qiskit_circ_gen_avqite_qiskit_pauli_rot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "18045b9d-fb93-45d8-9735-85392bbe4e0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "This notebook demonstrates how to construct a Qiskit QuantumCircuit from an\n",
    "AVQITE file, and use it to compute the expectation values of some observables\n",
    "using Qiskit StatevectorEstimator.\n",
    "\n",
    "Packages information:\n",
    "---------------------\n",
    "python version = 3.11 (python version >= 3.7 should suffice)\n",
    "qiskit version = 1.1.1\n",
    "qiskit[visualization] is required for visualization functionality\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f34684e7-09a3-4c23-9a90-84079191729a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pickle\n",
    "from typing import (\n",
    "    List,\n",
    "    Optional,\n",
    "    Tuple,\n",
    "    Union\n",
    ")\n",
    "from qiskit.circuit import Parameter, QuantumCircuit\n",
    "from qiskit.circuit.library import PauliEvolutionGate\n",
    "from qiskit.quantum_info import SparsePauliOp, Pauli\n",
    "from qiskit.primitives import StatevectorEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "12450709-11b8-44eb-9a72-e56e5b4f7dc6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class QiskitCircuitGeneratorAVQITE:\n",
    "    \"\"\"\n",
    "    Class for reading out the AVQITE ansatz and incar files, and constructing\n",
    "    a Qiskit QuantumCircuit object representing the ansatz.\n",
    "\n",
    "    Attributes\n",
    "    ----------\n",
    "    ansatz_filename : str\n",
    "        File name of the ansatz file, including the path.\n",
    "        For this implementation, \"ansatz_inp.pkle\" type of ansatz files is used.\n",
    "    incar_filename : str\n",
    "        File name of the incar file, including the path.\n",
    "        Incar file is used to read out the reference state.\n",
    "    \"\"\"\n",
    "    def __init__(\n",
    "        self,\n",
    "        ansatz_filename: str,\n",
    "        incar_filename: str\n",
    "    ):\n",
    "        self._ansatz_filename = ansatz_filename\n",
    "        self._incar_filename = incar_filename\n",
    "\n",
    "        #Reads out the operator list and the parameter list of the ansatz.\n",
    "        (self._ansatz_adaptvqite,\n",
    "         self._params_ansatz) = self.read_adaptvqite_ansatz(ansatz_filename)\n",
    "\n",
    "        #Reads out the number of qubits.\n",
    "        self._num_qubits = len(self._ansatz_adaptvqite[0])\n",
    "\n",
    "        #Reads out the incar file.\n",
    "        with open(incar_filename) as fp:\n",
    "            incar_content = fp.read()\n",
    "        ref_st_r_pos = incar_content.find(\"ref_state\")\n",
    "        #Reads out the reference state from the incar file.\n",
    "        self._ref_state = incar_content[\n",
    "                            ref_st_r_pos+13:ref_st_r_pos+13+self._num_qubits\n",
    "                            ]\n",
    "\n",
    "        #Initializes a QuantumCircuit object.\n",
    "        self._init_qc = QuantumCircuit(self._num_qubits)\n",
    "\n",
    "        #If the reference state contains \"1\"s, adds corresponding bit-flips.\n",
    "        if all([(el=='0') or (el=='1') for el in self._ref_state]):\n",
    "            self._init_qc.x(\n",
    "                [i for i,el in enumerate(self._ref_state) if el=='1']\n",
    "            )\n",
    "        else:\n",
    "            raise ImportError(\n",
    "                \"Reference state is supposed to be a string of 0s and 1s\"\n",
    "            )\n",
    "\n",
    "        #Constructs a QuantumCircuit object with high-level Pauli evolution\n",
    "        #gates.\n",
    "        #This circuit is not decomposed into primitive gates and does not\n",
    "        #include the initial bit-flips of the reference state\n",
    "        qc_interm = self.circuit_construction(\n",
    "                                    self._ansatz_adaptvqite,\n",
    "                                    self._params_ansatz\n",
    "                                    )\n",
    "        #Constructs a final QuantumCircuit object that represents the ansatz\n",
    "        self.qc = self._init_qc.compose(qc_interm.decompose())\n",
    "\n",
    "\n",
    "    def read_adaptvqite_ansatz(\n",
    "        self,\n",
    "        filename: str\n",
    "    ):\n",
    "        \"\"\"\n",
    "        Reads the ansatz from a file resulting from adaptvqite calculation.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        filename : str\n",
    "            Name of a file containing the results of adaptvqite calculation.\n",
    "            Has to be given in .pkle format.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        ansatz_adaptvqite : List[str]\n",
    "            List of Pauli strings entering the ansatz.\n",
    "        params_adaptvqite : List[float64]\n",
    "            Parameters (angles) of the ansatz.\n",
    "        \"\"\"\n",
    "        if filename[-5:] != '.pkle':\n",
    "            raise ImportError(\"Ansatz file should be given in .pkle format\")\n",
    "        with open(filename, 'rb') as inp:\n",
    "            data_inp = pickle.load(inp)\n",
    "            ansatz_adaptvqite = data_inp[0]\n",
    "            params_adaptvqite = data_inp[1]\n",
    "        return ansatz_adaptvqite, params_adaptvqite\n",
    "\n",
    "\n",
    "    def pauli_rotation_gate(\n",
    "        self,\n",
    "        theta: float,\n",
    "        pauli_string: str,\n",
    "    ):\n",
    "        \"\"\"\n",
    "        Generates a Pauli string rotation gate.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        theta : float\n",
    "            Pauli rotation angle.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        gate : Qiskit instruction\n",
    "        \"\"\"\n",
    "        operator = SparsePauliOp(pauli_string)\n",
    "        gate = PauliEvolutionGate(operator, time = theta/2)\n",
    "        return gate\n",
    "\n",
    "\n",
    "    def circuit_construction(\n",
    "        self,\n",
    "        operator_list,\n",
    "        parameter_list\n",
    "    ):\n",
    "        \"\"\"\n",
    "        Constructs a QuantumCircuit object consisting of high-level Pauli\n",
    "        evolution gates from the ansatz operator and parameter list.\n",
    "        Qiskit convention, by which the rightmost operator in a Pauli string\n",
    "        acts on the qubit0, is taken into account by reversing the order of\n",
    "        each Pauli string.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        qc : QuantumCircuit\n",
    "        \"\"\"\n",
    "        qc = QuantumCircuit(self._num_qubits)\n",
    "        for i, pauli_string in enumerate(operator_list):\n",
    "            theta = parameter_list[i]\n",
    "            qc.append(\n",
    "                self.pauli_rotation_gate(theta, pauli_string[::-1]),\n",
    "                range(self._num_qubits)\n",
    "                )\n",
    "        return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adcab35c-2d79-401f-88d7-93fed8cdf707",
   "metadata": {},
   "source": [
    "## Constructing the circuit from the ansatz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1cea9c69-423f-4fe4-abd1-50cb82644796",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#qc is the circuit in the final from that we need\n",
    "\n",
    "model = QiskitCircuitGeneratorAVQITE(ansatz_filename='ansatz_inp.pkle', incar_filename='incar')\n",
    "qc = model.qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8800b907-f713-464f-aeba-b0dcc54579ea",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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Ff/v27Ro+fLiio6PVoEEDjR49WgcOHPB6zN6yMuOAJk9brcHnJOnmEW1lt9v0wZPnymaTxjw43+fTn3lTSdZmOaLjqjyJI0nBDRJ8HBFgvN/X7jOt7z/W1d2HTp5Ok5EPSXaHsqY/XOXynVNvlbO8RMnj3/NtYICb8o6UatOOwyb1XaYtO4+Y0jc8R34E+J/f15r37NQ/TOy7tsgH4S9WZBxQZaU553KWpef61XkkALCiigqnlmeYc46uosKllRl1r1bit4WuGTNmyOl06tprr1VUVFSV64SHh0s6sdCVn5+vAQMGaPfu3ZoxY4beeustLViwQMOGDZPT6fRJ7N7wxFsrtWrDAT0/oadeva+XzurYSA+8ulybMs05UeYtoQmtVJl/QHmLPzc7lDqlqLJSuaWlVf7Aepanm3cwWZ5u3UJXWJPWiu17lfLX/Kz89SfOPb7v6yk6vGy2Wt33X9lD3XsoM+BrK0wcAyTrjgOBfCwkPzoqkN8D8C8VFU6t3nTQtP7NzEVri3wQ/sLMfCy/sFybTbroqrYCPRcI9P0H/MmG7YdUXFJpWv918byA305dOHfuXEnSgAHVP29g9+7dkk4sdL311lvas2eP5s+fr2bNmkmSkpKS1Lt3b3311Ve69NJLvRe0F1VUuDTmwflaOmO4bh+ZqgUrcvTyR+vMDstwTa58UPmr52jb0yMUmthGUal9FNmmh6I69Fd401SzwzPN4xvX6/GNvn1YNbxn/VbznqmXvu2QKiudcjiseZ1EwhUP6OCCGcqa/rDaPvmLJCl/zS/a/cG9avPwdwptnGxugEANmDkGSPL5Q8+NEsjHQvKjowL5PQD/sm13vkpKzTuxYdXjwJ/IB+EP1m89ZGr/67bkqW2LGFNj8ESg5wKBvv+AP6kLxwGjuFwuFRUVSZIiIiJks3n2qAS/LXTt2HF0ruLmzZtXubyiokKLFi2SdGKha/bs2erTp8+xIpck9erVSy1bttTXX3/tUaGre/fuyslx79kHTgVLsQ+63depHC4oU2lZpUKCHfp2wS65DLzTvE1Kiuwy7uF3tpBwNX55s9vbRbXrpdQXlmvvly/o8PLvdODnd3Xg53ePLkvrq+Tx7yk0oWXVfTqCZQ8J9zjmlJQ2cpUVe7z98cLtdqV36WVIW5J0U7OWGpHYtMplQ5bMM6SPlJQUFVv4rkercEkqjH2s2uVLZwxXQnz1V6AmxIcf+++uOVdVu15ObpF6XP3VSb93Ol1q2ryVoZ/3qng6BkR37K9uX1Y/uIU3TVW3L/53Yqh0b6a2PXelksY+p+iO/T0J9RgjxwDgVPLD+koR51e57HRjgFT7ceCV197Q+89+70bEngn0Y6Gn42BVapMfucPocTDQ3wNAdcocCVL926pc5ovjwNr1G5SUlORGxJ4hHwSqdyDqSimkfZXLjPpOKFU/Dtz813EaX7bajYg9E+i5QKDvP4DqFYacKUVdUuUyX+SD0z/+TN9Pu9qNiKvndDqVnZ0tSerSpYtWrlzpUTt+W+gqLCyUJBUXV51kzpw5U7m5uYqOjlaLFi2O/T49PV1XXHHFSeu3b99e6enpHsWSk5OjPXv2uLeRLUSK9ai7ar37eF+FBDuUvjVPD97SRbN+2K5tu/MNaTs7K0tylRnSliTZQyPk6eONw5M7HptTvXTfDhWsm6fcOW+rIH2Btjx1iVJfWC57cMhJ28X1v1Zx/a/1OOasrCw5S4s83v54EQ6H1MWQpiRJraOidF5D7z4wOisrS0WV5l1ZGlBOMTYkxEcoqXHkaZsIcthrtF5VjP68V6U2Y0BNOUuLtHXyparfc7gaDR1X6/aMHAOAU2qYL1WTs9Z0DJA8HwcKCwpVmO1mXuOBQD8WGj0OepofucPocTDQ3wNAtcIcUv2qF/niOFBRUen+91sPkA8Cp9CsRKrmsO2L74R5eYeUd4h8sCpG5gKBvv8ATqFBS6nqpzX5JB8sLi72Sj64d+9ej7f120JXQkKC8vLytGLFCvXqdeLVD9nZ2Zo4caIkqVOnTifcDpeXl6eYmJiT2ouNjdXGjRs9jsVdTgUr26PeqnbnNWka0DNR909Zpi9/2aEVMy/VO4/3Vf8bvjWk/SaJiYbf0WWE0EbNFTpwtGIHjNLG+/qqMGORijb/oai0Poa0f7zExERD7+iymsTERK7a8ZEsV5lctqq/1eTknvqLdUJ8uIIcdlVUOpWTW/37tdp2XE4lJjaSTd59+LBRY8Cp5P32mYq3r1bJnk3KWzjzpOXtX0tXSMNmVWxZNSPHAOBUCkLDVN1TEU43Bki1HweiIkNU/4wzahJqrQT6sdCb46C38iOjx8FAfw8A1Sm3x2hfNct8cRwIdjjVyAfHAfJBoHoHwxyq7p1m1HfCU7UVGxOh8EjywaoYmQsE+v4DqF5RSISqmzzQF/lgRJhDDQzKB4+/o6txY8+L8X5b6Dr//POVkZGhZ555RoMGDVJKSookaenSpRo1apRyc48+MK1Lly5ej2XZsmVub1NYVK6osz8wpP/Wzepp8vju+mPtfj3zzho5nS49+voKTR7fQ3dek6ZXp3t2p9rxNm/apMiIYAOiPaq4QuprTA1OkmSz2RSZcpYKMxap7IB3rjratGmzwg36RLlKSlRx5RhjGvORTZs2yRYWZnYYAaHnNV9q6bqqH/pY1e3Ex9s15yolNY5UTm6xmg762O2+27eO1bovdrm9nbuMHgOqEjdglOIGjDKsPSPHAOBUflqyR4NuqXrqwNONAVLtx4E3X35Y1wx93+3t3BXox0JfjING50dGj4OB/h4AqlNe7lR0rw9UWnbyFfO+OA6MvLSvPnzqIbe3cxf5IFC9Z99Zo3tfXlrlMm9/J5SkRXM/UTsfPKMr0HOBQN9/ANVbu+mgOv3liyqX+SIf/OdDt+ueUVPd3q4qhYWFioo6envawoULPW7HepcG1NCkSZMUFxenXbt2qX379urYsaPatGmjnj17qmXLlho4cKCkE5/PJUkNGjTQoUOHTmrv4MGDio01eC5BH7DZpPeeOFcOu01jHpwnp/PoXRjPvrtWS9ft1+Tx3dUyKdrkKI1zZNUcuSorTvq9s7RYR1b9KEkKb5rm67AAQ3VPizet724m9g3gKLM/h93bMw5YDfkR4F+Cg+3q0ta876Zm5qIAjjIzH4uKCFZK82rmTwUA+ERqyxiFhzlM678u5oN+W+hKSkrSggULNHToUIWFhSkzM1OxsbF688039c0332jTpk2STi50paamVvksrvT0dKWmpvokdiNNGNNR53RtrIenrtCG7f+b6MjpdGnsQ/MV5LDrncf7mhihsXZNu0drbmyqHVP/qn3fvKbcn95R1sePKf3uLirZsU6xA0YrPLmj2WECtdKzY0PT+u7Rwby+ARzVoF6o2jSvZ0rfMdEhat3MnL7hOfIjwP+QDwKB7czUONntttOv6AXd0szrGwBwVFCQXWemmlNsCgqyqUu7undDkN8WuqSjRavZs2crPz9f+fn5+v3333XLLbeosLBQmZmZstvt6tChwwnbDBs2TAsXLtTu3buP/e7333/X1q1bdfHFF/t6F2qlXYv6euKOM7V49T698P66k5anbz2kR19foX7dm+jOa/zjKt6mN7yoBmdfrsKNS5Q141Ht+Nct2jd7ioJjE9X8zmlKvutds0MEau2ygcmKNGFOlJBgu0YObuHzfgGcbNSw1qb0e92w1pzYsCDyI8D/mHUcaN2sns7u1MiUvgH8T0y9UA3vX/Pnxxlp9MVtTOkXAHAis/LBywYmKzoyxJS+TyUgZ49ev369XC6XUlJSFBERccKyW265Ra+++qouueQSPfbYYyopKdGkSZPUs2dPXXLJJSZF7JkN2w8rvMepn6Hx9LQ1enraGh9F5H31ul6gel0vMDuMOqNffCOVXXzlKdc53XLUPfWjQ3TdsNZ685MNPu33ysEt1DDW+w8FB3B6N13eVo+/uVIVFS6f9nvble182p8ROBaSH/EegD/q0aGhenSIr/a5rd5y+8hULngA6ojbR6bqv3N3+LTPBvVCdNWFLX3apxECPRcI9P0H/NW1Q1tp0kt/6EhBuU/7vX1k3Zz1zq/v6KrO2rVrJZ08baEk1atXT3PnzlWTJk101VVX6aabblLv3r01e/Zs2e0B+XIBqIPGXeX7kwx3Xt3ep/0BqF6ThhEaOdi3JxkG9UpUWqsGPu0TAFC98df6NjerFxWsMcO5kwOoK847K1HtW8X4tM9b/tJOESbMLgIAOFlURLBuurytT/vslBKrft0TfNpnTQVk5eZUhS5JatWqlWbPnq2CggIdOnRIH330kRo2ZB5yAHVHhzax+vuYDqdf0SB3XJVq6rMgTsdZVqItT12qdbelKH18Z216eJBKsrdUuW7O589p/Z0dtP6ONG196jJVFBw6aZ2s6Y9o+SU2FW1b5d3AgVp44e9nKS4m1Cd9hYc5NPWBc3zSFwCgZq65qJUG9Ur0WX8vTTxbsfV9c9w5lZKszdowqbfW3ZaijAk9VLxzfZXr5c6ZpnW3ttHav7bSjtdulqvi6NXOpXsztfGB/lp5dX2l393lhG3y1/6qFVeEK/3uLsd+nKXFkiSX06nd7/5d6+/soHW3t1PmqzfKWV7mzV0FTslut+ntR/v67ALIlknReuiWLj7pCwBQM4/e1lXNE6N80pfDYdPbj/aRzVY37+6n0AUAFvXY7WcqtWWMW9vk5BZp995C5eQW1XibFmdE6+m7e7gZne81vOAWtZ+6UWmvrFbMWZdox2s3nbTOkVVzdODnd9XumcVq/690RbTupqyPHjhhncJNf6hwy1KFNGruq9ABjzSOC9dr9/VyeztPxoGnx/dQ62b13O4LAOA9NtvRk9zRkcFubefJcWBInyRdf2nduJtr59S/Kn7wLerw+iYlXH6vMl8Ze9I6pXu3K+s/D6nt5AXq8MYWlR/aq/0/vCVJckTU0xnX/lMtJ0yvsv2wM9oq7eVVx37soUen7s79aZq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      "text/plain": [
       "<Figure size 2210.55x3712.33 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#draws the obtained circuit\n",
    "\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bc511683-30c9-4d36-8522-977e82011848",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#Saves qc as an object via pickle\n",
    "\n",
    "with open(\"qc.pkle\", \"wb\") as f:\n",
    "    pickle.dump(qc, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "732e1144-37dc-4914-9a61-9efdeccd30b1",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Computing expectation values of observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b8c791a9-30bb-4c70-9495-99f70e72af5c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "obs_list_2D = [\n",
    "        [\n",
    "            \"0.5*IIIIIIII\",\n",
    "            \"-0.5*ZIIIIIII\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.25*YZYIIIII\",\n",
    "            \"0.25*XZXIIIII\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.25*YZZZYIII\",\n",
    "            \"0.25*XZZZXIII\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.25*YZZZZZYI\",\n",
    "            \"0.25*XZZZZZXI\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.5*IIIIIIII\",\n",
    "            \"-0.5*IIZIIIII\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.25*IIYZYIII\",\n",
    "            \"0.25*IIXZXIII\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.25*IIYZZZYI\",\n",
    "            \"0.25*IIXZZZXI\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.5*IIIIIIII\",\n",
    "            \"-0.5*IIIIZIII\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.25*IIIIYZYI\",\n",
    "            \"0.25*IIIIXZXI\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.5*IIIIIIII\",\n",
    "            \"-0.5*IIIIIIZI\"\n",
    "        ],\n",
    "        [\n",
    "            \"0.25*IIIIIIII\",\n",
    "            \"-0.25*IZIIIIII\",\n",
    "            \"-0.25*ZIIIIIII\",\n",
    "            \"0.25*ZZIIIIII\"\n",
    "        ]\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "37586b75-06c3-4b55-bec9-3bbe2705d1dc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Converts the list of observables into the Qiskit format\n",
    "\n",
    "obs_list_qiskit=[]\n",
    "\n",
    "for obs_row in obs_list_2D:\n",
    "    pauli_strings_list = []\n",
    "    params_list = []\n",
    "    for obs in obs_row:\n",
    "        pauli = \"\".join([i for i in obs if (i==\"I\" or i==\"X\" or i==\"Y\" or i==\"Z\")])\n",
    "        coeff = float(\"\".join([i for i in obs if (i==\"-\" or i==\".\" or i.isdigit())]))\n",
    "        pauli_strings_list.append(pauli[::-1])\n",
    "        params_list.append(coeff)\n",
    "    \n",
    "    obs_list_qiskit.append([SparsePauliOp(pauli_strings_list, params_list)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0acec3bd-5e34-4687-bd51-ce68b6511506",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[SparsePauliOp(['IIIIIIII', 'IIIIIIIZ'],\n",
       "                coeffs=[ 0.5+0.j, -0.5+0.j])],\n",
       " [SparsePauliOp(['IIIIIYZY', 'IIIIIXZX'],\n",
       "                coeffs=[0.25+0.j, 0.25+0.j])],\n",
       " [SparsePauliOp(['IIIYZZZY', 'IIIXZZZX'],\n",
       "                coeffs=[0.25+0.j, 0.25+0.j])],\n",
       " [SparsePauliOp(['IYZZZZZY', 'IXZZZZZX'],\n",
       "                coeffs=[0.25+0.j, 0.25+0.j])],\n",
       " [SparsePauliOp(['IIIIIIII', 'IIIIIZII'],\n",
       "                coeffs=[ 0.5+0.j, -0.5+0.j])],\n",
       " [SparsePauliOp(['IIIYZYII', 'IIIXZXII'],\n",
       "                coeffs=[0.25+0.j, 0.25+0.j])],\n",
       " [SparsePauliOp(['IYZZZYII', 'IXZZZXII'],\n",
       "                coeffs=[0.25+0.j, 0.25+0.j])],\n",
       " [SparsePauliOp(['IIIIIIII', 'IIIZIIII'],\n",
       "                coeffs=[ 0.5+0.j, -0.5+0.j])],\n",
       " [SparsePauliOp(['IYZYIIII', 'IXZXIIII'],\n",
       "                coeffs=[0.25+0.j, 0.25+0.j])],\n",
       " [SparsePauliOp(['IIIIIIII', 'IZIIIIII'],\n",
       "                coeffs=[ 0.5+0.j, -0.5+0.j])],\n",
       " [SparsePauliOp(['IIIIIIII', 'IIIIIIZI', 'IIIIIIIZ', 'IIIIIIZZ'],\n",
       "                coeffs=[ 0.25+0.j, -0.25+0.j, -0.25+0.j,  0.25+0.j])]]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obs_list_qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d3efc776-08df-4775-88c1-3ff7eb8f99a6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Computes expectation values using Qiskit StatevectorEstimator\n",
    "\n",
    "estimator = StatevectorEstimator()\n",
    "pub = (qc, obs_list_qiskit)\n",
    "job = estimator.run([pub],precision=1e-10)\n",
    "result = job.result()[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f7799b19-df68-4d08-8029-dad4893c454b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.48911703],\n",
       "       [ 0.20681802],\n",
       "       [ 0.05769926],\n",
       "       [ 0.05068355],\n",
       "       [ 0.50892231],\n",
       "       [ 0.03037431],\n",
       "       [-0.01917516],\n",
       "       [ 0.00724491],\n",
       "       [-0.00123756],\n",
       "       [ 0.99470818],\n",
       "       [ 0.02384612]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.data.evs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9ee932fd-714d-40ee-a612-7d15102bcd1a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{\"['0.5*IIIIIIII', '-0.5*ZIIIIIII']\": array([0.48911703]),\n",
       " \"['0.25*YZYIIIII', '0.25*XZXIIIII']\": array([0.20681802]),\n",
       " \"['0.25*YZZZYIII', '0.25*XZZZXIII']\": array([0.05769926]),\n",
       " \"['0.25*YZZZZZYI', '0.25*XZZZZZXI']\": array([0.05068355]),\n",
       " \"['0.5*IIIIIIII', '-0.5*IIZIIIII']\": array([0.50892231]),\n",
       " \"['0.25*IIYZYIII', '0.25*IIXZXIII']\": array([0.03037431]),\n",
       " \"['0.25*IIYZZZYI', '0.25*IIXZZZXI']\": array([-0.01917516]),\n",
       " \"['0.5*IIIIIIII', '-0.5*IIIIZIII']\": array([0.00724491]),\n",
       " \"['0.25*IIIIYZYI', '0.25*IIIIXZXI']\": array([-0.00123756]),\n",
       " \"['0.5*IIIIIIII', '-0.5*IIIIIIZI']\": array([0.99470818]),\n",
       " \"['0.25*IIIIIIII', '-0.25*IZIIIIII', '-0.25*ZIIIIIII', '0.25*ZZIIIIII']\": array([0.02384612])}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Creates a dictionary of the expectation values and prints them out\n",
    "\n",
    "expec_val_data = dict()\n",
    "for i in range(len(obs_list_2D)):\n",
    "    expec_val_data[str(obs_list_2D[i])] = result.data.evs[i]\n",
    "expec_val_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b42f14a-3bdf-49ca-9784-8c4679d42056",
   "metadata": {},
   "source": [
    "## Check using SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3e140b55-594f-4031-bf67-3a9a5d818958",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "31a82b01-7392-4ae5-8801-719bb46bfe50",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "state = np.zeros(2**8)\n",
    "state[0] = 1.0\n",
    "\n",
    "state = SparsePauliOp(['IIIIIIIX'], [1.0]).to_matrix() @ state\n",
    "state = SparsePauliOp(['IIIIIIXI'], [1.0]).to_matrix() @ state\n",
    "state = SparsePauliOp(['IIIIIXII'], [1.0]).to_matrix() @ state\n",
    "state = SparsePauliOp(['IIIIXIII'], [1.0]).to_matrix() @ state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "73bc954d-fab9-4226-a14b-82832f41afe6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "for i,pauli_string in enumerate(model._ansatz_adaptvqite):\n",
    "    state = scipy.linalg.expm(-1j/2*SparsePauliOp([pauli_string[::-1]],[model._params_ansatz[i]]).to_matrix()) @ state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "69d88c39-9822-40df-97d6-605ba1bc67b0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.48911702639103727+0j)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state.conjugate().transpose() @ SparsePauliOp(['IIIIIIII','IIIIIIIZ'], [0.5,-0.5]).to_matrix() @ state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bee5414c-ee62-40d5-b06c-b6c6c270acab",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.20681802315313205+0j)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state.conjugate().transpose() @ SparsePauliOp(['IIIIIYZY','IIIIIXZX'], [0.25,0.25]).to_matrix() @ state"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "adaptvqite-quimb",
   "language": "python",
   "name": "adaptvqite-quimb"
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   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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