 X4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0031239863430885598) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z13]\n",
      "+ (-0.0031239863430885598) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z13]\n",
      "+ (-0.0031239863430885598) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Z12]\n",
      "+ (-0.0031239863430885598) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 Z12]\n",
      "+ (-0.002673266415087913) [Y0 Z1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.002673266415087913) [Y0 Z1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.002673266415087913) [X0 Z1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.002673266415087913) [X0 Z1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.002673266415087913) [Y1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.002673266415087913) [Y1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.002673266415087913) [X1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.002673266415087913) [X1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0023312560067732142) [Y2 Z3 Z4 Z5 Z6 Z7 Y8 Y9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0023312560067732142) [Y2 Z3 Z4 Z5 Z6 Z7 Y8 X9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0023312560067732142) [X2 Z3 Z4 Z5 Z6 Z7 X8 Y9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0023312560067732142) [X2 Z3 Z4 Z5 Z6 Z7 X8 X9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0023312560067726973) [Y2 Z3 Z4 Z5 Y6 Y7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0023312560067726973) [Y2 Z3 Z4 Z5 Y6 X7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0023312560067726973) [X2 Z3 Z4 Z5 X6 Y7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0023312560067726973) [X2 Z3 Z4 Z5 X6 X7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0020042105508832012) [Y0 Z1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.0020042105508832012) [X0 Z1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.0020042105508832012) [Y1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.0020042105508832012) [X1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0015617276684878893) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y9 Z10 Y11]\n",
      "+ (-0.0015617276684878893) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 X9 Z10 X11]\n",
      "+ (-0.0015617276684878893) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Y9 Z10 Y11]\n",
      "+ (-0.0015617276684878893) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 X9 Z10 X11]\n",
      "+ (-0.0015617276684875415) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.0015617276684875415) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0015617276684875415) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.0015617276684875415) [X0 Z1 Z2 Z3 Z4 Z5 X6 X7 Z8 Z9 Z10 X11]\n",
      "+ (-0.0011429426936436808) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z11]\n",
      "+ (-0.0011429426936436808) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z11]\n",
      "+ (-0.00016393815025696377) [Y0 X1 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.00016393815025696377) [Y0 Y1 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (-0.00016393815025696377) [X0 X1 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (-0.00016393815025696377) [X0 Y1 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.0005476367754453891) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z12]\n",
      "+ (0.0005476367754453891) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z12]\n",
      "+ (0.0005476367754453891) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Z13]\n",
      "+ (0.0005476367754453891) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 Z13]\n",
      "+ (0.001257134045960125) [Y0 Z1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.001257134045960125) [X0 Z1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.001257134045960125) [Y1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.001257134045960125) [X1 Z2 X3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0032613445968433237) [Y0 Z1 Y2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.0032613445968433237) [X0 Z1 X2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.0032613445968433237) [Y1 Z2 Y3 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0032613445968433237) [X1 Z2 X3 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.003930400461048038) [Y0 Z1 Y2 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.003930400461048038) [Y0 Z1 Y2 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.003930400461048038) [X0 Z1 X2 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.003930400461048038) [X0 Z1 X2 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.003930400461048038) [Y1 Z2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.003930400461048038) [Y1 Z2 Y3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.003930400461048038) [X1 Z2 X3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Y12]\n",
      "+ (0.003930400461048038) [X1 Z2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 X12]\n",
      "+ (0.008195432335436554) [Y0 Z1 Y2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.008195432335436554) [Y0 Z1 Y2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.008195432335436554) [X0 Z1 X2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.008195432335436554) [X0 Z1 X2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.011218370529167474) [Y2 Z3 Y4 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.011218370529167474) [Y2 Z3 Y4 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.011218370529167474) [X2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.011218370529167474) [X2 Z3 X4 X5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.029804138248567855) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Y11 Z12 Y13]\n",
      "+ (0.029804138248567855) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 X11 Z12 X13]\n",
      "+ (0.029804138248567855) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Y11 Z12 Y13]\n",
      "+ (0.029804138248567855) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 X11 Z12 X13]\n",
      "+ (0.043293922289028744) [Z0 Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.043293922289028744) [Z0 X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.003671623118533921) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 X12 X13]\n",
      "+ (-0.003671623118533921) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 Y12 Y13]\n",
      "+ (-0.0006690558642047136) [Y0 Z1 Z2 Y3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.0006690558642047136) [X0 Z1 Z2 X3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (-0.00016393815025696377) [Y0 Y1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (-0.00016393815025696377) [X0 X1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.00016393815025696377) [Y0 X1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.00016393815025696377) [X0 Y1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.0006690558642047136) [Y0 Z1 Z2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Y13]\n",
      "+ (0.0006690558642047136) [X0 Z1 Z2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 X13]\n",
      "+ (0.003671623118533921) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11 X12 Y13]\n",
      "+ (0.003671623118533921) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11 Y12 X13]\n",
      "--------------------\n",
      "Number of terms:  666\n"
     ]
    }
   ],
   "source": [
    "# 基于JW变换构建的H2哈密顿量\n",
    "H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)\n",
    "print(\"Number of qubits = \", qubits)\n",
    "print(\"The Hamiltonian is \\n\", H)\n",
    "print(\"-\" * 20)\n",
    "print(\"Number of terms: \", len(H.ops))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7d97765",
   "metadata": {},
   "source": [
    "## 4.1 Tapering using QML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "b918bf53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 892.9166102409363\n",
      "Number of qubit after tapering = 9\n",
      "The tapered Hamiltonian is \n",
      "   ((-6.086865240604816+0j)) [I0]\n",
      "+ ((-0.34126427287038+0j)) [Z10]\n",
      "+ ((-0.14536806738945063+0j)) [Z6]\n",
      "+ ((-0.1453680673894471+0j)) [Z8]\n",
      "+ ((-0.024996812058313084+0j)) [X5]\n",
      "+ ((0.00239851193788527+0j)) [X6]\n",
      "+ ((0.00239851193788583+0j)) [X8]\n",
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      "+ ((0.0015617276684878887+0j)) [X1 Z2 Z3 Z4 Z5 Y8 Y10]\n",
      "+ ((0.0015617276684878887+0j)) [X1 Z2 Z3 Z4 Z5 X8 X10]\n",
      "+ ((0.0020334594503994743-0j)) [X0 Z1 Z2 X5 Z6 Z8 Z10]\n",
      "+ ((0.0020334594503994743-0j)) [Z0 Y1 Z2 Y4 Z6 Z8 Z10]\n",
      "+ ((0.002094452846055853+0j)) [X1 Z2 Z3 Z4 Z5 Z6 Z10]\n",
      "+ ((0.002094452846056337+0j)) [X1 Z2 Z3 Z4 Z5 Z8 Z10]\n",
      "+ ((0.0022472158426066076-0j)) [X0 Z1 Z3 X4 Z6 Z8 Z10]\n",
      "+ ((0.0022472158426066076-0j)) [Y0 Z1 Z3 Y4 Z6 Z8 Z10]\n",
      "+ ((0.002331256006772696+0j)) [Z1 X2 Z3 Z4 X6 Z8 Z10]\n",
      "+ ((0.002331256006772696+0j)) [Z1 Y2 Z3 Z4 Y6 Z8 Z10]\n",
      "+ ((0.002331256006773211+0j)) [Z1 X2 Z3 Z4 Z6 X8 Z10]\n",
      "+ ((0.002331256006773211+0j)) [Z1 Y2 Z3 Z4 Z6 Y8 Z10]\n",
      "+ ((0.0026859121336796584+0j)) [Z1 Z2 X3 Z4 X5 Z6 Z8]\n",
      "+ ((0.0028436504083918335+0j)) [Z0 Y1 Y2 Z4 Z6 Z8 Z10]\n",
      "+ ((0.0030251432934169666+0j)) [X0 Z1 X3 Z4 Z6 Z8 Z10]\n",
      "+ ((0.0030251432934169666-0j)) [Z0 X1 Y2 Z3 Z4 Z5 Y10]\n",
      "+ ((0.0030251432934169666-0j)) [Z0 X1 X2 Z3 Z4 Z5 X10]\n",
      "+ ((0.003671623118533918-0j)) [Z0 Y1 Z2 Z5 Z6 Z8 Y10]\n",
      "+ ((0.004861795405820749+0j)) [Y0 Z1 Z2 Z3 Z4 X5 Y6]\n",
      "+ ((0.004861795405820749+0j)) [X0 Z1 Z2 Z3 Z4 X5 X6]\n",
      "+ ((0.004861795405820749+0j)) [X0 Z1 Z2 Z3 Z4 Y5 Y6]\n",
      "+ ((0.004861795405821831+0j)) [Y0 Z1 Z2 Z3 Z4 X5 Y8]\n",
      "+ ((0.004861795405821831+0j)) [X0 Z1 Z2 Z3 Z4 X5 X8]\n",
      "+ ((0.004861795405821831+0j)) [X0 Z1 Z2 Z3 Z4 Y5 Y8]\n",
      "+ ((0.0060802467240351574+0j)) [Z0 X1 X3 Z4 Z6 Z8 Z10]\n",
      "+ ((0.006261739609060291+0j)) [Z0 Y1 Y3 Z4 Z6 Z8 Z10]\n",
      "+ ((0.008195432335436546+0j)) [Y0 Z1 Y2 X3 Z4 Z5 Z10]\n",
      "+ ((0.008195432335436546+0j)) [X0 Z1 X2 X3 Z4 Z5 Z10]\n",
      "+ ((0.009105390017452123-0j)) [Z0 Y1 Z2 X3 Z4 Z5 Y10]\n",
      "+ ((0.011747610873581945-0j)) [Z0 Z3 X4 X5 Z6 Z8 Z10]\n",
      "+ ((0.014120945784627751+0j)) [Z1 X2 Z3 Z4 Z6 Z8 Z10]\n",
      "+ ((0.015535884180727145+0j)) [Z0 Z2 Y3 Y4 Z6 Z8 Z10]\n",
      "+ ((0.015535884180727145+0j)) [Z1 Z2 X3 X4 Z5 Z6 Z8]\n",
      "+ ((0.015771034329463977-0j)) [Z0 Z1 X2 Z3 Y4 Z5 Y10]\n",
      "+ ((0.015771034329463977+0j)) [Z0 Z2 X3 X5 Z6 Z8 Z10]\n",
      "+ ((0.015932894580459225-0j)) [Z0 Z3 Z4 Y5 Z6 Z8 Y10]\n",
      "+ ((0.018221796314406794+0j)) [Z0 X2 Z3 X5 Z6 Z8 Z10]\n",
      "+ ((0.018221796314406794-0j)) [Z0 Z1 Z2 X3 Y4 Z5 Y10]\n",
      "+ ((0.018221796314406794-0j)) [Z0 Z1 Z2 X3 X4 Z5 X10]\n",
      "+ ((0.018456946463143668+0j)) [Z0 Z2 Y3 Y5 Z6 Z8 Z10]\n",
      "+ ((0.026562088048244812+0j)) [Z0 Z1 Y2 X3 Z4 Z5 Y10]\n",
      "+ ((0.026562088048244812+0j)) [Z0 Z1 X2 X3 Z4 Z5 X10]\n",
      "+ ((0.029804138248567844+0j)) [Z0 Z2 Y3 Z5 Z6 Z8 Y10]\n",
      "+ ((0.029804138248567844+0j)) [Z1 Z2 X3 Z4 Z6 Z8 X10]\n",
      "+ ((0.04329392228902872+0j)) [Z0 X1 Z2 Z3 Z4 Z5 Z10]\n",
      "+ ((0.048277063636483104+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Y10]\n",
      "+ ((0.048277063636483104+0j)) [X0 Z1 Z2 Z3 Z4 Z5 X10]\n",
      "+ ((-0.03399283064387081+0j)) [Z1 Z2 Y3 Z4 X5 Z6 Z8 Y10]\n",
      "+ ((-0.02936065741347293+0j)) [Z0 Z1 Z2 X3 Z4 Z6 Z8 Z10]\n",
      "+ ((-0.018221796314406794+0j)) [Z1 Z2 X3 X4 Z5 Z6 Z8 X10]\n",
      "+ ((-0.018221796314406794+0j)) [Z1 Z2 X3 Y4 Z5 Z6 Z8 Y10]\n",
      "+ ((-0.015771034329463977+0j)) [Z1 X2 Z3 Y4 Z5 Z6 Z8 Y10]\n",
      "+ ((-0.011218370529167465+0j)) [Z1 Y2 Z3 X4 Y5 Z6 Z8 Z10]\n",
      "+ ((-0.010879917885169439+0j)) [Z1 Z2 X3 Z4 Z5 Z6 Z8 Z10]\n",
      "+ ((-0.0015617276684878887+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Y8 Z10]\n",
      "+ ((-0.0015617276684878887+0j)) [X0 Z1 Z2 Z3 Z4 Z5 X8 Z10]\n",
      "+ ((-0.0015617276684875413+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Z10]\n",
      "+ ((-0.0015617276684875413+0j)) [X0 Z1 Z2 Z3 Z4 Z5 X6 Z10]\n",
      "+ ((-0.00016393815025696372+0j)) [Y0 Y1 Z2 X3 Z4 Z6 Z8 Z10]\n",
      "+ ((-0.00016393815025696372+0j)) [Y0 X1 Y2 Z3 Z4 Z6 Z8 Z10]\n",
      "+ ((-0.00016393815025696372+0j)) [X0 X1 X2 Z3 Z4 Z6 Z8 Z10]\n",
      "+ ((0.00016393815025696372+0j)) [Y0 X1 Z2 Y3 Z4 Z6 Z8 Z10]\n",
      "+ ((0.002094452846055853+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Y10]\n",
      "+ ((0.002094452846055853+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 X10]\n",
      "+ ((0.002094452846056337+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Z8 Y10]\n",
      "+ ((0.002094452846056337+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z8 X10]\n",
      "+ ((0.0026859121336796584+0j)) [Z1 X2 Z3 X4 Z5 Z6 Z8 X10]\n",
      "+ ((0.011218370529167465+0j)) [Z1 X2 Z3 Y4 Y5 Z6 Z8 Z10]\n",
      "+ ((0.011218370529167465+0j)) [Z1 Z2 Y3 X4 Y5 Z6 Z8 Z10]\n",
      "+ ((0.011218370529167465+0j)) [Z1 Z2 X3 X4 X5 Z6 Z8 Z10]\n",
      "+ ((0.015535884180727145+0j)) [Z1 X2 Z3 Z4 X5 Z6 Z8 X10]\n",
      "+ ((0.015535884180727145+0j)) [Z1 Y2 Z3 Z4 X5 Z6 Z8 Y10]\n",
      "+ ((0.018456946463143668+0j)) [Z1 Y2 Z3 X4 Z5 Z6 Z8 Y10]\n",
      "+ ((0.02209828841433691+0j)) [Z1 X2 Z3 Z4 Z5 Z6 Z8 Z10]\n",
      "+ ((0.02919671926321598+0j)) [Z0 Z1 X2 Z3 Z4 Z6 Z8 Z10]\n",
      "+ ((0.03399283064387081+0j)) [Z1 Z2 X3 Z4 Y5 Z6 Z8 Y10]\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "generators_by_qml = qml.symmetry_generators(H)\n",
    "paulixops_by_qml = qml.paulix_ops(generators_by_qml, qubits)\n",
    "\n",
    "n_electrons = 6\n",
    "paulix_sector_by_qml = qml.qchem.optimal_sector(H, generators_by_qml, n_electrons)\n",
    "\n",
    "H_tapered = qml.taper(H, generators_by_qml, paulixops_by_qml, paulix_sector_by_qml)\n",
    "print(f'time cost: {time() - begin}')\n",
    "\n",
    "print(\"Number of qubit after tapering =\", len(H_tapered.wires))\n",
    "print(\"The tapered Hamiltonian is \\n\", H_tapered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "ecabdbcd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      " 0.005239568506 IIYXIIYIIII\n",
      "-0.005239568506 IIYYIIXIIII\n",
      " 0.005239568506 IIXXIIXIIII\n",
      " 0.005239568506 IIXYIIYIIII\n",
      " 0.005239568506 IIYXIIIIYII\n",
      "-0.005239568506 IIYYIIIIXII\n",
      " 0.005239568506 IIXXIIIIXII\n",
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      " 0.027168478471 ZZYXYIIIIII\n",
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      " 0.026562088048 ZZYXZZIIIIY\n",
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      " 0.026562088048 ZZXXZZIIIIX\n",
      " 0.026562088048 IIXYIIIIIIY\n",
      " 0.002152920301 ZZIXIIIIIII\n",
      " 0.002152920301 IZIXZIZIZIZ\n",
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      " 0.010879917885 IZXZIIZIZIZ\n",
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      "-0.015771034329 IZXZYZZIZIY\n",
      "-0.018456946463 ZZYZXZIIIIY\n",
      " 0.018456946463 IZYZXZZIZIY\n",
      " 0.015771034329 ZZXZYZIIIIY\n",
      "-0.002685912134 ZZXZXZIIIIX\n",
      " 0.123744329956 IIZIIZIIIII\n",
      " 0.022098288414 IZXZZZZIZIZ\n",
      " 0.022098288414 ZZXZIZIIIII\n",
      " 0.029894407857 ZZZIZXIIIII\n",
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      " 0.018221796314 ZIXZIXZIZIZ\n",
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      "-0.018221796314 ZZXZIXIIIIZ\n",
      "-0.011218370529 ZZXIXXIIIII\n",
      " 0.011218370529 IZXZYYZIZIZ\n",
      "-0.011218370529 ZZYIYXIIIII\n",
      "-0.011218370529 IZYZXYZIZIZ\n",
      "-0.015535884181 ZZXIIYIIIIY\n",
      " 0.015535884181 IZXZZXZIZIX\n",
      " 0.015535884181 ZZYIIYIIIIX\n",
      " 0.015535884181 IZYZZXZIZIY\n",
      " 0.204974939223 IIZIIIZIIII\n",
      " 0.023490448405 IZXZZIIIZIZ\n",
      " 0.023490448405 ZZXZIIZIIII\n",
      " 0.002331256007 ZZXIIIXIIII\n",
      " 0.002331256007 IZXZZIXIZIZ\n",
      " 0.002331256007 ZZYIIIYIIII\n",
      " 0.002331256007 IZYZZIYIZIZ\n",
      " 0.204974939223 IIZIIIIIZII\n",
      " 0.023490448405 IZXZZIZIIIZ\n",
      " 0.023490448405 ZZXZIIIIZII\n",
      " 0.002331256007 ZZXIIIIIXII\n",
      " 0.002331256007 IZXZZIZIXIZ\n",
      " 0.002331256007 ZZYIIIIIYII\n",
      " 0.002331256007 IZYZZIZIYIZ\n",
      " 0.094218580515 IIZIIIIIIIZ\n",
      "-0.000761659021 IZXZZIZIZII\n",
      "-0.000761659021 ZZXZIIIIIIZ\n",
      " 0.120780668563 ZZZIZZIIIIZ\n",
      " 0.029042479228 ZIXZIZZIZII\n",
      " 0.029042479228 IIXZZZIIIIZ\n",
      "-0.033992830644 ZZXIXZIIIIZ\n",
      "-0.033992830644 ZIXZXIZIZIZ\n",
      "-0.033992830644 ZZYIYZIIIIZ\n",
      "-0.033992830644 ZIYZYIZIZIZ\n",
      "-0.029804138249 ZZXIIIIIIIX\n",
      "-0.029804138249 ZIXZIZZIZIX\n",
      "-0.029804138249 ZZYIIIIIIIY\n",
      "-0.029804138249 ZIYZIZZIZIY\n",
      "-0.202004384016 ZIIIZIZIZIZ\n",
      "-0.245715327406 ZIZZZIZIZIZ\n",
      " 0.123744329956 IIIZZIIIIII\n",
      "-0.022098288414 ZZZXZIIIIII\n",
      "-0.022098288414 IZZXIIZIZIZ\n",
      "-0.029894407857 IIIZYZIIIIY\n",
      "-0.029894407857 IIIZXZIIIIX\n",
      " 0.018221796314 ZZZXYZIIIIY\n",
      " 0.018221796314 ZZZXXZIIIIX\n",
      "-0.018221796314 IZZXXZZIZIX\n",
      "-0.018221796314 IZZXYZZIZIY\n",
      " 0.011218370529 IZZYXYZIZIZ\n",
      " 0.011218370529 ZZIYXYIIIII\n",
      " 0.011218370529 IZZXXXZIZIZ\n",
      " 0.011218370529 ZZIXXXIIIII\n",
      " 0.015535884181 ZIZYYIZIZIZ\n",
      " 0.015535884181 IIIYYIIIIII\n",
      " 0.015535884181 IZZXXZZIZII\n",
      " 0.015535884181 ZZIXXZIIIIZ\n",
      " 0.086872372481 IIIZIZIIIII\n",
      " 0.002725929386 ZZIZZXIIIII\n",
      "-0.002725929386 IIIZIXIIIIZ\n",
      "-0.010879917885 ZZZXIZIIIII\n",
      "-0.010879917885 IZZXZZZIZIZ\n",
      "-0.002685912134 IIZXZXIIIII\n",
      "-0.015771034329 ZZZXIXIIIIZ\n",
      " 0.018456946463 ZIZYIYZIZIZ\n",
      "-0.018456946463 ZZZYIYIIIIZ\n",
      " 0.015771034329 ZIZXIXZIZIZ\n",
      " 0.002685912134 IZZXZXZIZII\n",
      " 0.204974939223 IIIZIIZIIII\n",
      "-0.023490448405 ZZZXIIZIIII\n",
      "-0.023490448405 IZZXZIIIZIZ\n",
      "-0.002331256007 IZZYZIYIZIZ\n",
      "-0.002331256007 ZZIYIIYIIII\n",
      "-0.002331256007 IZZXZIXIZIZ\n",
      "-0.002331256007 ZZIXIIXIIII\n",
      " 0.204974939223 IIIZIIIIZII\n",
      "-0.023490448405 ZZZXIIIIZII\n",
      "-0.023490448405 IZZXZIZIIIZ\n",
      "-0.002331256007 IZZYZIZIYIZ\n",
      "-0.002331256007 ZZIYIIIIYII\n",
      "-0.002331256007 IZZXZIZIXIZ\n",
      "-0.002331256007 ZZIXIIIIXII\n",
      " 0.120780668563 IIIZIIIIIIZ\n",
      "-0.029042479228 ZZZXIIIIIIZ\n",
      "-0.029042479228 IZZXZIZIZII\n",
      "-0.033992830644 IZZYZXZIZIY\n",
      "-0.033992830644 ZZIYIXIIIIY\n",
      " 0.033992830644 IZZXZYZIZIY\n",
      " 0.033992830644 ZZIXIYIIIIY\n",
      " 0.029804138249 ZIZYIZZIZIY\n",
      " 0.029804138249 IIIYZZIIIIY\n",
      " 0.029804138249 IZZXZIZIZIX\n",
      " 0.029804138249 ZZIXIIIIIIX\n",
      " 0.094218580515 ZZIZZZIIIIZ\n",
      " 0.000761659021 IIZXZZIIIIZ\n",
      " 0.000761659021 ZIZXIZZIZII\n",
      " 0.119897511974 IIIIZZIIIII\n",
      "-0.021980989825 IIIIYIIIIIY\n",
      "-0.021980989825 IIIIXIIIIIX\n",
      " 0.017658858081 IIIIYXYIIII\n",
      "-0.017658858081 IIIIYYXIIII\n",
      " 0.017658858081 IIIIXXXIIII\n",
      " 0.017658858081 IIIIXYYIIII\n",
      " 0.017658858081 IIIIYXIIYII\n",
      "-0.017658858081 IIIIYYIIXII\n",
      " 0.017658858081 IIIIXXIIXII\n",
      " 0.017658858081 IIIIXYIIYII\n",
      " 0.021980989825 ZZIIIXIIIII\n",
      "-0.021980989825 IIIIZXIIIIZ\n",
      " 0.018377485108 ZZIIXYIIIIY\n",
      "-0.018377485108 IIIIYYIIIIX\n",
      "-0.018377485108 ZZIIYYIIIIX\n",
      " 0.018377485108 IIIIXYIIIIY\n",
      " 0.011747610874 ZIIZXXZIZIZ\n",
      "-0.011747610874 IIIIYYIIIII\n",
      " 0.011747610874 IIZZXXIIIII\n",
      "-0.011747610874 ZIZIYYZIZIZ\n",
      " 0.197632440847 IIIIZIZIIII\n",
      "-0.027220781240 IIIIYZZIIIY\n",
      "-0.027220781240 IIIIXZZIIIX\n",
      "-0.009114676967 ZZIIXIXIIII\n",
      "-0.009114676967 IIIIYZYIIIZ\n",
      "-0.009114676967 ZZIIYIYIIII\n",
      "-0.009114676967 IIIIXZXIIIZ\n",
      " 0.197632440847 IIIIZIIIZII\n",
      "-0.027220781240 IIIIYZIIZIY\n",
      "-0.027220781240 IIIIXZIIZIX\n",
      "-0.009114676967 ZZIIXIIIXII\n",
      "-0.009114676967 IIIIYZIIYIZ\n",
      "-0.009114676967 ZZIIYIIIYII\n",
      "-0.009114676967 IIIIXZIIXIZ\n",
      " 0.094803915104 IIIIZIIIIIZ\n",
      " 0.113181400212 ZZIIIZIIIIZ\n",
      " 0.024996812058 ZZIIXIIIIIX\n",
      " 0.024996812058 ZZIIYIIIIIY\n",
      " 0.015932894580 ZIIZXZZIZII\n",
      " 0.015932894580 ZZIIXIIIIII\n",
      " 0.015932894580 IIZZXZIIIIZ\n",
      " 0.015932894580 IZZIXIZIZIZ\n",
      "-0.099753100831 ZIZIIIZIZIZ\n",
      "-0.012614494134 ZIZIXZZIZIX\n",
      "-0.012614494134 ZIZIYZZIZIY\n",
      "-0.111500711705 ZIIZIIZIZIZ\n",
      "-0.028547388714 ZIIZXZZIZIX\n",
      "-0.028547388714 ZIIZYZZIZIY\n",
      " 0.197632440847 IIIIIZZIIII\n",
      " 0.027220781240 ZZIIZXZIIII\n",
      "-0.027220781240 IIIIIXZIIIZ\n",
      "-0.009114676967 IIIIIYXIIIY\n",
      " 0.009114676967 IIIIIYYIIIX\n",
      " 0.009114676967 IIIIIXYIIIY\n",
      " 0.009114676967 IIIIIXXIIIX\n",
      " 0.197632440847 IIIIIZIIZII\n",
      " 0.027220781240 ZZIIZXIIZII\n",
      "-0.027220781240 IIIIIXIIZIZ\n",
      "-0.009114676967 IIIIIYIIXIY\n",
      " 0.009114676967 IIIIIYIIYIX\n",
      " 0.009114676967 IIIIIXIIYIY\n",
      " 0.009114676967 IIIIIXIIXIX\n",
      " 0.113181400212 IIIIIZIIIIZ\n",
      " 0.024996812058 ZZIIZXIIIIZ\n",
      "-0.024996812058 IIIIIXIIIII\n",
      " 0.015932894580 ZIIZZYZIZIY\n",
      " 0.015932894580 IIZZIYIIIIY\n",
      "-0.015932894580 IIIIIXIIIIX\n",
      "-0.015932894580 ZIZIZXZIZIX\n",
      " 0.094803915104 ZZIIZIIIIIZ\n",
      "-0.111500711705 ZIZIZZZIZIZ\n",
      "-0.028547388714 IZZIIXZIZIZ\n",
      " 0.028547388714 ZIZIZXZIZII\n",
      "-0.099753100831 ZIIZZZZIZIZ\n",
      "-0.012614494134 IZIZIXZIZIZ\n",
      " 0.012614494134 ZIIZZXZIZII\n",
      " 0.012124691337 IIIIIIYIYII\n",
      " 0.012124691337 IIIIIIXIXII\n",
      " 0.007890709359 ZZIIZZYIIIY\n",
      " 0.007890709359 IIIIIIXIIIX\n",
      " 0.007890709359 ZZIIZZXIIIX\n",
      " 0.007890709359 IIIIIIYIIIY\n",
      " 0.002398511938 ZIIZZIXIZIZ\n",
      " 0.002398511938 IIIIIIXIIII\n",
      " 0.002398511938 IIZZIIXIIII\n",
      " 0.002398511938 ZIZIZIXIZIZ\n",
      " 0.389235633557 IIIIIIZIZII\n",
      " 0.190380873170 IIIIIIZIIIZ\n",
      " 0.190380873170 ZZIIZZZIIIZ\n",
      "-0.185413854187 ZIZIZIIIZIZ\n",
      "-0.185413854187 ZIIZZIIIZIZ\n",
      " 0.007890709359 ZZIIZZIIYIY\n",
      " 0.007890709359 IIIIIIIIXIX\n",
      " 0.007890709359 ZZIIZZIIXIX\n",
      " 0.007890709359 IIIIIIIIYIY\n",
      " 0.002398511938 ZIIZZIZIXIZ\n",
      " 0.002398511938 IIIIIIIIXII\n",
      " 0.002398511938 IIZZIIIIXII\n",
      " 0.002398511938 ZIZIZIZIXIZ\n",
      " 0.190380873170 IIIIIIIIZIZ\n",
      " 0.190380873170 ZZIIZZIIZIZ\n",
      "-0.185413854187 ZIZIZIZIIIZ\n",
      "-0.185413854187 ZIIZZIZIIIZ\n",
      " 0.115143201940 ZZIIZZIIIII\n",
      " 0.038640664631 ZIIZZIZIZIX\n",
      " 0.038640664631 ZZIIZZIIIIX\n",
      " 0.038640664631 IIZZIIIIIIX\n",
      " 0.038640664631 IZZIIZZIZIX\n",
      "-0.077170806134 ZIZIZIZIZII\n",
      "-0.115811470765 ZIIZZIZIZII\n",
      "-0.115811470765 IZZIIZZIZII\n",
      "-0.077170806134 IZIZIZZIZII\n"
     ]
    }
   ],
   "source": [
    "Hami_reduced_by_qml = create_pauliwords_from_hamilton(H_tapered, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b1f9e68",
   "metadata": {},
   "source": [
    "## 4.2 Tapering using mytarpering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "59de12ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-6.311794785724 IIIIIIIIIIIIII\n",
      " 2.467346884917 ZIIIIIIIIIIIII\n",
      " 2.467346884917 IZIIIIIIIIIIII\n",
      " 0.559461224125 ZZIIIIIIIIIIII\n",
      " 0.067832693201 YZZZYIIIIIIIII\n",
      " 0.078415863800 YIZZYIIIIIIIII\n",
      " 0.067832693201 XZZZXIIIIIIIII\n",
      " 0.078415863800 XIZZXIIIIIIIII\n",
      " 0.048277063636 YZZZZZZZZZYIII\n",
      " 0.043293922289 YIZZZZZZZZYIII\n",
      " 0.048277063636 XZZZZZZZZZXIII\n",
      " 0.043293922289 XIZZZZZZZZXIII\n",
      " 0.004668976323 YXXYIIIIIIIIII\n",
      "-0.004668976323 YYXXIIIIIIIIII\n",
      "-0.004668976323 XXYYIIIIIIIIII\n",
      " 0.004668976323 XYYXIIIIIIIIII\n",
      "-0.000163938150 YXIXZZZZZZZZYI\n",
      "-0.000163938150 YYIYZZZZZZZZYI\n",
      "-0.000163938150 XXIXZZZZZZZZXI\n",
      "-0.000163938150 XYIYZZZZZZZZXI\n",
      " 0.067832693201 IYZZZYIIIIIIII\n",
      " 0.078415863800 ZYZZZYIIIIIIII\n",
      " 0.067832693201 IXZZZXIIIIIIII\n",
      " 0.078415863800 ZXZZZXIIIIIIII\n",
      " 0.018021322949 YXIIXYIIIIIIII\n",
      "-0.018021322949 YYIIXXIIIIIIII\n",
      "-0.018021322949 XXIIYYIIIIIIII\n",
      " 0.018021322949 XYIIYXIIIIIIII\n",
      "-0.010764826109 YXIIIXZZZZYIII\n",
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      " 0.018456946463 IIXZXIIIIIYZYI\n",
      " 0.015771034329 IIXZXIIIIIXZXI\n",
      "-0.002685912134 IIXZYIIIIIYZXI\n",
      " 0.123744329956 IIZIIZIIIIIIII\n",
      "-0.022098288414 IIYZZIZZZZZZYI\n",
      "-0.022098288414 IIXZZIZZZZZZXI\n",
      "-0.029894407857 IIZIIYZZZZZYII\n",
      "-0.029894407857 IIZIIXZZZZZXII\n",
      "-0.018221796314 IIYZZXIIIIIXYI\n",
      "-0.018221796314 IIYZZYIIIIIYYI\n",
      "-0.018221796314 IIXZZXIIIIIXXI\n",
      "-0.018221796314 IIXZZYIIIIIYXI\n",
      " 0.011218370529 IIYZYYZZZZZZZY\n",
      " 0.011218370529 IIYZYXZZZZZZZX\n",
      " 0.011218370529 IIXZXYZZZZZZZY\n",
      " 0.011218370529 IIXZXXZZZZZZZX\n",
      " 0.015535884181 IIYZZXIIIIXZZY\n",
      "-0.015535884181 IIYZZYIIIIXZZX\n",
      "-0.015535884181 IIXZZXIIIIYZZY\n",
      " 0.015535884181 IIXZZYIIIIYZZX\n",
      " 0.099867685359 IIZIIIZIIIIIII\n",
      "-0.012910852206 IIYZZZIZZZZZYI\n",
      "-0.012910852206 IIXZZZIZZZZZXI\n",
      " 0.105107253865 IIZIIIIZIIIIII\n",
      "-0.010579596199 IIYZZZZIZZZZYI\n",
      "-0.010579596199 IIXZZZZIZZZZXI\n",
      "-0.002331256007 IIYZZZYYZZZZZY\n",
      "-0.002331256007 IIYZZZYXZZZZZX\n",
      "-0.002331256007 IIXZZZXYZZZZZY\n",
      "-0.002331256007 IIXZZZXXZZZZZX\n",
      " 0.099867685359 IIZIIIIIZIIIII\n",
      "-0.012910852206 IIYZZZZZIZZZYI\n",
      "-0.012910852206 IIXZZZZZIZZZXI\n",
      " 0.105107253865 IIZIIIIIIZIIII\n",
      "-0.010579596199 IIYZZZZZZIZZYI\n",
      "-0.010579596199 IIXZZZZZZIZZXI\n",
      "-0.002331256007 IIYZZZZZYYZZZY\n",
      "-0.002331256007 IIYZZZZZYXZZZX\n",
      "-0.002331256007 IIXZZZZZXYZZZY\n",
      "-0.002331256007 IIXZZZZZXXZZZX\n",
      " 0.094218580515 IIZIIIIIIIZIII\n",
      " 0.000761659021 IIYZZZZZZZIZYI\n",
      " 0.000761659021 IIXZZZZZZZIZXI\n",
      " 0.120780668563 IIZIIIIIIIIZII\n",
      "-0.029042479228 IIYZZZZZZZZIYI\n",
      "-0.029042479228 IIXZZZZZZZZIXI\n",
      " 0.033992830644 IIYZYIIIIIIYZY\n",
      " 0.033992830644 IIYZYIIIIIIXZX\n",
      " 0.033992830644 IIXZXIIIIIIYZY\n",
      " 0.033992830644 IIXZXIIIIIIXZX\n",
      " 0.029804138249 IIYZZZZZZZYYZY\n",
      " 0.029804138249 IIYZZZZZZZYXZX\n",
      " 0.029804138249 IIXZZZZZZZXYZY\n",
      " 0.029804138249 IIXZZZZZZZXXZX\n",
      " 0.101002192008 IIZIIIIIIIIIZI\n",
      " 0.122857663703 IIZIIIIIIIIIIZ\n",
      "-0.032704353418 IIYZZZZZZZZZYZ\n",
      "-0.032704353418 IIXZZZZZZZZZXZ\n",
      " 0.123744329956 IIIZZIIIIIIIII\n",
      "-0.022098288414 IIIYIZZZZZZZZY\n",
      "-0.022098288414 IIIXIZZZZZZZZX\n",
      "-0.029894407857 IIIZYZZZZZYIII\n",
      "-0.029894407857 IIIZXZZZZZXIII\n",
      "-0.018221796314 IIIYXIIIIIXZZY\n",
      "-0.018221796314 IIIYYIIIIIYZZY\n",
      "-0.018221796314 IIIXXIIIIIXZZX\n",
      "-0.018221796314 IIIXYIIIIIYZZX\n",
      " 0.011218370529 IIIYXXZZZZZZYI\n",
      "-0.011218370529 IIIYYXZZZZZZXI\n",
      "-0.011218370529 IIIXXYZZZZZZYI\n",
      " 0.011218370529 IIIXYYZZZZZZXI\n",
      " 0.015535884181 IIIYXIIIIIIXYI\n",
      "-0.015535884181 IIIYYIIIIIIXXI\n",
      "-0.015535884181 IIIXXIIIIIIYYI\n",
      " 0.015535884181 IIIXYIIIIIIYXI\n",
      " 0.086872372481 IIIZIZIIIIIIII\n",
      "-0.002725929386 IIIZIYZZZZZYII\n",
      "-0.002725929386 IIIZIXZZZZZXII\n",
      "-0.010879917885 IIIYZIZZZZZZZY\n",
      "-0.010879917885 IIIXZIZZZZZZZX\n",
      "-0.002685912134 IIIYZXIIIIIXZY\n",
      " 0.015771034329 IIIYZYIIIIIYZY\n",
      " 0.018456946463 IIIYZYIIIIIXZX\n",
      " 0.018456946463 IIIXZXIIIIIYZY\n",
      " 0.015771034329 IIIXZXIIIIIXZX\n",
      "-0.002685912134 IIIXZYIIIIIYZX\n",
      " 0.105107253865 IIIZIIZIIIIIII\n",
      "-0.010579596199 IIIYZZIZZZZZZY\n",
      "-0.010579596199 IIIXZZIZZZZZZX\n",
      "-0.002331256007 IIIYZZXXZZZZYI\n",
      " 0.002331256007 IIIYZZYXZZZZXI\n",
      " 0.002331256007 IIIXZZXYZZZZYI\n",
      "-0.002331256007 IIIXZZYYZZZZXI\n",
      " 0.099867685359 IIIZIIIZIIIIII\n",
      "-0.012910852206 IIIYZZZIZZZZZY\n",
      "-0.012910852206 IIIXZZZIZZZZZX\n",
      " 0.105107253865 IIIZIIIIZIIIII\n",
      "-0.010579596199 IIIYZZZZIZZZZY\n",
      "-0.010579596199 IIIXZZZZIZZZZX\n",
      "-0.002331256007 IIIYZZZZXXZZYI\n",
      " 0.002331256007 IIIYZZZZYXZZXI\n",
      " 0.002331256007 IIIXZZZZXYZZYI\n",
      "-0.002331256007 IIIXZZZZYYZZXI\n",
      " 0.099867685359 IIIZIIIIIZIIII\n",
      "-0.012910852206 IIIYZZZZZIZZZY\n",
      "-0.012910852206 IIIXZZZZZIZZZX\n",
      " 0.120780668563 IIIZIIIIIIZIII\n",
      "-0.029042479228 IIIYZZZZZZIZZY\n",
      "-0.029042479228 IIIXZZZZZZIZZX\n",
      " 0.033992830644 IIIYZYIIIIYZYI\n",
      " 0.033992830644 IIIYZYIIIIXZXI\n",
      " 0.033992830644 IIIXZXIIIIYZYI\n",
      " 0.033992830644 IIIXZXIIIIXZXI\n",
      " 0.029804138249 IIIYZZZZZZXXYI\n",
      "-0.029804138249 IIIYZZZZZZYXXI\n",
      "-0.029804138249 IIIXZZZZZZXYYI\n",
      " 0.029804138249 IIIXZZZZZZYYXI\n",
      " 0.094218580515 IIIZIIIIIIIZII\n",
      " 0.000761659021 IIIYZZZZZZZIZY\n",
      " 0.000761659021 IIIXZZZZZZZIZX\n",
      " 0.122857663703 IIIZIIIIIIIIZI\n",
      "-0.032704353418 IIIYZZZZZZZZIY\n",
      "-0.032704353418 IIIXZZZZZZZZIX\n",
      " 0.101002192008 IIIZIIIIIIIIIZ\n",
      " 0.119897511974 IIIIZZIIIIIIII\n",
      "-0.021980989825 IIIIYIZZZZYIII\n",
      "-0.021980989825 IIIIXIZZZZXIII\n",
      " 0.017658858081 IIIIYXXYIIIIII\n",
      "-0.017658858081 IIIIYYXXIIIIII\n",
      "-0.017658858081 IIIIXXYYIIIIII\n",
      " 0.017658858081 IIIIXYYXIIIIII\n",
      " 0.017658858081 IIIIYXIIXYIIII\n",
      "-0.017658858081 IIIIYYIIXXIIII\n",
      "-0.017658858081 IIIIXXIIYYIIII\n",
      " 0.017658858081 IIIIXYIIYXIIII\n",
      "-0.021980989825 IIIIZYZZZZZYII\n",
      "-0.021980989825 IIIIZXZZZZZXII\n",
      " 0.018377485108 IIIIYXIIIIXYII\n",
      "-0.018377485108 IIIIYYIIIIXXII\n",
      "-0.018377485108 IIIIXXIIIIYYII\n",
      " 0.018377485108 IIIIXYIIIIYXII\n",
      " 0.011747610874 IIIIYXIIIIIIXY\n",
      "-0.011747610874 IIIIYYIIIIIIXX\n",
      "-0.011747610874 IIIIXXIIIIIIYY\n",
      " 0.011747610874 IIIIXYIIIIIIYX\n",
      " 0.089986791383 IIIIZIZIIIIIII\n",
      "-0.018167729103 IIIIYZIZZZYIII\n",
      "-0.018167729103 IIIIXZIZZZXIII\n",
      " 0.107645649464 IIIIZIIZIIIIII\n",
      "-0.009053052136 IIIIYZZIZZYIII\n",
      "-0.009053052136 IIIIXZZIZZXIII\n",
      "-0.009114676967 IIIIYZYYZZZYII\n",
      "-0.009114676967 IIIIYZYXZZZXII\n",
      "-0.009114676967 IIIIXZXYZZZYII\n",
      "-0.009114676967 IIIIXZXXZZZXII\n",
      " 0.089986791383 IIIIZIIIZIIIII\n",
      "-0.018167729103 IIIIYZZZIZYIII\n",
      "-0.018167729103 IIIIXZZZIZXIII\n",
      " 0.107645649464 IIIIZIIIIZIIII\n",
      "-0.009053052136 IIIIYZZZZIYIII\n",
      "-0.009053052136 IIIIXZZZZIXIII\n",
      "-0.009114676967 IIIIYZZZYYZYII\n",
      "-0.009114676967 IIIIYZZZYXZXII\n",
      "-0.009114676967 IIIIXZZZXYZYII\n",
      "-0.009114676967 IIIIXZZZXXZXII\n",
      " 0.094803915104 IIIIZIIIIIZIII\n",
      " 0.113181400212 IIIIZIIIIIIZII\n",
      "-0.024996812058 IIIIYZZZZZYZII\n",
      "-0.024996812058 IIIIXZZZZZXZII\n",
      " 0.015932894580 IIIIYZZZZZZXXY\n",
      "-0.015932894580 IIIIYZZZZZZYXX\n",
      "-0.015932894580 IIIIXZZZZZZXYY\n",
      " 0.015932894580 IIIIXZZZZZZYYX\n",
      " 0.099753100831 IIIIZIIIIIIIZI\n",
      "-0.012614494134 IIIIYZZZZZYIZI\n",
      "-0.012614494134 IIIIXZZZZZXIZI\n",
      " 0.111500711705 IIIIZIIIIIIIIZ\n",
      "-0.028547388714 IIIIYZZZZZYIIZ\n",
      "-0.028547388714 IIIIXZZZZZXIIZ\n",
      " 0.107645649464 IIIIIZZIIIIIII\n",
      "-0.009053052136 IIIIIYIZZZZYII\n",
      "-0.009053052136 IIIIIXIZZZZXII\n",
      "-0.009114676967 IIIIIYXXZZYIII\n",
      " 0.009114676967 IIIIIYYXZZXIII\n",
      " 0.009114676967 IIIIIXXYZZYIII\n",
      "-0.009114676967 IIIIIXYYZZXIII\n",
      " 0.089986791383 IIIIIZIZIIIIII\n",
      "-0.018167729103 IIIIIYZIZZZYII\n",
      "-0.018167729103 IIIIIXZIZZZXII\n",
      " 0.107645649464 IIIIIZIIZIIIII\n",
      "-0.009053052136 IIIIIYZZIZZYII\n",
      "-0.009053052136 IIIIIXZZIZZXII\n",
      "-0.009114676967 IIIIIYZZXXYIII\n",
      " 0.009114676967 IIIIIYZZYXXIII\n",
      " 0.009114676967 IIIIIXZZXYYIII\n",
      "-0.009114676967 IIIIIXZZYYXIII\n",
      " 0.089986791383 IIIIIZIIIZIIII\n",
      "-0.018167729103 IIIIIYZZZIZYII\n",
      "-0.018167729103 IIIIIXZZZIZXII\n",
      " 0.113181400212 IIIIIZIIIIZIII\n",
      "-0.024996812058 IIIIIYZZZZIYII\n",
      "-0.024996812058 IIIIIXZZZZIXII\n",
      "-0.015932894580 IIIIIYZZZZXIXY\n",
      "-0.015932894580 IIIIIYZZZZYIYY\n",
      "-0.015932894580 IIIIIXZZZZXIXX\n",
      "-0.015932894580 IIIIIXZZZZYIYX\n",
      " 0.094803915104 IIIIIZIIIIIZII\n",
      " 0.111500711705 IIIIIZIIIIIIZI\n",
      "-0.028547388714 IIIIIYZZZZZYZI\n",
      "-0.028547388714 IIIIIXZZZZZXZI\n",
      " 0.099753100831 IIIIIZIIIIIIIZ\n",
      "-0.012614494134 IIIIIYZZZZZYIZ\n",
      "-0.012614494134 IIIIIXZZZZZXIZ\n",
      " 0.112464772560 IIIIIIZZIIIIII\n",
      " 0.006062345668 IIIIIIYXXYIIII\n",
      "-0.006062345668 IIIIIIYYXXIIII\n",
      "-0.006062345668 IIIIIIXXYYIIII\n",
      " 0.006062345668 IIIIIIXYYXIIII\n",
      " 0.007890709359 IIIIIIYXIIXYII\n",
      "-0.007890709359 IIIIIIYYIIXXII\n",
      "-0.007890709359 IIIIIIXXIIYYII\n",
      " 0.007890709359 IIIIIIXYIIYXII\n",
      " 0.002398511938 IIIIIIYXIIIIXY\n",
      "-0.002398511938 IIIIIIYYIIIIXX\n",
      "-0.002398511938 IIIIIIXXIIIIYY\n",
      " 0.002398511938 IIIIIIXYIIIIYX\n",
      " 0.094277735555 IIIIIIZIZIIIII\n",
      " 0.100340081223 IIIIIIZIIZIIII\n",
      " 0.091245081906 IIIIIIZIIIZIII\n",
      " 0.099135791264 IIIIIIZIIIIZII\n",
      " 0.091507671124 IIIIIIZIIIIIZI\n",
      " 0.093906183062 IIIIIIZIIIIIIZ\n",
      " 0.100340081223 IIIIIIIZZIIIII\n",
      " 0.094277735555 IIIIIIIZIZIIII\n",
      " 0.099135791264 IIIIIIIZIIZIII\n",
      " 0.091245081906 IIIIIIIZIIIZII\n",
      " 0.093906183062 IIIIIIIZIIIIZI\n",
      " 0.091507671124 IIIIIIIZIIIIIZ\n",
      " 0.112464772560 IIIIIIIIZZIIII\n",
      " 0.007890709359 IIIIIIIIYXXYII\n",
      "-0.007890709359 IIIIIIIIYYXXII\n",
      "-0.007890709359 IIIIIIIIXXYYII\n",
      " 0.007890709359 IIIIIIIIXYYXII\n",
      " 0.002398511938 IIIIIIIIYXIIXY\n",
      "-0.002398511938 IIIIIIIIYYIIXX\n",
      "-0.002398511938 IIIIIIIIXXIIYY\n",
      " 0.002398511938 IIIIIIIIXYIIYX\n",
      " 0.091245081906 IIIIIIIIZIZIII\n",
      " 0.099135791264 IIIIIIIIZIIZII\n",
      " 0.091507671124 IIIIIIIIZIIIZI\n",
      " 0.093906183062 IIIIIIIIZIIIIZ\n",
      " 0.099135791264 IIIIIIIIIZZIII\n",
      " 0.091245081906 IIIIIIIIIZIZII\n",
      " 0.093906183062 IIIIIIIIIZIIZI\n",
      " 0.091507671124 IIIIIIIIIZIIIZ\n",
      " 0.115143201940 IIIIIIIIIIZZII\n",
      " 0.038640664631 IIIIIIIIIIYXXY\n",
      "-0.038640664631 IIIIIIIIIIYYXX\n",
      "-0.038640664631 IIIIIIIIIIXXYY\n",
      " 0.038640664631 IIIIIIIIIIXYYX\n",
      " 0.077170806134 IIIIIIIIIIZIZI\n",
      " 0.115811470765 IIIIIIIIIIZIIZ\n",
      " 0.115811470765 IIIIIIIIIIIZZI\n",
      " 0.077170806134 IIIIIIIIIIIZIZ\n",
      " 0.121236784142 IIIIIIIIIIIIZZ\n"
     ]
    }
   ],
   "source": [
    "Hami_ori = create_pauliwords_from_hamilton(H, qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "cb3f3df9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 1.999345302581787\n",
      "Number of qubit after tapering = 9\n",
      "The tapered Hamiltonian is \n",
      " -6.08686524+0.00000000j IIIIIIIII\n",
      "2.46734688+0.00000000j ZIIIIIIII\n",
      "2.46734688+0.00000000j IZIIIIIII\n",
      "0.55946122+0.00000000j ZZIIIIIII\n",
      "0.06783269+0.00000000j YZZZYIIII\n",
      "0.07841586+0.00000000j YIZZYIIII\n",
      "0.06783269+0.00000000j XZZZXIIII\n",
      "0.07841586+0.00000000j XIZZXIIII\n",
      "0.04827706+0.00000000j YZZZZZIIY\n",
      "0.04329392+0.00000000j YIZZZZIIY\n",
      "0.04827706+0.00000000j XZZZZZIIX\n",
      "0.04329392+0.00000000j XIZZZZIIX\n",
      "0.00466898+0.00000000j YXXYIIIII\n",
      "-0.00466898+0.00000000j YYXXIIIII\n",
      "-0.00466898+0.00000000j XXYYIIIII\n",
      "0.00466898+0.00000000j XYYXIIIII\n",
      "0.00016394+0.00000000j YYZXZIZZZ\n",
      "-0.00016394+0.00000000j YXZYZIZZZ\n",
      "0.00016394+0.00000000j YYIXIIIII\n",
      "-0.00016394+0.00000000j YXIYIIIII\n",
      "0.06783269+0.00000000j IYZZZYIII\n",
      "0.07841586+0.00000000j ZYZZZYIII\n",
      "0.06783269+0.00000000j IXZZZXIII\n",
      "0.07841586+0.00000000j ZXZZZXIII\n",
      "0.01802132+0.00000000j YXIIXYIII\n",
      "-0.01802132+0.00000000j YYIIXXIII\n",
      "-0.01802132+0.00000000j XXIIYYIII\n",
      "0.01802132+0.00000000j XYIIYXIII\n",
      "-0.01076483+0.00000000j YXIIIXIIY\n",
      "-0.01076483+0.00000000j YYIIIYIIY\n",
      "-0.01076483+0.00000000j XXIIIXIIX\n",
      "-0.01076483+0.00000000j XYIIIYIIX\n",
      "0.00396402+0.00000000j YXIIIIYII\n",
      "-0.00396402+0.00000000j YYIIIIXII\n",
      "0.00396402+0.00000000j XXIIIIXII\n",
      "0.00396402+0.00000000j XYIIIIYII\n",
      "0.00396402+0.00000000j YXIIIIIYI\n",
      "-0.00396402+0.00000000j YYIIIIIXI\n",
      "0.00396402+0.00000000j XXIIIIIXI\n",
      "0.00396402+0.00000000j XYIIIIIYI\n",
      "-0.04827706+0.00000000j ZXZZIIIII\n",
      "-0.04329392+0.00000000j IXZZIIIII\n",
      "0.04827706+0.00000000j IXZZZZIIZ\n",
      "0.04329392+0.00000000j ZXZZZZIIZ\n",
      "0.01076483+0.00000000j XYIIYIIII\n",
      "-0.01076483+0.00000000j YYIIXZIIZ\n",
      "-0.01076483+0.00000000j YYIIXIIII\n",
      "0.01076483+0.00000000j XYIIYZIIZ\n",
      "0.00707027+0.00000000j XYIIZZIIY\n",
      "-0.00707027+0.00000000j YYIIIIIIX\n",
      "-0.00707027+0.00000000j YYIIZZIIX\n",
      "0.00707027+0.00000000j XYIIIIIIY\n",
      "0.00016394+0.00000000j XYYIIIIII\n",
      "0.00016394+0.00000000j YXYZZIZZZ\n",
      "-0.00016394+0.00000000j YYXIIIIII\n",
      "0.00016394+0.00000000j XXXZZIZZZ\n",
      "0.00087277+0.00000000j XXIZZIZZZ\n",
      "-0.00087277+0.00000000j YYIIIIIII\n",
      "0.00087277+0.00000000j XXZZIIIII\n",
      "-0.00087277+0.00000000j YYZIZIZZZ\n",
      "0.08400533+0.00000000j IIZIIIIII\n",
      "0.15056039+0.00000000j ZIZIIIIII\n",
      "-0.01412095+0.00000000j IZXZZIZZZ\n",
      "-0.02919672+0.00000000j ZZXZZIZZZ\n",
      "-0.01412095+0.00000000j ZZXZIIIII\n",
      "-0.02919672+0.00000000j IZXZIIIII\n",
      "0.01072043+0.00000000j YZIZYIIII\n",
      "0.01072043+0.00000000j XZIZXIIII\n",
      "0.00615512+0.00000000j YZIZZZIIY\n",
      "0.00615512+0.00000000j XZIZZZIIX\n",
      "0.00200421+0.00000000j YIYIXIZZZ\n",
      "0.00125713+0.00000000j YIXIYIZZZ\n",
      "0.00326134+0.00000000j XIYIYIIII\n",
      "-0.00326134+0.00000000j XIYIYIZZZ\n",
      "-0.00125713+0.00000000j YIXIYIIII\n",
      "-0.00200421+0.00000000j YIYIXIIII\n",
      "0.00018149+0.00000000j YIYIIZZZX\n",
      "0.00608025+0.00000000j YIXIIZZZY\n",
      "0.00626174+0.00000000j XIYIZZIIY\n",
      "-0.00626174+0.00000000j XIYIIZZZY\n",
      "-0.00608025+0.00000000j YIXIZZIIY\n",
      "-0.00018149+0.00000000j YIYIZZIIX\n",
      "0.08400533+0.00000000j IIIZIIIII\n",
      "0.15522937+0.00000000j ZIIZIIIII\n",
      "0.00145185+0.00000000j YZZIYIIII\n",
      "0.00145185+0.00000000j XZZIXIIII\n",
      "-0.00204031+0.00000000j YZZIZZIIY\n",
      "-0.00204031+0.00000000j XZZIZZIIX\n",
      "0.00926858+0.00000000j YZYYZYIII\n",
      "0.00926858+0.00000000j YZYXZXIII\n",
      "0.00926858+0.00000000j XZXYZYIII\n",
      "0.00926858+0.00000000j XZXXZXIII\n",
      "0.00267327+0.00000000j YIIXIYZZZ\n",
      "-0.00267327+0.00000000j YIIYIXZZZ\n",
      "0.00267327+0.00000000j YIZXZYIII\n",
      "-0.00267327+0.00000000j YIZYZXIII\n",
      "-0.00819543+0.00000000j XIYYIIIII\n",
      "0.00819543+0.00000000j YZYXZZIIZ\n",
      "0.00819543+0.00000000j YIXYIIIII\n",
      "0.00819543+0.00000000j XZXXZZIIZ\n",
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      "0.20497494+0.00000000j IIIZIIZII\n",
      "0.02349045+0.00000000j ZZZXIIZII\n",
      "0.02349045+0.00000000j IZZXZIIZZ\n",
      "0.00233126+0.00000000j IZZYZIYZZ\n",
      "0.00233126+0.00000000j ZZIYIIYII\n",
      "0.00233126+0.00000000j IZZXZIXZZ\n",
      "0.00233126+0.00000000j ZZIXIIXII\n",
      "0.20497494+0.00000000j IIIZIIIZI\n",
      "0.02349045+0.00000000j ZZZXIIIZI\n",
      "0.02349045+0.00000000j IZZXZIZIZ\n",
      "0.00233126+0.00000000j IZZYZIZYZ\n",
      "0.00233126+0.00000000j ZZIYIIIYI\n",
      "0.00233126+0.00000000j IZZXZIZXZ\n",
      "0.00233126+0.00000000j ZZIXIIIXI\n",
      "0.12078067+0.00000000j IIIZIIIIZ\n",
      "0.02904248+0.00000000j ZZZXIIIIZ\n",
      "0.02904248+0.00000000j IZZXZIZZI\n",
      "0.03399283+0.00000000j IZZYZXZZY\n",
      "0.03399283+0.00000000j ZZIYIXIIY\n",
      "-0.03399283+0.00000000j IZZXZYZZY\n",
      "-0.03399283+0.00000000j ZZIXIYIIY\n",
      "-0.02980414+0.00000000j ZIZYIZZZY\n",
      "-0.02980414+0.00000000j IIIYZZIIY\n",
      "-0.02980414+0.00000000j IZZXZIZZX\n",
      "-0.02980414+0.00000000j ZZIXIIIIX\n",
      "0.09421858+0.00000000j ZZIZZZIIZ\n",
      "-0.00076166+0.00000000j IIZXZZIIZ\n",
      "-0.00076166+0.00000000j ZIZXIZZZI\n",
      "0.11989751+0.00000000j IIIIZZIII\n",
      "-0.02198099+0.00000000j IIIIYIIIY\n",
      "-0.02198099+0.00000000j IIIIXIIIX\n",
      "0.01765886+0.00000000j IIIIYXYII\n",
      "-0.01765886+0.00000000j IIIIYYXII\n",
      "0.01765886+0.00000000j IIIIXXXII\n",
      "0.01765886+0.00000000j IIIIXYYII\n",
      "0.01765886+0.00000000j IIIIYXIYI\n",
      "-0.01765886+0.00000000j IIIIYYIXI\n",
      "0.01765886+0.00000000j IIIIXXIXI\n",
      "0.01765886+0.00000000j IIIIXYIYI\n",
      "0.02198099+0.00000000j ZZIIIXIII\n",
      "-0.02198099+0.00000000j IIIIZXIIZ\n",
      "0.01837749+0.00000000j ZZIIXYIIY\n",
      "-0.01837749+0.00000000j IIIIYYIIX\n",
      "-0.01837749+0.00000000j ZZIIYYIIX\n",
      "0.01837749+0.00000000j IIIIXYIIY\n",
      "0.01174761+0.00000000j ZIIZXXZZZ\n",
      "-0.01174761+0.00000000j IIIIYYIII\n",
      "0.01174761+0.00000000j IIZZXXIII\n",
      "-0.01174761+0.00000000j ZIZIYYZZZ\n",
      "0.19763244+0.00000000j IIIIZIZII\n",
      "-0.02722078+0.00000000j IIIIYZZIY\n",
      "-0.02722078+0.00000000j IIIIXZZIX\n",
      "-0.00911468+0.00000000j ZZIIXIXII\n",
      "-0.00911468+0.00000000j IIIIYZYIZ\n",
      "-0.00911468+0.00000000j ZZIIYIYII\n",
      "-0.00911468+0.00000000j IIIIXZXIZ\n",
      "0.19763244+0.00000000j IIIIZIIZI\n",
      "-0.02722078+0.00000000j IIIIYZIZY\n",
      "-0.02722078+0.00000000j IIIIXZIZX\n",
      "-0.00911468+0.00000000j ZZIIXIIXI\n",
      "-0.00911468+0.00000000j IIIIYZIYZ\n",
      "-0.00911468+0.00000000j ZZIIYIIYI\n",
      "-0.00911468+0.00000000j IIIIXZIXZ\n",
      "0.09480392+0.00000000j IIIIZIIIZ\n",
      "0.11318140+0.00000000j ZZIIIZIIZ\n",
      "0.02499681+0.00000000j ZZIIXIIIX\n",
      "0.02499681+0.00000000j ZZIIYIIIY\n",
      "0.01593289+0.00000000j ZIIZXZZZI\n",
      "0.01593289+0.00000000j ZZIIXIIII\n",
      "0.01593289+0.00000000j IIZZXZIIZ\n",
      "0.01593289+0.00000000j IZZIXIZZZ\n",
      "-0.09975310+0.00000000j ZIZIIIZZZ\n",
      "-0.01261449+0.00000000j ZIZIXZZZX\n",
      "-0.01261449+0.00000000j ZIZIYZZZY\n",
      "-0.11150071+0.00000000j ZIIZIIZZZ\n",
      "-0.02854739+0.00000000j ZIIZXZZZX\n",
      "-0.02854739+0.00000000j ZIIZYZZZY\n",
      "0.19763244+0.00000000j IIIIIZZII\n",
      "0.02722078+0.00000000j ZZIIZXZII\n",
      "-0.02722078+0.00000000j IIIIIXZIZ\n",
      "-0.00911468+0.00000000j IIIIIYXIY\n",
      "0.00911468+0.00000000j IIIIIYYIX\n",
      "0.00911468+0.00000000j IIIIIXYIY\n",
      "0.00911468+0.00000000j IIIIIXXIX\n",
      "0.19763244+0.00000000j IIIIIZIZI\n",
      "0.02722078+0.00000000j ZZIIZXIZI\n",
      "-0.02722078+0.00000000j IIIIIXIZZ\n",
      "-0.00911468+0.00000000j IIIIIYIXY\n",
      "0.00911468+0.00000000j IIIIIYIYX\n",
      "0.00911468+0.00000000j IIIIIXIYY\n",
      "0.00911468+0.00000000j IIIIIXIXX\n",
      "0.11318140+0.00000000j IIIIIZIIZ\n",
      "0.02499681+0.00000000j ZZIIZXIIZ\n",
      "-0.02499681+0.00000000j IIIIIXIII\n",
      "0.01593289+0.00000000j ZIIZZYZZY\n",
      "0.01593289+0.00000000j IIZZIYIIY\n",
      "-0.01593289+0.00000000j IIIIIXIIX\n",
      "-0.01593289+0.00000000j ZIZIZXZZX\n",
      "0.09480392+0.00000000j ZZIIZIIIZ\n",
      "-0.11150071+0.00000000j ZIZIZZZZZ\n",
      "-0.02854739+0.00000000j IZZIIXZZZ\n",
      "0.02854739+0.00000000j ZIZIZXZZI\n",
      "-0.09975310+0.00000000j ZIIZZZZZZ\n",
      "-0.01261449+0.00000000j IZIZIXZZZ\n",
      "0.01261449+0.00000000j ZIIZZXZZI\n",
      "0.01212469+0.00000000j IIIIIIYYI\n",
      "0.01212469+0.00000000j IIIIIIXXI\n",
      "0.00789071+0.00000000j ZZIIZZYIY\n",
      "0.00789071+0.00000000j IIIIIIXIX\n",
      "0.00789071+0.00000000j ZZIIZZXIX\n",
      "0.00789071+0.00000000j IIIIIIYIY\n",
      "0.00239851+0.00000000j ZIIZZIXZZ\n",
      "0.00239851+0.00000000j IIIIIIXII\n",
      "0.00239851+0.00000000j IIZZIIXII\n",
      "0.00239851+0.00000000j ZIZIZIXZZ\n",
      "0.38923563+0.00000000j IIIIIIZZI\n",
      "0.19038087+0.00000000j IIIIIIZIZ\n",
      "0.19038087+0.00000000j ZZIIZZZIZ\n",
      "-0.18541385+0.00000000j ZIZIZIIZZ\n",
      "-0.18541385+0.00000000j ZIIZZIIZZ\n",
      "0.00789071+0.00000000j ZZIIZZIYY\n",
      "0.00789071+0.00000000j IIIIIIIXX\n",
      "0.00789071+0.00000000j ZZIIZZIXX\n",
      "0.00789071+0.00000000j IIIIIIIYY\n",
      "0.00239851+0.00000000j ZIIZZIZXZ\n",
      "0.00239851+0.00000000j IIIIIIIXI\n",
      "0.00239851+0.00000000j IIZZIIIXI\n",
      "0.00239851+0.00000000j ZIZIZIZXZ\n",
      "0.19038087+0.00000000j IIIIIIIZZ\n",
      "0.19038087+0.00000000j ZZIIZZIZZ\n",
      "-0.18541385+0.00000000j ZIZIZIZIZ\n",
      "-0.18541385+0.00000000j ZIIZZIZIZ\n",
      "0.11514320+0.00000000j ZZIIZZIII\n",
      "0.03864066+0.00000000j ZIIZZIZZX\n",
      "0.03864066+0.00000000j ZZIIZZIIX\n",
      "0.03864066+0.00000000j IIZZIIIIX\n",
      "0.03864066+0.00000000j IZZIIZZZX\n",
      "-0.07717081+0.00000000j ZIZIZIZZI\n",
      "-0.11581147+0.00000000j ZIIZZIZZI\n",
      "-0.11581147+0.00000000j IZZIIZZZI\n",
      "-0.07717081+0.00000000j IZIZIZZZI\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "Hami_reduced_by_tapering = tapering(Hami_ori, n_electrons)\n",
    "print(f'time cost: {time() - begin}')\n",
    "print(\"Number of qubit after tapering =\", Hami_reduced_by_tapering.num_qubits)\n",
    "print(\"The tapered Hamiltonian is \\n\", Hami_reduced_by_tapering)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a59865fa",
   "metadata": {},
   "source": [
    "## 4.3 compare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1add8449",
   "metadata": {},
   "source": [
    "### 4.3.1 generators and paulixops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "d67b5413",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1:   (1.0) [Z6 Z7], paulix_op: PauliX(wires=[7])\n",
      "generator 2:   (1.0) [Z8 Z9], paulix_op: PauliX(wires=[9])\n",
      "generator 3:   (1.0) [Z0 Z1 Z4 Z5 Z10 Z11], paulix_op: PauliX(wires=[11])\n",
      "generator 4:   (1.0) [Z0 Z2 Z4 Z6 Z8 Z10 Z12], paulix_op: PauliX(wires=[12])\n",
      "generator 5:   (1.0) [Z0 Z3 Z4 Z6 Z8 Z10 Z13], paulix_op: PauliX(wires=[13])\n"
     ]
    }
   ],
   "source": [
    "for idx, generator in enumerate(generators_by_qml):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulixops_by_qml[idx]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "3c6ab8b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1: 1.00000000 IIIIIIZZIIIIII, paulix_op: 1.00000000 IIIIIIIXIIIIII\n",
      "generator 2: 1.00000000 IIIIIIIIZZIIII, paulix_op: 1.00000000 IIIIIIIIIXIIII\n",
      "generator 3: 1.00000000 ZZIIZZIIIIZZII, paulix_op: 1.00000000 IIIIIIIIIIIXII\n",
      "generator 4: 1.00000000 ZIZIZIZIZIZIZI, paulix_op: 1.00000000 IIIIIIIIIIIIXI\n",
      "generator 5: 1.00000000 ZIIZZIZIZIZIIZ, paulix_op: 1.00000000 IIIIIIIIIIIIIX\n"
     ]
    }
   ],
   "source": [
    "generators_by_tapering_ = get_generators_from_kernel(\n",
    "    kernel_of_E(create_parity_check_matrix_E(*create_binary_matrix_G(Hami_ori)))\n",
    ")\n",
    "generators_by_tapering, paulix_ops_by_tapering = get_paulix_ops_from_generators(generators_by_tapering_)\n",
    "\n",
    "for idx, generator in enumerate(generators_by_tapering.terms):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulix_ops_by_tapering.terms[idx]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38e501cd",
   "metadata": {},
   "source": [
    "### 4.3.2 optimal sectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "000707d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sectors by qml: [1, 1, 1, -1, -1]\n",
      "sectors by tapering: [1, 1, 1, -1, -1]\n"
     ]
    }
   ],
   "source": [
    "print(f'sectors by qml: {paulix_sector_by_qml}')\n",
    "print(f'sectors by tapering: {optimal_sector(Hami_ori, generators_by_tapering, n_electrons)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dce4f8c0",
   "metadata": {},
   "source": [
    "# 5. Example: H6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bb568a86",
   "metadata": {},
   "outputs": [],
   "source": [
    "symbols = [\"H\", \"H\", \"H\", \"H\", \"H\", \"H\"]\n",
    "coordinates = np.array([\n",
    "    0.0, 0.0, 0.0,\n",
    "    0.0, 0.0, 0.5,\n",
    "    0.0, 0.0, 1.0,\n",
    "    0.0, 0.0, 1.5,\n",
    "    0.0, 0.0, 2.0,\n",
    "    0.0, 0.0, 2.5\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fe343f59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of qubits =  12\n",
      "The Hamiltonian is \n",
      "   (-5.517857995732383) [Z10]\n",
      "+ (-5.517857995732383) [Z11]\n",
      "+ (-2.975845114540733) [Z8]\n",
      "+ (-2.975845114540733) [Z9]\n",
      "+ (-1.2016688151928356) [Z6]\n",
      "+ (-1.2016688151928352) [Z7]\n",
      "+ (-0.3251277147960169) [Z4]\n",
      "+ (-0.3251277147960169) [Z5]\n",
      "+ (0.1581048642489347) [Z3]\n",
      "+ (0.1581048642489349) [Z2]\n",
      "+ (0.45859219444170546) [Z1]\n",
      "+ (0.45859219444170574) [Z0]\n",
      "+ (23.712173132473378) [I0]\n",
      "+ (-3.022426753318541e-11) [Y9 Y11]\n",
      "+ (-3.022426753318541e-11) [X9 X11]\n",
      "+ (-1.2464695942071558e-11) [Y8 Y10]\n",
      "+ (-1.2464695942071558e-11) [X8 X10]\n",
      "+ (-3.4363623058197845e-12) [Y6 Y8]\n",
      "+ (-3.4363623058197845e-12) [X6 X8]\n",
      "+ (-1.2825296380469808e-12) [Y7 Y9]\n",
      "+ (-1.2825296380469808e-12) [X7 X9]\n",
      "+ (0.11976424626602511) [Z2 Z4]\n",
      "+ (0.11976424626602511) [Z3 Z5]\n",
      "+ (0.1330796508182468) [Z0 Z2]\n",
      "+ (0.1330796508182468) [Z1 Z3]\n",
      "+ (0.13456238001270737) [Z4 Z6]\n",
      "+ (0.13456238001270737) [Z5 Z7]\n",
      "+ (0.13674367059913745) [Z0 Z4]\n",
      "+ (0.13674367059913745) [Z1 Z5]\n",
      "+ (0.14245208941941903) [Z2 Z6]\n",
      "+ (0.14245208941941903) [Z3 Z7]\n",
      "+ (0.15778728563045896) [Z0 Z5]\n",
      "+ (0.15778728563045896) [Z1 Z4]\n",
      "+ (0.1578077527220963) [Z2 Z5]\n",
      "+ (0.1578077527220963) [Z3 Z4]\n",
      "+ (0.16014029660776763) [Z4 Z8]\n",
      "+ (0.16014029660776763) [Z5 Z9]\n",
      "+ (0.16100668262843562) [Z0 Z6]\n",
      "+ (0.16100668262843562) [Z1 Z7]\n",
      "+ (0.16209443712517418) [Z4 Z5]\n",
      "+ (0.16409977462201278) [Z0 Z3]\n",
      "+ (0.16409977462201278) [Z1 Z2]\n",
      "+ (0.1662541541024697) [Z2 Z3]\n",
      "+ (0.1691410651020142) [Z4 Z7]\n",
      "+ (0.1691410651020142) [Z5 Z6]\n",
      "+ (0.17131204382534976) [Z2 Z8]\n",
      "+ (0.17131204382534976) [Z3 Z9]\n",
      "+ (0.17399354990281563) [Z2 Z7]\n",
      "+ (0.17399354990281563) [Z3 Z6]\n",
      "+ (0.17709098766654852) [Z4 Z10]\n",
      "+ (0.17709098766654852) [Z5 Z11]\n",
      "+ (0.1785346647102104) [Z6 Z8]\n",
      "+ (0.1785346647102104) [Z7 Z9]\n",
      "+ (0.18219775707037084) [Z0 Z7]\n",
      "+ (0.18219775707037084) [Z1 Z6]\n",
      "+ (0.18650350047920816) [Z2 Z10]\n",
      "+ (0.18650350047920816) [Z3 Z11]\n",
      "+ (0.18686865778039663) [Z4 Z9]\n",
      "+ (0.18686865778039663) [Z5 Z8]\n",
      "+ (0.19357026976186997) [Z2 Z9]\n",
      "+ (0.19357026976186997) [Z3 Z8]\n",
      "+ (0.19494437013254307) [Z4 Z11]\n",
      "+ (0.19494437013254307) [Z5 Z10]\n",
      "+ (0.19735801866826766) [Z0 Z1]\n",
      "+ (0.1981858479284604) [Z6 Z7]\n",
      "+ (0.19978387012086685) [Z0 Z8]\n",
      "+ (0.19978387012086685) [Z1 Z9]\n",
      "+ (0.2000035201642107) [Z2 Z11]\n",
      "+ (0.2000035201642107) [Z3 Z10]\n",
      "+ (0.20699892686051946) [Z6 Z10]\n",
      "+ (0.20699892686051946) [Z7 Z11]\n",
      "+ (0.21880674002503273) [Z0 Z9]\n",
      "+ (0.21880674002503273) [Z1 Z8]\n",
      "+ (0.2229372441548989) [Z6 Z9]\n",
      "+ (0.2229372441548989) [Z7 Z8]\n",
      "+ (0.2232522467220996) [Z0 Z10]\n",
      "+ (0.2232522467220996) [Z1 Z11]\n",
      "+ (0.2368954848924254) [Z6 Z11]\n",
      "+ (0.2368954848924254) [Z7 Z10]\n",
      "+ (0.23826929914681888) [Z0 Z11]\n",
      "+ (0.23826929914681888) [Z1 Z10]\n",
      "+ (0.24965503928473076) [Z8 Z10]\n",
      "+ (0.24965503928473076) [Z9 Z11]\n",
      "+ (0.2816867405800565) [Z8 Z9]\n",
      "+ (0.2977647650562876) [Z8 Z11]\n",
      "+ (0.2977647650562876) [Z9 Z10]\n",
      "+ (0.3379171678937851) [Z10 Z11]\n",
      "+ (-7.850747829607485e-12) [Y2 Z3 Y4]\n",
      "+ (-7.850747829607485e-12) [X2 Z3 X4]\n",
      "+ (-7.850747829607485e-12) [Y3 Z4 Y5]\n",
      "+ (-7.850747829607485e-12) [X3 Z4 X5]\n",
      "+ (-5.807137756774772e-12) [Y8 Z9 Y10]\n",
      "+ (-5.807137756774772e-12) [X8 Z9 X10]\n",
      "+ (-5.807137756774772e-12) [Y9 Z10 Y11]\n",
      "+ (-5.807137756774772e-12) [X9 Z10 X11]\n",
      "+ (8.823435038163296e-12) [Y4 Z5 Y6]\n",
      "+ (8.823435038163296e-12) [X4 Z5 X6]\n",
      "+ (8.823435038163296e-12) [Y5 Z6 Y7]\n",
      "+ (8.823435038163296e-12) [X5 Z6 X7]\n",
      "+ (1.0569316255537586e-11) [Y0 Z1 Y2]\n",
      "+ (1.0569316255537586e-11) [X0 Z1 X2]\n",
      "+ (1.0569316255537586e-11) [Y1 Z2 Y3]\n",
      "+ (1.0569316255537586e-11) [X1 Z2 X3]\n",
      "+ (1.6970359145718206e-11) [Y6 Z7 Y8]\n",
      "+ (1.6970359145718206e-11) [X6 Z7 X8]\n",
      "+ (1.6970359145718206e-11) [Y7 Z8 Y9]\n",
      "+ (1.6970359145718206e-11) [X7 Z8 X9]\n",
      "+ (-0.04810972577159944) [Y8 Y9 X10 X11]\n",
      "+ (-0.04810972577159944) [X8 X9 Y10 Y11]\n",
      "+ (-0.04440257944469472) [Y6 Y7 X8 X9]\n",
      "+ (-0.04440257944469472) [X6 X7 Y8 Y9]\n",
      "+ (-0.04361829361341196) [Y2 Z3 Z5 Y6]\n",
      "+ (-0.04361829361341196) [X2 Z3 Z5 X6]\n",
      "+ (-0.04361829361341196) [Y3 Z4 Z6 Y7]\n",
      "+ (-0.04361829361341196) [X3 Z4 Z6 X7]\n",
      "+ (-0.038043506456071234) [Y2 Y3 X4 X5]\n",
      "+ (-0.038043506456071234) [X2 X3 Y4 Y5]\n",
      "+ (-0.037589429913268635) [Y7 Y8 X9 X10]\n",
      "+ (-0.037589429913268635) [X7 X8 Y9 Y10]\n",
      "+ (-0.03457868508930684) [Y4 Y5 X6 X7]\n",
      "+ (-0.03457868508930684) [X4 X5 Y6 Y7]\n",
      "+ (-0.034392300627581335) [Y0 Z2 Z3 Y4]\n",
      "+ (-0.034392300627581335) [X0 Z2 Z3 X4]\n",
      "+ (-0.0340793410037879) [Y3 Z4 Z5 Y7]\n",
      "+ (-0.0340793410037879) [X3 Z4 Z5 X7]\n",
      "+ (-0.03375239040579545) [Y0 Z1 Z3 Y4]\n",
      "+ (-0.03375239040579545) [X0 Z1 Z3 X4]\n",
      "+ (-0.03375239040579545) [Y1 Z2 Z4 Y5]\n",
      "+ (-0.03375239040579545) [X1 Z2 Z4 X5]\n",
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      "+ (3.1719071813540722e-12) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X11]\n",
      "+ (3.205651022408773e-12) [Y1 Z2 Z3 Y4 X5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (3.205651022408773e-12) [X1 Z2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (3.493927369646599e-12) [Y2 Z3 Z4 Y5 X6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (3.493927369646599e-12) [X2 Z3 Z4 X5 Y6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (5.122319235439932e-12) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 X9 X10 Y11]\n",
      "+ (5.122319235439932e-12) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Y9 Y10 X11]\n",
      "+ (9.27238229141425e-05) [Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z11]\n",
      "+ (9.27238229141425e-05) [X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z11]\n",
      "+ (0.00023720635554858342) [Z0 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.00023720635554858342) [Z0 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.00023720635554858342) [Z1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.00023720635554858342) [Z1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.00045764520974532485) [Y2 Z3 Y4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.00045764520974532485) [Y2 Z3 Y4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.00045764520974532485) [X2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.00045764520974532485) [X2 Z3 X4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0021120059842583694) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Z9]\n",
      "+ (0.0021120059842583694) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Z9]\n",
      "+ (0.002856074535157923) [Y0 X1 X3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.002856074535157923) [Y0 Y1 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.002856074535157923) [X0 X1 X3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.002856074535157923) [X0 Y1 Y3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.004314373571140229) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 X8 X10 Y11]\n",
      "+ (0.004314373571140229) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y10 Y11]\n",
      "+ (0.004314373571140229) [X1 Z2 Z3 Z4 Z5 Z6 Z7 X8 X10 X11]\n",
      "+ (0.004314373571140229) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y10 X11]\n",
      "+ (0.004387623224511195) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Z10]\n",
      "+ (0.004387623224511195) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Z10]\n",
      "+ (0.004387623224511195) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y9 Z11]\n",
      "+ (0.004387623224511195) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X9 Z11]\n",
      "+ (0.0052575936455824535) [Y0 Z1 Z2 Z3 Z4 X5 X7 Z8 Z9 Y10]\n",
      "+ (0.0052575936455824535) [Y0 Z1 Z2 Z3 Z4 Y5 Y7 Z8 Z9 Y10]\n",
      "+ (0.0052575936455824535) [X0 Z1 Z2 Z3 Z4 X5 X7 Z8 Z9 X10]\n",
      "+ (0.0052575936455824535) [X0 Z1 Z2 Z3 Z4 Y5 Y7 Z8 Z9 X10]\n",
      "+ (0.0052575936455824535) [Y1 Z2 Z3 X4 X6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0052575936455824535) [Y1 Z2 Z3 Y4 Y6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.0052575936455824535) [X1 Z2 Z3 X4 X6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0052575936455824535) [X1 Z2 Z3 Y4 Y6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.005717758188931693) [Y0 Z1 Z2 X3 X5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.005717758188931693) [Y0 Z1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (0.005717758188931693) [X0 Z1 Z2 X3 X5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.005717758188931693) [X0 Z1 Z2 Y3 Y5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (0.005717758188931693) [Y1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.005717758188931693) [Y1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.005717758188931693) [X1 X2 X4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.005717758188931693) [X1 Y2 Y4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.005968376362975319) [Z0 Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y9]\n",
      "+ (0.005968376362975319) [Z0 X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X9]\n",
      "+ (0.008701996795648093) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Z11]\n",
      "+ (0.008701996795648093) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Z11]\n",
      "+ (0.008701996795648093) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y9 Z10]\n",
      "+ (0.008701996795648093) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X9 Z10]\n",
      "+ (0.009247238638247057) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X8 Z9 X10]\n",
      "+ (0.009247238638247057) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y8 Z9 Y10]\n",
      "+ (0.009247238638247057) [Y1 Z2 Z3 Z4 Z5 Z6 Y7 X9 Z10 X11]\n",
      "+ (0.009247238638247057) [X1 Z2 Z3 Z4 Z5 Z6 X7 Y9 Z10 Y11]\n",
      "+ (0.01097809352727358) [Y0 Z1 Z2 Z3 Z4 Z5 X6 X8 Z9 Y10]\n",
      "+ (0.01097809352727358) [X0 Z1 Z2 Z3 Z4 Z5 Y6 Y8 Z9 X10]\n",
      "+ (0.01097809352727358) [Y1 Z2 Z3 Z4 Z5 Z6 X7 X9 Z10 Y11]\n",
      "+ (0.01097809352727358) [X1 Z2 Z3 Z4 Z5 Z6 Y7 Y9 Z10 X11]\n",
      "+ (0.01737798563350058) [Y0 Z1 Y2 Y3 Z4 Z5 Z6 Z7 Z8 Y9]\n",
      "+ (0.01737798563350058) [Y0 Z1 Y2 X3 Z4 Z5 Z6 Z7 Z8 X9]\n",
      "+ (0.01737798563350058) [X0 Z1 X2 Y3 Z4 Z5 Z6 Z7 Z8 Y9]\n",
      "+ (0.01737798563350058) [X0 Z1 X2 X3 Z4 Z5 Z6 Z7 Z8 X9]\n",
      "+ (0.018395805092511458) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Y9]\n",
      "+ (0.018395805092511458) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X7 Z8 X9]\n",
      "+ (0.018395805092511458) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y7 Z8 Y9]\n",
      "+ (0.018395805092511458) [X0 Z1 Z2 Z3 Z4 Z5 X6 X7 Z8 X9]\n",
      "+ (0.020225332165524412) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y8 Z9 Y10]\n",
      "+ (0.020225332165524412) [X0 Z1 Z2 Z3 Z4 Z5 X6 X8 Z9 X10]\n",
      "+ (0.020225332165524412) [Y1 Z2 Z3 Z4 Z5 Z6 Y7 Y9 Z10 Y11]\n",
      "+ (0.020225332165524412) [X1 Z2 Z3 Z4 Z5 Z6 X7 X9 Z10 X11]\n",
      "+ (0.02310584032152868) [Y2 Z3 Z4 Z5 Z6 Z7 Y8 Y9 Z10 Y11]\n",
      "+ (0.02310584032152868) [Y2 Z3 Z4 Z5 Z6 Z7 Y8 X9 Z10 X11]\n",
      "+ (0.02310584032152868) [X2 Z3 Z4 Z5 Z6 Z7 X8 Y9 Z10 Y11]\n",
      "+ (0.02310584032152868) [X2 Z3 Z4 Z5 Z6 Z7 X8 X9 Z10 X11]\n",
      "+ (0.023114007814136472) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y9 Z10 Y11]\n",
      "+ (0.023114007814136472) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X9 Z10 X11]\n",
      "+ (0.023114007814136472) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y9 Z10 Y11]\n",
      "+ (0.023114007814136472) [X0 Z1 Z2 Z3 Z4 Z5 X6 X9 Z10 X11]\n",
      "+ (0.023114007814136472) [Y1 Z2 Z3 Z4 Z5 Z6 Y7 Y8 Z9 Y10]\n",
      "+ (0.023114007814136472) [Y1 Z2 Z3 Z4 Z5 Z6 Y7 X8 Z9 X10]\n",
      "+ (0.023114007814136472) [X1 Z2 Z3 Z4 Z5 Z6 X7 Y8 Z9 Y10]\n",
      "+ (0.023114007814136472) [X1 Z2 Z3 Z4 Z5 Z6 X7 X8 Z9 X10]\n",
      "+ (-6.319932858295241e-12) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10]\n",
      "+ (-6.319932858295241e-12) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10]\n",
      "+ (-6.319932858295241e-12) [Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-6.319932858295241e-12) [X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.016849724636877297) [Y0 Z1 Z2 Z3 Z4 X5 X6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.016849724636877297) [X0 Z1 Z2 Z3 Z4 Y5 Y6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.013866769175887472) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Y7 X8 Z9 Z10 X11]\n",
      "+ (-0.013866769175887472) [X0 Z1 Z2 Z3 Z4 Z5 Z6 X7 Y8 Z9 Z10 Y11]\n",
      "+ (-0.007936317282797714) [Y0 Z1 Z2 X3 X4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.007936317282797714) [X0 Z1 Z2 Y3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-0.004314373571140229) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X9 X10 Y11]\n",
      "+ (-0.004314373571140229) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y9 Y10 X11]\n",
      "+ (-0.0028560745351579224) [Y0 X1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-0.0028560745351579224) [X0 Y1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-3.205651022408773e-12) [Y0 Z1 Z2 Z3 Y4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-3.205651022408773e-12) [Y0 Z1 Z2 Z3 Y4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (-3.205651022408773e-12) [X0 Z1 Z2 Z3 X4 Y5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (-3.205651022408773e-12) [X0 Z1 Z2 Z3 X4 X5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (1.3703912137008611e-12) [Z0 Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (1.3703912137008611e-12) [Z0 X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (1.6484591469634324e-12) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y9 Z10 Y11]\n",
      "+ (1.6484591469634324e-12) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 X9 Z10 X11]\n",
      "+ (1.6484591469634324e-12) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Y9 Z10 Y11]\n",
      "+ (1.6484591469634324e-12) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 X9 Z10 X11]\n",
      "+ (2.3770152512980758e-12) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (2.3770152512980758e-12) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X7 Z8 Z9 Z10 X11]\n",
      "+ (2.3770152512980758e-12) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y7 Z8 Z9 Z10 Y11]\n",
      "+ (2.3770152512980758e-12) [X0 Z1 Z2 Z3 Z4 Z5 X6 X7 Z8 Z9 Z10 X11]\n",
      "+ (2.856721803556894e-12) [Y0 Z1 Y2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (2.856721803556894e-12) [Y0 Z1 Y2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (2.856721803556894e-12) [X0 Z1 X2 Y3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (2.856721803556894e-12) [X0 Z1 X2 X3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (3.1719071813540722e-12) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Y10 Z11]\n",
      "+ (3.1719071813540722e-12) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 X10 Z11]\n",
      "+ (0.0028560745351579224) [Y0 Y1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.0028560745351579224) [X0 X1 Y2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.004314373571140229) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y9 X10 X11]\n",
      "+ (0.004314373571140229) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X9 Y10 Y11]\n",
      "+ (0.007936317282797714) [Y0 Z1 Z2 Y3 X4 Z5 Z6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.007936317282797714) [X0 Z1 Z2 X3 Y4 Z5 Z6 Z7 Z8 Z9 Z10 Y11]\n",
      "+ (0.013866769175887472) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 X7 X8 Z9 Z10 Y11]\n",
      "+ (0.013866769175887472) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Y7 Y8 Z9 Z10 X11]\n",
      "+ (0.016849724636877297) [Y0 Z1 Z2 Z3 Z4 Y5 X6 Z7 Z8 Z9 Z10 X11]\n",
      "+ (0.016849724636877297) [X0 Z1 Z2 Z3 Z4 X5 Y6 Z7 Z8 Z9 Z10 Y11]\n",
      "--------------------\n",
      "Number of terms:  1471\n"
     ]
    }
   ],
   "source": [
    "# 基于JW变换构建的H2哈密顿量\n",
    "H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)\n",
    "print(\"Number of qubits = \", qubits)\n",
    "print(\"The Hamiltonian is \\n\", H)\n",
    "print(\"-\" * 20)\n",
    "print(\"Number of terms: \", len(H.ops))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76fd0c83",
   "metadata": {},
   "source": [
    "## 5.1 Tapering using QML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fb8b403b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 17.71953511238098\n",
      "Number of qubit after tapering = 10\n",
      "The tapered Hamiltonian is \n",
      "   ((-2.975845114540732+0j)) [Z8]\n",
      "+ ((-2.975845114540732+0j)) [Z9]\n",
      "+ ((-1.2016688151928352+0j)) [Z6]\n",
      "+ ((-1.2016688151928347+0j)) [Z7]\n",
      "+ ((-0.32512771479601676+0j)) [Z4]\n",
      "+ ((-0.32512771479601676+0j)) [Z5]\n",
      "+ ((3.1719071813540706e-12-0j)) [X0]\n",
      "+ ((1.2464695942071551e-11-0j)) [X8]\n",
      "+ ((3.02242675331854e-11-0j)) [X9]\n",
      "+ ((0.15810486424893463+0j)) [Z3]\n",
      "+ ((0.15810486424893486+0j)) [Z2]\n",
      "+ ((0.45859219444170524+0j)) [Z1]\n",
      "+ ((0.4585921944417055+0j)) [Z0]\n",
      "+ ((23.71217313247337+0j)) [I0]\n",
      "+ ((-0.048109725771599415+0j)) [Y8 Y9]\n",
      "+ ((-0.029896558031927242+0j)) [Y6 Y7]\n",
      "+ ((-0.017853382465998317+0j)) [Y4 Y5]\n",
      "+ ((-0.015017052424719027+0j)) [Y0 Y1]\n",
      "+ ((-0.013500019685003018+0j)) [Y2 Y3]\n",
      "+ ((-6.3199328582952375e-12+0j)) [Z0 X1]\n",
      "+ ((-4.90540941200379e-12+0j)) [X7 X8]\n",
      "+ ((-3.436362305819783e-12+0j)) [Y6 Y8]\n",
      "+ ((-3.436362305819783e-12+0j)) [X6 X8]\n",
      "+ ((-2.372078228285445e-12+0j)) [X1 X2]\n",
      "+ ((5.8071377567747685e-12-0j)) [X8 Z9]\n",
      "+ ((0.004314373571140227+0j)) [Y0 Y9]\n",
      "+ ((0.11976424626602505+0j)) [Z2 Z4]\n",
      "+ ((0.11976424626602505+0j)) [Z3 Z5]\n",
      "+ ((0.13307965081824674+0j)) [Z0 Z2]\n",
      "+ ((0.13307965081824674+0j)) [Z1 Z3]\n",
      "+ ((0.13456238001270732+0j)) [Z4 Z6]\n",
      "+ ((0.13456238001270732+0j)) [Z5 Z7]\n",
      "+ ((0.1367436705991374+0j)) [Z0 Z4]\n",
      "+ ((0.1367436705991374+0j)) [Z1 Z5]\n",
      "+ ((0.14245208941941898+0j)) [Z2 Z6]\n",
      "+ ((0.14245208941941898+0j)) [Z3 Z7]\n",
      "+ ((0.1577872856304589+0j)) [Z0 Z5]\n",
      "+ ((0.1577872856304589+0j)) [Z1 Z4]\n",
      "+ ((0.15780775272209624+0j)) [Z2 Z5]\n",
      "+ ((0.15780775272209624+0j)) [Z3 Z4]\n",
      "+ ((0.16014029660776757+0j)) [Z4 Z8]\n",
      "+ ((0.16014029660776757+0j)) [Z5 Z9]\n",
      "+ ((0.16100668262843557+0j)) [Z0 Z6]\n",
      "+ ((0.16100668262843557+0j)) [Z1 Z7]\n",
      "+ ((0.16209443712517413+0j)) [Z4 Z5]\n",
      "+ ((0.16409977462201272+0j)) [Z0 Z3]\n",
      "+ ((0.16409977462201272+0j)) [Z1 Z2]\n",
      "+ ((0.16625415410246963+0j)) [Z2 Z3]\n",
      "+ ((0.16914106510201415+0j)) [Z4 Z7]\n",
      "+ ((0.16914106510201415+0j)) [Z5 Z6]\n",
      "+ ((0.1713120438253497+0j)) [Z2 Z8]\n",
      "+ ((0.1713120438253497+0j)) [Z3 Z9]\n",
      "+ ((0.17399354990281557+0j)) [Z2 Z7]\n",
      "+ ((0.17399354990281557+0j)) [Z3 Z6]\n",
      "+ ((0.17853466471021034+0j)) [Z6 Z8]\n",
      "+ ((0.17853466471021034+0j)) [Z7 Z9]\n",
      "+ ((0.18219775707037078+0j)) [Z0 Z7]\n",
      "+ ((0.18219775707037078+0j)) [Z1 Z6]\n",
      "+ ((0.18686865778039657+0j)) [Z4 Z9]\n",
      "+ ((0.18686865778039657+0j)) [Z5 Z8]\n",
      "+ ((0.19357026976186986+0j)) [Z2 Z9]\n",
      "+ ((0.19357026976186986+0j)) [Z3 Z8]\n",
      "+ ((0.19735801866826755+0j)) [Z0 Z1]\n",
      "+ ((0.19818584792846028+0j)) [Z6 Z7]\n",
      "+ ((0.19978387012086674+0j)) [Z0 Z8]\n",
      "+ ((0.19978387012086674+0j)) [Z1 Z9]\n",
      "+ ((0.21880674002503261+0j)) [Z0 Z9]\n",
      "+ ((0.21880674002503261+0j)) [Z1 Z8]\n",
      "+ ((0.2229372441548988+0j)) [Z6 Z9]\n",
      "+ ((0.2229372441548988+0j)) [Z7 Z8]\n",
      "+ ((0.2816867405800564+0j)) [Z8 Z9]\n",
      "+ ((-0.07064488397496135+0j)) [X6 Z7 Z9]\n",
      "+ ((-0.053931282874605885+0j)) [X7 Z8 Z9]\n",
      "+ ((-0.03758942991326862+0j)) [X7 Y8 Y9]\n",
      "+ ((-0.0330554540616914+0j)) [X6 Z7 Z8]\n",
      "+ ((-0.020624550009860736+0j)) [X5 Y6 Y9]\n",
      "+ ((-0.020270256936758095+0j)) [X6 Z8 Z9]\n",
      "+ ((-0.01684972463687729+0j)) [Y0 Y5 X6]\n",
      "+ ((-0.013866769175887465+0j)) [X0 Y7 Y8]\n",
      "+ ((-0.013596309801359889+0j)) [Y3 Y4 X9]\n",
      "+ ((-0.012029395807666016+0j)) [X1 Y2 Y9]\n",
      "+ ((-0.011033703334686068+0j)) [Z0 Z1 X3]\n",
      "+ ((-0.00793631728279771+0j)) [Y0 Y3 X4]\n",
      "+ ((-0.0028560745351579216+0j)) [Y0 Y1 X2]\n",
      "+ ((-0.0026188681796093915+0j)) [Z0 Z2 X3]\n",
      "+ ((-7.850747829607482e-12+0j)) [Y2 Z3 Y4]\n",
      "+ ((-7.850747829607482e-12+0j)) [X2 Z3 X4]\n",
      "+ ((-7.850747829607482e-12+0j)) [Y3 Z4 Y5]\n",
      "+ ((-7.850747829607482e-12+0j)) [X3 Z4 X5]\n",
      "+ ((-2.8567218035568926e-12+0j)) [X0 X2 X3]\n",
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      "+ ((2.4415348215400804e-12-0j)) [Z0 Z1 Y2 Y3 Z4 Z5 Z6 Z7 X8]\n",
      "+ ((2.4980920110273522e-12-0j)) [X0 Z1 Z2 Z3 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((2.662425835353587e-12-0j)) [Z0 Z1 Z2 Z3 Y4 Y5 Z6 Z7 X8]\n",
      "+ ((2.8567218035568926e-12-0j)) [Y1 Y2 X3 Z4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((3.2056510224087715e-12-0j)) [X1 Z2 Z3 Y4 Y5 Z6 Z7 Z8 Z9]\n",
      "+ ((3.4918734570510407e-12-0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 X8]\n",
      "+ ((0.0010783795746871767-0j)) [Z0 Z1 Z2 X3 Y4 Z5 Z6 Z7 Y8]\n",
      "+ ((0.0010783795746871767-0j)) [Z0 Z1 Z2 X3 X4 Z5 Z6 Z7 X8]\n",
      "+ ((0.002218559093866068-0j)) [X0 Z1 Y2 Y4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((0.0026188681796093915-0j)) [Z0 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((0.002681267991708195-0j)) [Z0 X1 Y2 Z3 Z4 Z5 Z6 Z7 Y8]\n",
      "+ ((0.002681267991708195-0j)) [Z0 X1 X2 Z3 Z4 Z5 Z6 Z7 X8]\n",
      "+ ((0.0028886756486127254-0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 X7 X9]\n",
      "+ ((0.0028886756486127254-0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Y7 Y9]\n",
      "+ ((0.005273836928800344-0j)) [Y0 Z1 Z2 Z3 Y4 X6 Z7 Z8 Z9]\n",
      "+ ((0.005965305154249383-0j)) [Y0 Z1 Y2 X4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((0.008183864248115198-0j)) [X0 Z1 X2 X4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((0.011592130991294924-0j)) [X0 Z1 Z2 Z3 Y4 Y6 Z7 Z8 Z9]\n",
      "+ ((0.01180497133366603-0j)) [Z0 Z1 Z2 Y3 Y5 Z6 Z7 Z8 X9]\n",
      "+ ((0.013901622437046889-0j)) [Y1 Z2 Y3 X4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((0.013901622437046889-0j)) [X1 Z2 X3 X4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((0.014674689376047788-0j)) [Z0 Z1 Z2 X3 Y5 Z6 Z7 Z8 Y9]\n",
      "+ ((0.016865967920096085-0j)) [X0 Z1 Z2 Z3 X4 X6 Z7 Z8 Z9]\n",
      "+ ((0.022123561565678067-0j)) [Y1 Z2 Z3 Z4 Y5 X6 Z7 Z8 Z9]\n",
      "+ ((0.022123561565678067-0j)) [X1 Z2 Z3 Z4 X5 X6 Z7 Z8 Z9]\n",
      "+ ((0.025401281135027445-0j)) [Z0 Z1 X2 X4 Z5 Z6 Z7 Z8 X9]\n",
      "+ ((0.025401281135027445-0j)) [Z0 Z1 Y2 Y4 Z5 Z6 Z7 Z8 X9]\n",
      "+ ((0.026479660709713373-0j)) [Z0 Z1 Z2 X3 X5 Z6 Z7 Z8 X9]\n",
      "+ ((0.0330554540616914-0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 X7 Z8]\n",
      "+ ((0.07064488397496135-0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 X7 Z9]\n",
      "+ ((-0.048109725771599415+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Y9]\n",
      "+ ((-0.029896558031927242+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Z9]\n",
      "+ ((-0.02027083183022905+0j)) [Y0 Z1 Z2 Z3 Y4 Y5 Z6 Z7 Z8 Y9]\n",
      "+ ((-0.02027083183022905+0j)) [Y0 Z1 Z2 Z3 Y4 X5 Z6 Z7 Z8 X9]\n",
      "+ ((-0.02027083183022905+0j)) [X0 Z1 Z2 Z3 X4 Y5 Z6 Z7 Z8 Y9]\n",
      "+ ((-0.02027083183022905+0j)) [X0 Z1 Z2 Z3 X4 X5 Z6 Z7 Z8 X9]\n",
      "+ ((-0.017853382465998317+0j)) [Z0 Z1 Z2 Z3 Y4 Y5 Z6 Z7 Z8 Z9]\n",
      "+ ((-0.015017052424719027+0j)) [Y0 Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((-0.013500019685003018+0j)) [Z0 Z1 Y2 Y3 Z4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((-5.8071377567747685e-12+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X9]\n",
      "+ ((-4.90540941200379e-12+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 X7 X8 Z9]\n",
      "+ ((-2.372078228285445e-12+0j)) [Z0 X1 X2 Z3 Z4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((6.3199328582952375e-12-0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9]\n",
      "+ ((0.0021120059842583685+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Y8 Z9]\n",
      "+ ((0.0021120059842583685+0j)) [X0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 X8 Z9]\n",
      "+ ((0.004314373571140227+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y9]\n",
      "+ ((0.005968376362975316+0j)) [Z0 Y1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Y9]\n",
      "+ ((0.005968376362975316+0j)) [Z0 X1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 X9]\n",
      "+ ((0.017377985633500573+0j)) [Y0 Z1 Y2 Y3 Z4 Z5 Z6 Z7 Z8 Y9]\n",
      "+ ((0.017377985633500573+0j)) [Y0 Z1 Y2 X3 Z4 Z5 Z6 Z7 Z8 X9]\n",
      "+ ((0.017377985633500573+0j)) [X0 Z1 X2 Y3 Z4 Z5 Z6 Z7 Z8 Y9]\n",
      "+ ((0.017377985633500573+0j)) [X0 Z1 X2 X3 Z4 Z5 Z6 Z7 Z8 X9]\n",
      "+ ((0.01839580509251145+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 Y7 Z8 Y9]\n",
      "+ ((0.01839580509251145+0j)) [Y0 Z1 Z2 Z3 Z4 Z5 Y6 X7 Z8 X9]\n",
      "+ ((0.01839580509251145+0j)) [X0 Z1 Z2 Z3 Z4 Z5 X6 Y7 Z8 Y9]\n",
      "+ ((0.01839580509251145+0j)) [X0 Z1 Z2 Z3 Z4 Z5 X6 X7 Z8 X9]\n",
      "+ ((0.337917167893785+0j)) [Z0 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9]\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "generators_by_qml = qml.symmetry_generators(H)\n",
    "paulixops_by_qml = qml.paulix_ops(generators_by_qml, qubits)\n",
    "\n",
    "n_electrons = 6\n",
    "paulix_sector_by_qml = qml.qchem.optimal_sector(H, generators_by_qml, n_electrons)\n",
    "\n",
    "H_tapered = qml.taper(H, generators_by_qml, paulixops_by_qml, paulix_sector_by_qml)\n",
    "print(f'time cost: {time() - begin}')\n",
    "\n",
    "print(\"Number of qubit after tapering =\", len(H_tapered.wires))\n",
    "print(\"The tapered Hamiltonian is \\n\", H_tapered)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4bf00a0",
   "metadata": {},
   "source": [
    "## 5.2 Tapering using mytarpering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7aeff86d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "-0.000000000004 IIIXZYIYZZZX\n",
      "-0.014674689376 IIIYZXIIIXZY\n",
      "-0.026479660710 IIIYZYIIIYZY\n",
      "-0.011804971334 IIIYZYIIIXZX\n",
      "-0.011804971334 IIIXZXIIIYZY\n",
      "-0.026479660710 IIIXZXIIIXZX\n",
      "-0.014674689376 IIIXZYIIIYZX\n",
      " 0.173993549903 IIIZIIZIIIII\n",
      "-0.000000000008 IIIYZYIIIIII\n",
      "-0.000000000008 IIIXZXIIIIII\n",
      "-0.034079341004 IIIYZZIYIIII\n",
      "-0.034079341004 IIIXZZIXIIII\n",
      "-0.003528878861 IIIYZZIZZZZY\n",
      "-0.003528878861 IIIXZZIZZZZX\n",
      "-0.000000000003 IIIZIIYZYIII\n",
      "-0.000000000003 IIIZIIXZXIII\n",
      "-0.030566792991 IIIYZYYZYIII\n",
      "-0.030566792991 IIIYZYXZXIII\n",
      "-0.030566792991 IIIXZXYZYIII\n",
      "-0.030566792991 IIIXZXXZXIII\n",
      " 0.000000000002 IIIYZZXXYIII\n",
      "-0.000000000002 IIIYZZYXXIII\n",
      "-0.000000000002 IIIXZZXYYIII\n",
      " 0.000000000002 IIIXZZYYXIII\n",
      "-0.021127123077 IIIYZZXIXYII\n",
      "-0.021127123077 IIIYZZYIYYII\n",
      "-0.021127123077 IIIXZZXIXXII\n",
      "-0.021127123077 IIIXZZYIYXII\n",
      "-0.000000000002 IIIYZZXIXZZY\n",
      "-0.000000000002 IIIYZZYIYZZY\n",
      "-0.000000000002 IIIXZZXIXZZX\n",
      "-0.000000000002 IIIXZZYIYZZX\n",
      " 0.007098243186 IIIZIIYZZZYI\n",
      " 0.007098243186 IIIZIIXZZZXI\n",
      "-0.000000000004 IIIYZYYZZZYI\n",
      "-0.000000000004 IIIYZYXZZZXI\n",
      "-0.000000000004 IIIXZXYZZZYI\n",
      "-0.000000000004 IIIXZXXZZZXI\n",
      "-0.018512709435 IIIYZZXXZZYI\n",
      " 0.018512709435 IIIYZZYXZZXI\n",
      " 0.018512709435 IIIXZZXYZZYI\n",
      "-0.018512709435 IIIXZZYYZZXI\n",
      " 0.000000000002 IIIYZZXIIXYI\n",
      "-0.000000000002 IIIYZZYIIXXI\n",
      "-0.000000000002 IIIXZZXIIYYI\n",
      " 0.000000000002 IIIXZZYIIYXI\n",
      "-0.012560079329 IIIYZZXIIIXY\n",
      "-0.012560079329 IIIYZZYIIIYY\n",
      "-0.012560079329 IIIXZZXIIIXX\n",
      "-0.012560079329 IIIXZZYIIIYX\n",
      " 0.142452089419 IIIZIIIZIIII\n",
      "-0.000000000002 IIIZIIIYZYII\n",
      "-0.000000000002 IIIZIIIXZXII\n",
      " 0.009427467598 IIIZIIIYZZZY\n",
      " 0.009427467598 IIIZIIIXZZZX\n",
      "-0.022041588296 IIIYZZZIZZZY\n",
      "-0.022041588296 IIIXZZZIZZZX\n",
      " 0.000000000001 IIIYZZZYIXZX\n",
      " 0.000000000001 IIIXZZZXIYZY\n",
      " 0.193570269762 IIIZIIIIZIII\n",
      "-0.000000000003 IIIYZYIIZIII\n",
      "-0.000000000003 IIIXZXIIZIII\n",
      "-0.054978844122 IIIYZZZYZIII\n",
      "-0.054978844122 IIIXZZZXZIII\n",
      " 0.000000000001 IIIYZZZZIYII\n",
      " 0.000000000001 IIIXZZZZIXII\n",
      "-0.007828348972 IIIYZZZZIZZY\n",
      "-0.007828348972 IIIXZZZZIZZX\n",
      "-0.000000000013 IIIZIIIIYZYI\n",
      "-0.000000000013 IIIZIIIIXZXI\n",
      "-0.025401281135 IIIYZYIIYZYI\n",
      "-0.025401281135 IIIYZYIIXZXI\n",
      "-0.025401281135 IIIXZXIIYZYI\n",
      "-0.025401281135 IIIXZXIIXZXI\n",
      " 0.000000000003 IIIYZZZYYZYI\n",
      " 0.000000000003 IIIYZZZYXZXI\n",
      " 0.000000000003 IIIXZZZXYZYI\n",
      " 0.000000000003 IIIXZZZXXZXI\n",
      " 0.023105840322 IIIYZZZZXXYI\n",
      "-0.023105840322 IIIYZZZZYXXI\n",
      "-0.023105840322 IIIXZZZZXYYI\n",
      " 0.023105840322 IIIXZZZZYYXI\n",
      "-0.000000000005 IIIYZZZZXIXY\n",
      "-0.000000000005 IIIYZZZZYIYY\n",
      "-0.000000000005 IIIXZZZZXIXX\n",
      "-0.000000000005 IIIXZZZZYIYX\n",
      " 0.171312043825 IIIZIIIIIZII\n",
      "-0.000000000011 IIIZIIIIIYZY\n",
      "-0.000000000011 IIIZIIIIIXZX\n",
      "-0.000000000002 IIIYZYIIIZII\n",
      "-0.000000000002 IIIXZXIIIZII\n",
      "-0.033851721044 IIIYZZZYIZII\n",
      "-0.033851721044 IIIXZZZXIZII\n",
      " 0.015277491349 IIIYZZZZZIZY\n",
      " 0.015277491349 IIIXZZZZZIZX\n",
      " 0.200003520164 IIIZIIIIIIZI\n",
      " 0.000000000008 IIIYZYIIIIZI\n",
      " 0.000000000008 IIIXZXIIIIZI\n",
      "-0.065472389315 IIIYZZZYIIZI\n",
      "-0.065472389315 IIIXZZZXIIZI\n",
      "-0.000000000010 IIIYZZZZZYZI\n",
      "-0.000000000010 IIIXZZZZZXZI\n",
      " 0.000092723823 IIIYZZZZZZIY\n",
      " 0.000092723823 IIIXZZZZZZIX\n",
      " 0.186503500479 IIIZIIIIIIIZ\n",
      " 0.000000000006 IIIYZYIIIIIZ\n",
      " 0.000000000006 IIIXZXIIIIIZ\n",
      "-0.052912309986 IIIYZZZYIIIZ\n",
      "-0.052912309986 IIIXZZZXIIIZ\n",
      "-0.000000000004 IIIYZZZZZYIZ\n",
      "-0.000000000004 IIIXZZZZZXIZ\n",
      " 0.162094437125 IIIIZZIIIIII\n",
      " 0.014707942346 IIIIYIZZYIII\n",
      " 0.014707942346 IIIIXIZZXIII\n",
      " 0.000000000003 IIIIYIZZZZYI\n",
      " 0.000000000003 IIIIXIZZZZXI\n",
      " 0.034578685089 IIIIYXXYIIII\n",
      "-0.034578685089 IIIIYYXXIIII\n",
      "-0.034578685089 IIIIXXYYIIII\n",
      " 0.034578685089 IIIIXYYXIIII\n",
      " 0.004798878748 IIIIYXIXZZYI\n",
      " 0.004798878748 IIIIYYIYZZYI\n",
      " 0.004798878748 IIIIXXIXZZXI\n",
      " 0.004798878748 IIIIXYIYZZXI\n",
      " 0.014707942346 IIIIZYZZZYII\n",
      " 0.014707942346 IIIIZXZZZXII\n",
      " 0.026728361173 IIIIYXIIXYII\n",
      "-0.026728361173 IIIIYYIIXXII\n",
      "-0.026728361173 IIIIXXIIYYII\n",
      " 0.026728361173 IIIIXYIIYXII\n",
      "-0.000000000003 IIIIYXIIIXYI\n",
      "-0.000000000003 IIIIYYIIIYYI\n",
      "-0.000000000003 IIIIXXIIIXXI\n",
      "-0.000000000003 IIIIXYIIIYXI\n",
      " 0.000000000003 IIIIZYZZZZZY\n",
      " 0.000000000003 IIIIZXZZZZZX\n",
      "-0.004798878748 IIIIYXXZZZZY\n",
      " 0.004798878748 IIIIYYXZZZZX\n",
      " 0.004798878748 IIIIXXYZZZZY\n",
      "-0.004798878748 IIIIXYYZZZZX\n",
      " 0.000000000003 IIIIYXIIXZZY\n",
      "-0.000000000003 IIIIYYIIXZZX\n",
      "-0.000000000003 IIIIXXIIYZZY\n",
      " 0.000000000003 IIIIXYIIYZZX\n",
      " 0.017853382466 IIIIYXIIIIXY\n",
      "-0.017853382466 IIIIYYIIIIXX\n",
      "-0.017853382466 IIIIXXIIIIYY\n",
      " 0.017853382466 IIIIXYIIIIYX\n",
      " 0.134562380013 IIIIZIZIIIII\n",
      "-0.000000000002 IIIIZIYZYIII\n",
      "-0.000000000002 IIIIZIXZXIII\n",
      " 0.005933238474 IIIIZIYZZZYI\n",
      " 0.005933238474 IIIIZIXZZZXI\n",
      " 0.052529335626 IIIIYZIZYIII\n",
      " 0.052529335626 IIIIXZIZXIII\n",
      " 0.000000000008 IIIIYZIZZZYI\n",
      " 0.000000000008 IIIIXZIZZZXI\n",
      " 0.030721659550 IIIIYZXIXZYI\n",
      " 0.036295559354 IIIIYZYIYZYI\n",
      " 0.005573899804 IIIIYZYIXZXI\n",
      " 0.005573899804 IIIIXZXIYZYI\n",
      " 0.036295559354 IIIIXZXIXZXI\n",
      " 0.030721659550 IIIIXZYIYZXI\n",
      " 0.169141065102 IIIIZIIZIIII\n",
      " 0.023531801948 IIIIYZZIYIII\n",
      " 0.023531801948 IIIIXZZIXIII\n",
      " 0.000000000005 IIIIYZZIZZYI\n",
      " 0.000000000005 IIIIXZZIZZXI\n",
      "-0.000000000003 IIIIZIIYZYII\n",
      "-0.000000000003 IIIIZIIXZXII\n",
      " 0.028997533679 IIIIYZYYZYII\n",
      " 0.028997533679 IIIIYZYXZXII\n",
      " 0.028997533679 IIIIXZXYZYII\n",
      " 0.028997533679 IIIIXZXXZXII\n",
      " 0.010097109540 IIIIYZZXIXYI\n",
      " 0.010097109540 IIIIYZZYIYYI\n",
      " 0.010097109540 IIIIXZZXIXXI\n",
      " 0.010097109540 IIIIXZZYIYXI\n",
      " 0.010732117222 IIIIZIIYZZZY\n",
      " 0.010732117222 IIIIZIIXZZZX\n",
      " 0.000000000004 IIIIYZYYZZZY\n",
      " 0.000000000004 IIIIYZYXZZZX\n",
      " 0.000000000004 IIIIXZXYZZZY\n",
      " 0.000000000004 IIIIXZXXZZZX\n",
      " 0.020624550010 IIIIYZZXXZZY\n",
      "-0.020624550010 IIIIYZZYXZZX\n",
      "-0.020624550010 IIIIXZZXYZZY\n",
      " 0.020624550010 IIIIXZZYYZZX\n",
      " 0.000000000002 IIIIYZZXIIXY\n",
      "-0.000000000002 IIIIYZZYIIXX\n",
      "-0.000000000002 IIIIXZZXIIYY\n",
      " 0.000000000002 IIIIXZZYIIYX\n",
      " 0.160140296608 IIIIZIIIZIII\n",
      "-0.000000000010 IIIIZIIIYZYI\n",
      "-0.000000000010 IIIIZIIIXZXI\n",
      " 0.000000000002 IIIIYZYIZIII\n",
      " 0.000000000002 IIIIXZXIZIII\n",
      " 0.000000000006 IIIIYZZZIZYI\n",
      " 0.000000000006 IIIIXZZZIZXI\n",
      " 0.186868657780 IIIIZIIIIZII\n",
      " 0.000000000003 IIIIYZYIIZII\n",
      " 0.000000000003 IIIIXZXIIZII\n",
      " 0.050611338763 IIIIYZZZYZII\n",
      " 0.050611338763 IIIIXZZZXZII\n",
      " 0.000000000006 IIIIYZZZZIYI\n",
      " 0.000000000006 IIIIXZZZZIXI\n",
      "-0.000000000013 IIIIZIIIIYZY\n",
      "-0.000000000013 IIIIZIIIIXZX\n",
      " 0.026198449814 IIIIYZYIIYZY\n",
      " 0.026198449814 IIIIYZYIIXZX\n",
      " 0.026198449814 IIIIXZXIIYZY\n",
      " 0.026198449814 IIIIXZXIIXZX\n",
      "-0.021353309934 IIIIYZZZZXXY\n",
      " 0.021353309934 IIIIYZZZZYXX\n",
      " 0.021353309934 IIIIXZZZZXYY\n",
      "-0.021353309934 IIIIXZZZZYYX\n",
      " 0.177090987667 IIIIZIIIIIZI\n",
      "-0.000000000007 IIIIYZYIIIZI\n",
      "-0.000000000007 IIIIXZXIIIZI\n",
      " 0.039869926016 IIIIYZZZYIZI\n",
      " 0.039869926016 IIIIXZZZXIZI\n",
      " 0.194944370133 IIIIZIIIIIIZ\n",
      "-0.000000000008 IIIIYZYIIIIZ\n",
      "-0.000000000008 IIIIXZXIIIIZ\n",
      " 0.061223235950 IIIIYZZZYIIZ\n",
      " 0.061223235950 IIIIXZZZXIIZ\n",
      " 0.000000000017 IIIIYZZZZZYZ\n",
      " 0.000000000017 IIIIXZZZZZXZ\n",
      " 0.169141065102 IIIIIZZIIIII\n",
      " 0.023531801948 IIIIIYIZZYII\n",
      " 0.023531801948 IIIIIXIZZXII\n",
      " 0.000000000005 IIIIIYIZZZZY\n",
      " 0.000000000005 IIIIIXIZZZZX\n",
      "-0.000000000003 IIIIIZYZYIII\n",
      "-0.000000000003 IIIIIZXZXIII\n",
      " 0.028997533679 IIIIIYXXYIII\n",
      "-0.028997533679 IIIIIYYXXIII\n",
      "-0.028997533679 IIIIIXXYYIII\n",
      " 0.028997533679 IIIIIXYYXIII\n",
      " 0.010097109540 IIIIIYXIXZZY\n",
      " 0.010097109540 IIIIIYYIYZZY\n",
      " 0.010097109540 IIIIIXXIXZZX\n",
      " 0.010097109540 IIIIIXYIYZZX\n",
      " 0.010732117222 IIIIIZYZZZYI\n",
      " 0.010732117222 IIIIIZXZZZXI\n",
      " 0.000000000004 IIIIIYXXZZYI\n",
      "-0.000000000004 IIIIIYYXZZXI\n",
      "-0.000000000004 IIIIIXXYZZYI\n",
      " 0.000000000004 IIIIIXYYZZXI\n",
      " 0.020624550010 IIIIIYXIIXYI\n",
      "-0.020624550010 IIIIIYYIIXXI\n",
      "-0.020624550010 IIIIIXXIIYYI\n",
      " 0.020624550010 IIIIIXYIIYXI\n",
      "-0.000000000002 IIIIIYXIIIXY\n",
      "-0.000000000002 IIIIIYYIIIYY\n",
      "-0.000000000002 IIIIIXXIIIXX\n",
      "-0.000000000002 IIIIIXYIIIYX\n",
      " 0.134562380013 IIIIIZIZIIII\n",
      "-0.000000000002 IIIIIZIYZYII\n",
      "-0.000000000002 IIIIIZIXZXII\n",
      " 0.005933238474 IIIIIZIYZZZY\n",
      " 0.005933238474 IIIIIZIXZZZX\n",
      " 0.052529335626 IIIIIYZIZYII\n",
      " 0.052529335626 IIIIIXZIZXII\n",
      " 0.000000000008 IIIIIYZIZZZY\n",
      " 0.000000000008 IIIIIXZIZZZX\n",
      " 0.030721659550 IIIIIYZXIXZY\n",
      " 0.036295559354 IIIIIYZYIYZY\n",
      " 0.005573899804 IIIIIYZYIXZX\n",
      " 0.005573899804 IIIIIXZXIYZY\n",
      " 0.036295559354 IIIIIXZXIXZX\n",
      " 0.030721659550 IIIIIXZYIYZX\n",
      " 0.186868657780 IIIIIZIIZIII\n",
      " 0.000000000003 IIIIIYZYZIII\n",
      " 0.000000000003 IIIIIXZXZIII\n",
      " 0.050611338763 IIIIIYZZIYII\n",
      " 0.050611338763 IIIIIXZZIXII\n",
      " 0.000000000006 IIIIIYZZIZZY\n",
      " 0.000000000006 IIIIIXZZIZZX\n",
      "-0.000000000013 IIIIIZIIYZYI\n",
      "-0.000000000013 IIIIIZIIXZXI\n",
      " 0.026198449814 IIIIIYZYYZYI\n",
      " 0.026198449814 IIIIIYZYXZXI\n",
      " 0.026198449814 IIIIIXZXYZYI\n",
      " 0.026198449814 IIIIIXZXXZXI\n",
      " 0.021353309934 IIIIIYZZXIXY\n",
      " 0.021353309934 IIIIIYZZYIYY\n",
      " 0.021353309934 IIIIIXZZXIXX\n",
      " 0.021353309934 IIIIIXZZYIYX\n",
      " 0.160140296608 IIIIIZIIIZII\n",
      "-0.000000000010 IIIIIZIIIYZY\n",
      "-0.000000000010 IIIIIZIIIXZX\n",
      " 0.000000000002 IIIIIYZYIZII\n",
      " 0.000000000002 IIIIIXZXIZII\n",
      " 0.000000000006 IIIIIYZZZIZY\n",
      " 0.000000000006 IIIIIXZZZIZX\n",
      " 0.194944370133 IIIIIZIIIIZI\n",
      "-0.000000000008 IIIIIYZYIIZI\n",
      "-0.000000000008 IIIIIXZXIIZI\n",
      " 0.061223235950 IIIIIYZZZYZI\n",
      " 0.061223235950 IIIIIXZZZXZI\n",
      " 0.000000000017 IIIIIYZZZZIY\n",
      " 0.000000000017 IIIIIXZZZZIX\n",
      " 0.177090987667 IIIIIZIIIIIZ\n",
      "-0.000000000007 IIIIIYZYIIIZ\n",
      "-0.000000000007 IIIIIXZXIIIZ\n",
      " 0.039869926016 IIIIIYZZZYIZ\n",
      " 0.039869926016 IIIIIXZZZXIZ\n",
      " 0.198185847928 IIIIIIZZIIII\n",
      "-0.000000000003 IIIIIIYIYIII\n",
      "-0.000000000003 IIIIIIXIXIII\n",
      " 0.020270256937 IIIIIIYIZZYI\n",
      " 0.020270256937 IIIIIIXIZZXI\n",
      "-0.000000000003 IIIIIIZYZYII\n",
      "-0.000000000003 IIIIIIZXZXII\n",
      " 0.044402579445 IIIIIIYXXYII\n",
      "-0.044402579445 IIIIIIYYXXII\n",
      "-0.044402579445 IIIIIIXXYYII\n",
      " 0.044402579445 IIIIIIXYYXII\n",
      "-0.000000000003 IIIIIIYXIXYI\n",
      "-0.000000000003 IIIIIIYYIYYI\n",
      "-0.000000000003 IIIIIIXXIXXI\n",
      "-0.000000000003 IIIIIIXYIYXI\n",
      " 0.020270256937 IIIIIIZYZZZY\n",
      " 0.020270256937 IIIIIIZXZZZX\n",
      " 0.000000000003 IIIIIIYXXZZY\n",
      "-0.000000000003 IIIIIIYYXZZX\n",
      "-0.000000000003 IIIIIIXXYZZY\n",
      " 0.000000000003 IIIIIIXYYZZX\n",
      " 0.029896558032 IIIIIIYXIIXY\n",
      "-0.029896558032 IIIIIIYYIIXX\n",
      "-0.029896558032 IIIIIIXXIIYY\n",
      " 0.029896558032 IIIIIIXYIIYX\n",
      " 0.178534664710 IIIIIIZIZIII\n",
      "-0.000000000010 IIIIIIZIYZYI\n",
      "-0.000000000010 IIIIIIZIXZXI\n",
      " 0.070644883975 IIIIIIYZIZYI\n",
      " 0.070644883975 IIIIIIXZIZXI\n",
      " 0.222937244155 IIIIIIZIIZII\n",
      "-0.000000000001 IIIIIIYZYZII\n",
      "-0.000000000001 IIIIIIXZXZII\n",
      " 0.033055454062 IIIIIIYZZIYI\n",
      " 0.033055454062 IIIIIIXZZIXI\n",
      "-0.000000000014 IIIIIIZIIYZY\n",
      "-0.000000000014 IIIIIIZIIXZX\n",
      " 0.037589429913 IIIIIIYZYYZY\n",
      " 0.037589429913 IIIIIIYZYXZX\n",
      " 0.037589429913 IIIIIIXZXYZY\n",
      " 0.037589429913 IIIIIIXZXXZX\n",
      " 0.000000000005 IIIIIIYZZXXY\n",
      "-0.000000000005 IIIIIIYZZYXX\n",
      "-0.000000000005 IIIIIIXZZXYY\n",
      " 0.000000000005 IIIIIIXZZYYX\n",
      " 0.206998926861 IIIIIIZIIIZI\n",
      "-0.000000000013 IIIIIIYZYIZI\n",
      "-0.000000000013 IIIIIIXZXIZI\n",
      " 0.236895484892 IIIIIIZIIIIZ\n",
      "-0.000000000018 IIIIIIYZYIIZ\n",
      "-0.000000000018 IIIIIIXZXIIZ\n",
      " 0.053931282875 IIIIIIYZZZYZ\n",
      " 0.053931282875 IIIIIIXZZZXZ\n",
      " 0.222937244155 IIIIIIIZZIII\n",
      "-0.000000000001 IIIIIIIYIYII\n",
      "-0.000000000001 IIIIIIIXIXII\n",
      " 0.033055454062 IIIIIIIYIZZY\n",
      " 0.033055454062 IIIIIIIXIZZX\n",
      "-0.000000000014 IIIIIIIZYZYI\n",
      "-0.000000000014 IIIIIIIZXZXI\n",
      " 0.037589429913 IIIIIIIYXXYI\n",
      "-0.037589429913 IIIIIIIYYXXI\n",
      "-0.037589429913 IIIIIIIXXYYI\n",
      " 0.037589429913 IIIIIIIXYYXI\n",
      "-0.000000000005 IIIIIIIYXIXY\n",
      "-0.000000000005 IIIIIIIYYIYY\n",
      "-0.000000000005 IIIIIIIXXIXX\n",
      "-0.000000000005 IIIIIIIXYIYX\n",
      " 0.178534664710 IIIIIIIZIZII\n",
      "-0.000000000010 IIIIIIIZIYZY\n",
      "-0.000000000010 IIIIIIIZIXZX\n",
      " 0.070644883975 IIIIIIIYZIZY\n",
      " 0.070644883975 IIIIIIIXZIZX\n",
      " 0.236895484892 IIIIIIIZIIZI\n",
      "-0.000000000018 IIIIIIIYZYZI\n",
      "-0.000000000018 IIIIIIIXZXZI\n",
      " 0.053931282875 IIIIIIIYZZIY\n",
      " 0.053931282875 IIIIIIIXZZIX\n",
      " 0.206998926861 IIIIIIIZIIIZ\n",
      "-0.000000000013 IIIIIIIYZYIZ\n",
      "-0.000000000013 IIIIIIIXZXIZ\n",
      " 0.281686740580 IIIIIIIIZZII\n",
      "-0.000000000012 IIIIIIIIYIYI\n",
      "-0.000000000012 IIIIIIIIXIXI\n",
      "-0.000000000012 IIIIIIIIZYZY\n",
      "-0.000000000012 IIIIIIIIZXZX\n",
      " 0.048109725772 IIIIIIIIYXXY\n",
      "-0.048109725772 IIIIIIIIYYXX\n",
      "-0.048109725772 IIIIIIIIXXYY\n",
      " 0.048109725772 IIIIIIIIXYYX\n",
      " 0.249655039285 IIIIIIIIZIZI\n",
      " 0.297764765056 IIIIIIIIZIIZ\n",
      "-0.000000000030 IIIIIIIIYZYZ\n",
      "-0.000000000030 IIIIIIIIXZXZ\n",
      " 0.297764765056 IIIIIIIIIZZI\n",
      "-0.000000000030 IIIIIIIIIYIY\n",
      "-0.000000000030 IIIIIIIIIXIX\n",
      " 0.249655039285 IIIIIIIIIZIZ\n",
      " 0.337917167894 IIIIIIIIIIZZ\n"
     ]
    }
   ],
   "source": [
    "Hami_ori = create_pauliwords_from_hamilton(H, qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fd4f069a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time cost: 2.0893712043762207\n",
      "Number of qubit after tapering = 10\n",
      "The tapered Hamiltonian is \n",
      " 23.71217313+0.00000000j IIIIIIIIII\n",
      "0.45859219+0.00000000j ZIIIIIIIII\n",
      "0.45859219+0.00000000j IZIIIIIIII\n",
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      "0.01180497+0.00000000j ZIZYIYZIZX\n",
      "-0.01180497+0.00000000j ZZZYIYZZZX\n",
      "0.02647966+0.00000000j ZIZXIXZIZX\n",
      "0.01467469+0.00000000j ZIZXIYZIZY\n",
      "0.17399355+0.00000000j IIIZIIZIII\n",
      "-0.03407934+0.00000000j IIIYZZIYII\n",
      "-0.03407934+0.00000000j IIIXZZIXII\n",
      "0.00352888+0.00000000j ZZZXIIZIII\n",
      "0.00352888+0.00000000j ZIZXIZZZIZ\n",
      "-0.03056679+0.00000000j IIIYZYYZYI\n",
      "-0.03056679+0.00000000j IIIYZYXZXI\n",
      "-0.03056679+0.00000000j IIIXZXYZYI\n",
      "-0.03056679+0.00000000j IIIXZXXZXI\n",
      "-0.02112712+0.00000000j IIIYZZXIXY\n",
      "-0.02112712+0.00000000j IIIYZZYIYY\n",
      "-0.02112712+0.00000000j IIIXZZXIXX\n",
      "-0.02112712+0.00000000j IIIXZZYIYX\n",
      "0.00709824+0.00000000j ZIZZZIXZIZ\n",
      "0.00709824+0.00000000j IIIZIIXZZZ\n",
      "0.01851271+0.00000000j ZIZYIZYXIZ\n",
      "0.01851271+0.00000000j IIIYZZYXZZ\n",
      "-0.01851271+0.00000000j ZIZXIZYYIZ\n",
      "-0.01851271+0.00000000j IIIXZZYYZZ\n",
      "-0.01256008+0.00000000j IZIXZIXZIZ\n",
      "-0.01256008+0.00000000j ZZZXIIXZZZ\n",
      "-0.01256008+0.00000000j IIIXZZXIII\n",
      "-0.01256008+0.00000000j ZIZXIZXIZI\n",
      "0.14245209+0.00000000j IIIZIIIZII\n",
      "-0.00942747+0.00000000j ZZZIZZZXII\n",
      "-0.00942747+0.00000000j ZIZZZIZXIZ\n",
      "0.02204159+0.00000000j ZZZXIIIZII\n",
      "0.02204159+0.00000000j ZIZXIZIIIZ\n",
      "0.19357027+0.00000000j IIIZIIIIZI\n",
      "-0.05497884+0.00000000j IIIYZZZYZI\n",
      "-0.05497884+0.00000000j IIIXZZZXZI\n",
      "0.00782835+0.00000000j ZZZXIIIIZI\n",
      "0.00782835+0.00000000j ZIZXIZIZZZ\n",
      "-0.02540128+0.00000000j ZIZYIYZIXZ\n",
      "-0.02540128+0.00000000j IIIYZYIIXZ\n",
      "-0.02540128+0.00000000j ZIZXIXZIXZ\n",
      "-0.02540128+0.00000000j IIIXZXIIXZ\n",
      "-0.02310584+0.00000000j ZIZYIZIZYX\n",
      "-0.02310584+0.00000000j IIIYZZZZYX\n",
      "0.02310584+0.00000000j ZIZXIZIZYY\n",
      "0.02310584+0.00000000j IIIXZZZZYY\n",
      "0.17131204+0.00000000j IIIZIIIIIZ\n",
      "-0.03385172+0.00000000j IIIYZZZYIZ\n",
      "-0.03385172+0.00000000j IIIXZZZXIZ\n",
      "-0.01527749+0.00000000j ZZZXIIIIIZ\n",
      "-0.01527749+0.00000000j ZIZXIZIZII\n",
      "-0.20000352+0.00000000j ZIZZZIZIZI\n",
      "0.06547239+0.00000000j ZIZYIZIYZI\n",
      "0.06547239+0.00000000j ZIZXIZIXZI\n",
      "0.00009272+0.00000000j IZIXZIZIZI\n",
      "0.00009272+0.00000000j IIIXZZZZZZ\n",
      "-0.18650350+0.00000000j IZIIIZIZIZ\n",
      "-0.05291231+0.00000000j IZIXZIZXIZ\n",
      "-0.05291231+0.00000000j IZIYZIZYIZ\n",
      "0.16209444+0.00000000j IIIIZZIIII\n",
      "0.01470794+0.00000000j IIIIYIZZYI\n",
      "0.01470794+0.00000000j IIIIXIZZXI\n",
      "0.03457869+0.00000000j IIIIYXXYII\n",
      "-0.03457869+0.00000000j IIIIYYXXII\n",
      "-0.03457869+0.00000000j IIIIXXYYII\n",
      "0.03457869+0.00000000j IIIIXYYXII\n",
      "0.00479888+0.00000000j ZIZIXXZXIZ\n",
      "0.00479888+0.00000000j ZIZIXYZYIZ\n",
      "0.00479888+0.00000000j IIIIXXIXZZ\n",
      "0.00479888+0.00000000j IIIIXYIYZZ\n",
      "0.01470794+0.00000000j IIIIZYZZZY\n",
      "0.01470794+0.00000000j IIIIZXZZZX\n",
      "0.02672836+0.00000000j IIIIYXIIXY\n",
      "-0.02672836+0.00000000j IIIIYYIIXX\n",
      "-0.02672836+0.00000000j IIIIXXIIYY\n",
      "0.02672836+0.00000000j IIIIXYIIYX\n",
      "-0.00479888+0.00000000j ZZZZXYYIII\n",
      "-0.00479888+0.00000000j ZIZIXYYZIZ\n",
      "0.00479888+0.00000000j ZZZZYYXIII\n",
      "0.00479888+0.00000000j ZIZIYYXZIZ\n",
      "-0.01785338+0.00000000j IZIZYYIZIZ\n",
      "-0.01785338+0.00000000j IIIIYYIIII\n",
      "-0.01785338+0.00000000j ZZZZYYZZZZ\n",
      "-0.01785338+0.00000000j ZIZIYYZIZI\n",
      "0.13456238+0.00000000j IIIIZIZIII\n",
      "0.00593324+0.00000000j ZIZIIIXZIZ\n",
      "0.00593324+0.00000000j IIIIZIXZZZ\n",
      "0.05252934+0.00000000j IIIIYZIZYI\n",
      "0.05252934+0.00000000j IIIIXZIZXI\n",
      "-0.03072166+0.00000000j ZIZIXZYIYZ\n",
      "-0.03629556+0.00000000j ZIZIXZXIXZ\n",
      "0.00557390+0.00000000j IIIIYZYIXZ\n",
      "-0.00557390+0.00000000j ZIZIYZYIXZ\n",
      "0.03629556+0.00000000j IIIIXZXIXZ\n",
      "0.03072166+0.00000000j IIIIXZYIYZ\n",
      "0.16914107+0.00000000j IIIIZIIZII\n",
      "0.02353180+0.00000000j IIIIYZZIYI\n",
      "0.02353180+0.00000000j IIIIXZZIXI\n",
      "0.02899753+0.00000000j IIIIYZYYZY\n",
      "0.02899753+0.00000000j IIIIYZYXZX\n",
      "0.02899753+0.00000000j IIIIXZXYZY\n",
      "0.02899753+0.00000000j IIIIXZXXZX\n",
      "0.01009711+0.00000000j ZIZIXZIXZX\n",
      "0.01009711+0.00000000j ZIZIXZIYZY\n",
      "0.01009711+0.00000000j IIIIXZZXIX\n",
      "0.01009711+0.00000000j IIIIXZZYIY\n",
      "-0.01073212+0.00000000j ZZZZIZZXII\n",
      "-0.01073212+0.00000000j ZIZIIIZXIZ\n",
      "0.02062455+0.00000000j ZZZZXIIYYI\n",
      "0.02062455+0.00000000j ZIZIXZIYYZ\n",
      "-0.02062455+0.00000000j ZZZZYIIYXI\n",
      "-0.02062455+0.00000000j ZIZIYZIYXZ\n",
      "0.16014030+0.00000000j IIIIZIIIZI\n",
      "0.18686866+0.00000000j IIIIZIIIIZ\n",
      "0.05061134+0.00000000j IIIIYZZZYZ\n",
      "0.05061134+0.00000000j IIIIXZZZXZ\n",
      "0.02619845+0.00000000j ZZZZXIXZZX\n",
      "0.02619845+0.00000000j ZIZIXZXIZX\n",
      "0.02619845+0.00000000j ZZZZYIYZZX\n",
      "0.02619845+0.00000000j ZIZIYZYIZX\n",
      "0.02135331+0.00000000j IZIZYIZIZY\n",
      "0.02135331+0.00000000j IIIIYZZZZY\n",
      "0.02135331+0.00000000j ZZZZYIIIIY\n",
      "0.02135331+0.00000000j ZIZIYZIZIY\n",
      "-0.17709099+0.00000000j ZIZIIIZIZI\n",
      "0.03986993+0.00000000j ZIZIXZIZXI\n",
      "0.03986993+0.00000000j ZIZIYZIZYI\n",
      "-0.19494437+0.00000000j IZIZZZIZIZ\n",
      "-0.06122324+0.00000000j IZIZYIZIYZ\n",
      "-0.06122324+0.00000000j IZIZXIZIXZ\n",
      "0.16914107+0.00000000j IIIIIZZIII\n",
      "0.02353180+0.00000000j IIIIIYIZZY\n",
      "0.02353180+0.00000000j IIIIIXIZZX\n",
      "0.02899753+0.00000000j IIIIIYXXYI\n",
      "-0.02899753+0.00000000j IIIIIYYXXI\n",
      "-0.02899753+0.00000000j IIIIIXXYYI\n",
      "0.02899753+0.00000000j IIIIIXYYXI\n",
      "0.01009711+0.00000000j ZZZZZXYZYI\n",
      "0.01009711+0.00000000j ZZZZZXXZXI\n",
      "0.01009711+0.00000000j ZIZIZXYIYZ\n",
      "0.01009711+0.00000000j ZIZIZXXIXZ\n",
      "0.01073212+0.00000000j ZIZIZZXZIZ\n",
      "0.01073212+0.00000000j IIIIIZXZZZ\n",
      "-0.02062455+0.00000000j ZIZIZYYIZX\n",
      "-0.02062455+0.00000000j IIIIIYYIIX\n",
      "0.02062455+0.00000000j ZIZIZXYIZY\n",
      "0.02062455+0.00000000j IIIIIXYIIY\n",
      "0.13456238+0.00000000j IIIIIZIZII\n",
      "-0.00593324+0.00000000j ZZZZZIZXII\n",
      "-0.00593324+0.00000000j ZIZIZZZXIZ\n",
      "0.05252934+0.00000000j IIIIIYZIZY\n",
      "0.05252934+0.00000000j IIIIIXZIZX\n",
      "0.03072166+0.00000000j ZZZZZXIYZY\n",
      "0.03629556+0.00000000j ZZZZZXIXZX\n",
      "-0.00557390+0.00000000j ZIZIZYIYZX\n",
      "0.00557390+0.00000000j ZZZZZYIYZX\n",
      "-0.03629556+0.00000000j ZIZIZXIXZX\n",
      "-0.03072166+0.00000000j ZIZIZXIYZY\n",
      "0.18686866+0.00000000j IIIIIZIIZI\n",
      "0.05061134+0.00000000j IIIIIYZZIY\n",
      "0.05061134+0.00000000j IIIIIXZZIX\n",
      "0.02619845+0.00000000j ZIZIZYIYXZ\n",
      "0.02619845+0.00000000j IIIIIYZYXZ\n",
      "0.02619845+0.00000000j ZIZIZXIXXZ\n",
      "0.02619845+0.00000000j IIIIIXZXXZ\n",
      "0.02135331+0.00000000j IZIZIXZIXZ\n",
      "0.02135331+0.00000000j ZZZZZXIIXZ\n",
      "0.02135331+0.00000000j IIIIIXZZXI\n",
      "0.02135331+0.00000000j ZIZIZXIZXI\n",
      "0.16014030+0.00000000j IIIIIZIIIZ\n",
      "-0.19494437+0.00000000j ZIZIZZZIZI\n",
      "-0.06122324+0.00000000j ZIZIZYIZIY\n",
      "-0.06122324+0.00000000j ZIZIZXIZIX\n",
      "-0.17709099+0.00000000j IZIZIIIZIZ\n",
      "0.03986993+0.00000000j IZIZIXZIZX\n",
      "0.03986993+0.00000000j IZIZIYZIZY\n",
      "0.19818585+0.00000000j IIIIIIZZII\n",
      "0.02027026+0.00000000j ZIZIZIXIIZ\n",
      "0.02027026+0.00000000j IIIIIIXIZZ\n",
      "0.04440258+0.00000000j IIIIIIYXXY\n",
      "-0.04440258+0.00000000j IIIIIIYYXX\n",
      "-0.04440258+0.00000000j IIIIIIXXYY\n",
      "0.04440258+0.00000000j IIIIIIXYYX\n",
      "-0.02027026+0.00000000j ZZZZZZIXII\n",
      "-0.02027026+0.00000000j ZIZIZIIXIZ\n",
      "-0.02989656+0.00000000j IZIZIZYYIZ\n",
      "-0.02989656+0.00000000j IIIIIIYYII\n",
      "-0.02989656+0.00000000j ZZZZZZYYZZ\n",
      "-0.02989656+0.00000000j ZIZIZIYYZI\n",
      "0.17853466+0.00000000j IIIIIIZIZI\n",
      "0.07064488+0.00000000j ZIZIZIXZZZ\n",
      "0.07064488+0.00000000j IIIIIIXZIZ\n",
      "0.22293724+0.00000000j IIIIIIZIIZ\n",
      "0.03305545+0.00000000j ZIZIZIXZII\n",
      "0.03305545+0.00000000j IIIIIIXZZI\n",
      "0.03758943+0.00000000j ZZZZZZXIXX\n",
      "0.03758943+0.00000000j ZIZIZIXZXX\n",
      "0.03758943+0.00000000j ZZZZZZYIYX\n",
      "0.03758943+0.00000000j ZIZIZIYZYX\n",
      "-0.20699893+0.00000000j ZIZIZIIIZI\n",
      "-0.23689548+0.00000000j IZIZIZZZIZ\n",
      "-0.05393128+0.00000000j ZZZZZZXIII\n",
      "-0.05393128+0.00000000j IZIZIZXIZI\n",
      "0.22293724+0.00000000j IIIIIIIZZI\n",
      "-0.03305545+0.00000000j ZZZZZZZXZI\n",
      "-0.03305545+0.00000000j ZIZIZIZXZZ\n",
      "-0.03758943+0.00000000j ZIZIZIZYYX\n",
      "-0.03758943+0.00000000j IIIIIIIYYX\n",
      "0.03758943+0.00000000j ZIZIZIZXYY\n",
      "0.03758943+0.00000000j IIIIIIIXYY\n",
      "0.17853466+0.00000000j IIIIIIIZIZ\n",
      "-0.07064488+0.00000000j ZZZZZZZXIZ\n",
      "-0.07064488+0.00000000j ZIZIZIZXII\n",
      "-0.23689548+0.00000000j ZIZIZIZZZI\n",
      "0.05393128+0.00000000j IZIZIZIXZI\n",
      "0.05393128+0.00000000j IIIIIIIXZZ\n",
      "-0.20699893+0.00000000j IZIZIZIIIZ\n",
      "0.28168674+0.00000000j IIIIIIIIZZ\n",
      "-0.04810973+0.00000000j IZIZIZIZYY\n",
      "-0.04810973+0.00000000j IIIIIIIIYY\n",
      "-0.04810973+0.00000000j ZZZZZZZZYY\n",
      "-0.04810973+0.00000000j ZIZIZIZIYY\n",
      "-0.24965504+0.00000000j ZIZIZIZIII\n",
      "-0.29776477+0.00000000j IZIZIZIZZZ\n",
      "-0.29776477+0.00000000j ZIZIZIZIZZ\n",
      "-0.24965504+0.00000000j IZIZIZIZII\n",
      "0.33791717+0.00000000j ZZZZZZZZZZ\n"
     ]
    }
   ],
   "source": [
    "begin = time()\n",
    "Hami_reduced_by_tapering = tapering(Hami_ori, 6)\n",
    "print(f'time cost: {time() - begin}')\n",
    "print(\"Number of qubit after tapering =\", Hami_reduced_by_tapering.num_qubits)\n",
    "print(\"The tapered Hamiltonian is \\n\", Hami_reduced_by_tapering)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83237c85",
   "metadata": {},
   "source": [
    "## 5.3 compare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14abb46f",
   "metadata": {},
   "source": [
    "### 5.3.1 generators and paulixops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2d23c258",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1:   (1.0) [Z0 Z2 Z4 Z6 Z8 Z10], paulix_op: PauliX(wires=[10])\n",
      "generator 2:   (1.0) [Z1 Z3 Z5 Z7 Z9 Z11], paulix_op: PauliX(wires=[11])\n"
     ]
    }
   ],
   "source": [
    "for idx, generator in enumerate(generators_by_qml):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulixops_by_qml[idx]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "70571e35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator 1: 1.00000000 ZIZIZIZIZIZI, paulix_op: 1.00000000 IIIIIIIIIIXI\n",
      "generator 2: 1.00000000 IZIZIZIZIZIZ, paulix_op: 1.00000000 IIIIIIIIIIIX\n"
     ]
    }
   ],
   "source": [
    "generators_by_tapering_ = get_generators_from_kernel(\n",
    "    kernel_of_E(create_parity_check_matrix_E(*create_binary_matrix_G(Hami_ori)))\n",
    ")\n",
    "generators_by_tapering, paulix_ops_by_tapering = get_paulix_ops_from_generators(generators_by_tapering_)\n",
    "\n",
    "for idx, generator in enumerate(generators_by_tapering.terms):\n",
    "    print(f\"generator {idx+1}: {generator}, paulix_op: {paulix_ops_by_tapering.terms[idx]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd222d6f",
   "metadata": {},
   "source": [
    "### 5.3.2 optimal sectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "43e2169e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sectors by qml: [-1, -1]\n",
      "sectors by tapering: [-1, -1]\n"
     ]
    }
   ],
   "source": [
    "print(f'sectors by qml: {paulix_sector_by_qml}')\n",
    "print(f'sectors by tapering: {optimal_sector(Hami_ori, generators_by_tapering, n_electrons)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "72342b16",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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    "name": "ipython",
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
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