VQE.ipynb

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   "outputs": [],
   "source": [
    "%reset "
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  {
   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "# This code is part of Qiskit.\n",
    "#\n",
    "# (C) Copyright IBM 2022.\n",
    "#\n",
    "# This code is licensed under the Apache License, Version 2.0. You may\n",
    "# obtain a copy of this license in the LICENSE.txt file in the root directory\n",
    "# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.\n",
    "#\n",
    "# Any modifications or derivative works of this code must retain this\n",
    "# copyright notice, and modified files need to carry a notice indicating\n",
    "# that they have been altered from the originals.\n",
    "\n",
    "\"\"\"The variational quantum eigensolver algorithm.\"\"\"\n",
    "\n",
    "from __future__ import annotations\n",
    "\n",
    "import logging\n",
    "from time import time\n",
    "from collections.abc import Callable, Sequence\n",
    "from typing import Any\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from qiskit.algorithms.gradients import BaseEstimatorGradient\n",
    "from qiskit.circuit import QuantumCircuit\n",
    "from qiskit.opflow import PauliSumOp\n",
    "from qiskit.primitives import BaseEstimator\n",
    "from qiskit.quantum_info.operators.base_operator import BaseOperator\n",
    "\n",
    "from qiskit.algorithms.exceptions import AlgorithmError\n",
    "from qiskit.algorithms.list_or_dict import ListOrDict\n",
    "from qiskit.algorithms.optimizers import Optimizer, Minimizer, OptimizerResult\n",
    "from qiskit.algorithms.variational_algorithm import VariationalAlgorithm, VariationalResult\n",
    "from qiskit.algorithms.minimum_eigensolvers import MinimumEigensolver, MinimumEigensolverResult\n",
    "from qiskit.algorithms.observables_evaluator import estimate_observables\n",
    "from qiskit.algorithms.utils import validate_initial_point, validate_bounds\n",
    "\n",
    "# private function as we expect this to be updated in the next released\n",
    "from qiskit.algorithms.utils.set_batching import _set_default_batchsize\n",
    "\n",
    "logger = logging.getLogger(__name__)\n",
    "\n",
    "\n",
    "class VQE(VariationalAlgorithm, MinimumEigensolver):\n",
    "    r\"\"\"The variational quantum eigensolver (VQE) algorithm.\n",
    "\n",
    "    VQE is a hybrid quantum-classical algorithm that uses a variational technique to find the\n",
    "    minimum eigenvalue of a given Hamiltonian operator :math:`H`.\n",
    "\n",
    "    The ``VQE`` algorithm is executed using an :attr:`estimator` primitive, which computes\n",
    "    expectation values of operators (observables).\n",
    "\n",
    "    An instance of ``VQE`` also requires an :attr:`ansatz`, a parameterized\n",
    "    :class:`.QuantumCircuit`, to prepare the trial state :math:`|\\psi(\\vec\\theta)\\rangle`. It also\n",
    "    needs a classical :attr:`optimizer` which varies the circuit parameters :math:`\\vec\\theta` such\n",
    "    that the expectation value of the operator on the corresponding state approaches a minimum,\n",
    "\n",
    "    .. math::\n",
    "\n",
    "        \\min_{\\vec\\theta} \\langle\\psi(\\vec\\theta)|H|\\psi(\\vec\\theta)\\rangle.\n",
    "\n",
    "    The :attr:`estimator` is used to compute this expectation value for every optimization step.\n",
    "\n",
    "    The optimizer can either be one of Qiskit's optimizers, such as\n",
    "    :class:`~qiskit.algorithms.optimizers.SPSA` or a callable with the following signature:\n",
    "\n",
    "    .. code-block:: python\n",
    "\n",
    "        from qiskit.algorithms.optimizers import OptimizerResult\n",
    "\n",
    "        def my_minimizer(fun, x0, jac=None, bounds=None) -> OptimizerResult:\n",
    "            # Note that the callable *must* have these argument names!\n",
    "            # Args:\n",
    "            #     fun (callable): the function to minimize\n",
    "            #     x0 (np.ndarray): the initial point for the optimization\n",
    "            #     jac (callable, optional): the gradient of the objective function\n",
    "            #     bounds (list, optional): a list of tuples specifying the parameter bounds\n",
    "\n",
    "            result = OptimizerResult()\n",
    "            result.x = # optimal parameters\n",
    "            result.fun = # optimal function value\n",
    "            return result\n",
    "\n",
    "    The above signature also allows one to use any SciPy minimizer, for instance as\n",
    "\n",
    "    .. code-block:: python\n",
    "\n",
    "        from functools import partial\n",
    "        from scipy.optimize import minimize\n",
    "\n",
    "        optimizer = partial(minimize, method=\"L-BFGS-B\")\n",
    "\n",
    "    The following attributes can be set via the initializer but can also be read and updated once\n",
    "    the VQE object has been constructed.\n",
    "\n",
    "    Attributes:\n",
    "        estimator (BaseEstimator): The estimator primitive to compute the expectation value of the\n",
    "            Hamiltonian operator.\n",
    "        ansatz (QuantumCircuit): A parameterized quantum circuit to prepare the trial state.\n",
    "        optimizer (Optimizer | Minimizer): A classical optimizer to find the minimum energy. This\n",
    "            can either be a Qiskit :class:`.Optimizer` or a callable implementing the\n",
    "            :class:`.Minimizer` protocol.\n",
    "        gradient (BaseEstimatorGradient | None): An optional estimator gradient to be used with the\n",
    "            optimizer.\n",
    "        callback (Callable[[int, np.ndarray, float, dict[str, Any]], None] | None): A callback that\n",
    "            can access the intermediate data at each optimization step. These data are: the\n",
    "            evaluation count, the optimizer parameters for the ansatz, the evaluated mean, and the\n",
    "            metadata dictionary.\n",
    "\n",
    "    References:\n",
    "        [1]: Peruzzo, A., et al, \"A variational eigenvalue solver on a quantum processor\"\n",
    "            `arXiv:1304.3061 <https://arxiv.org/abs/1304.3061>`__\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(\n",
    "        self,\n",
    "        estimator: BaseEstimator,\n",
    "        ansatz: QuantumCircuit,\n",
    "        optimizer: Optimizer | Minimizer,\n",
    "        *,\n",
    "        gradient: BaseEstimatorGradient | None = None,\n",
    "        initial_point: Sequence[float] | None = None,\n",
    "        callback: Callable[[int, np.ndarray, float, dict[str, Any]], None] | None = None,\n",
    "    ) -> None:\n",
    "        r\"\"\"\n",
    "        Args:\n",
    "            estimator: The estimator primitive to compute the expectation value of the\n",
    "                Hamiltonian operator.\n",
    "            ansatz: A parameterized quantum circuit to prepare the trial state.\n",
    "            optimizer: A classical optimizer to find the minimum energy. This can either be a\n",
    "                Qiskit :class:`.Optimizer` or a callable implementing the :class:`.Minimizer`\n",
    "                protocol.\n",
    "            gradient: An optional estimator gradient to be used with the optimizer.\n",
    "            initial_point: An optional initial point (i.e. initial parameter values) for the\n",
    "                optimizer. The length of the initial point must match the number of :attr:`ansatz`\n",
    "                parameters. If ``None``, a random point will be generated within certain parameter\n",
    "                bounds. ``VQE`` will look to the ansatz for these bounds. If the ansatz does not\n",
    "                specify bounds, bounds of :math:`-2\\pi`, :math:`2\\pi` will be used.\n",
    "            callback: A callback that can access the intermediate data at each optimization step.\n",
    "                These data are: the evaluation count, the optimizer parameters for the ansatz, the\n",
    "                estimated value, and the metadata dictionary.\n",
    "        \"\"\"\n",
    "        super().__init__()\n",
    "\n",
    "        self.estimator = estimator\n",
    "        self.ansatz = ansatz\n",
    "        self.optimizer = optimizer\n",
    "        self.gradient = gradient\n",
    "        # this has to go via getters and setters due to the VariationalAlgorithm interface\n",
    "        self.initial_point = initial_point\n",
    "        self.callback = callback\n",
    "\n",
    "    @property\n",
    "    def initial_point(self) -> Sequence[float] | None:\n",
    "        return self._initial_point\n",
    "\n",
    "    @initial_point.setter\n",
    "    def initial_point(self, value: Sequence[float] | None) -> None:\n",
    "        self._initial_point = value\n",
    "\n",
    "    def compute_minimum_eigenvalue(\n",
    "        self,\n",
    "        operator: BaseOperator | PauliSumOp,\n",
    "        aux_operators: ListOrDict[BaseOperator | PauliSumOp] | None = None,\n",
    "    ) -> VQEResult:\n",
    "        self._check_operator_ansatz(operator)\n",
    "\n",
    "        initial_point = validate_initial_point(self.initial_point, self.ansatz)\n",
    "\n",
    "        bounds = validate_bounds(self.ansatz)\n",
    "\n",
    "        start_time = time()\n",
    "\n",
    "        evaluate_energy = self._get_evaluate_energy(self.ansatz, operator)\n",
    "\n",
    "        if self.gradient is not None:\n",
    "            evaluate_gradient = self._get_evaluate_gradient(self.ansatz, operator)\n",
    "        else:\n",
    "            evaluate_gradient = None\n",
    "\n",
    "        # perform optimization\n",
    "        if callable(self.optimizer):\n",
    "            optimizer_result = self.optimizer(\n",
    "                fun=evaluate_energy, x0=initial_point, jac=evaluate_gradient, bounds=bounds\n",
    "            )\n",
    "        else:\n",
    "            # we always want to submit as many estimations per job as possible for minimal\n",
    "            # overhead on the hardware\n",
    "            was_updated = _set_default_batchsize(self.optimizer)\n",
    "\n",
    "            optimizer_result = self.optimizer.minimize(\n",
    "                fun=evaluate_energy, x0=initial_point, jac=evaluate_gradient, bounds=bounds\n",
    "            )\n",
    "\n",
    "            # reset to original value\n",
    "            if was_updated:\n",
    "                self.optimizer.set_max_evals_grouped(None)\n",
    "\n",
    "        optimizer_time = time() - start_time\n",
    "\n",
    "        logger.info(\n",
    "            \"Optimization complete in %s seconds.\\nFound optimal point %s\",\n",
    "            optimizer_time,\n",
    "            optimizer_result.x,\n",
    "        )\n",
    "\n",
    "        if aux_operators is not None:\n",
    "            aux_operators_evaluated = estimate_observables(\n",
    "                self.estimator, self.ansatz, aux_operators, optimizer_result.x\n",
    "            )\n",
    "        else:\n",
    "            aux_operators_evaluated = None\n",
    "\n",
    "        return self._build_vqe_result(\n",
    "            self.ansatz, optimizer_result, aux_operators_evaluated, optimizer_time\n",
    "        )\n",
    "\n",
    "\n",
    "    @classmethod\n",
    "    def supports_aux_operators(cls) -> bool:\n",
    "        return True\n",
    "\n",
    "\n",
    "    def _get_evaluate_energy(\n",
    "        self,\n",
    "        ansatz: QuantumCircuit,\n",
    "        operator: BaseOperator | PauliSumOp,\n",
    "    ) -> Callable[[np.ndarray], np.ndarray | float]:\n",
    "        \"\"\"Returns a function handle to evaluate the energy at given parameters for the ansatz.\n",
    "        This is the objective function to be passed to the optimizer that is used for evaluation.\n",
    "\n",
    "        Args:\n",
    "            ansatz: The ansatz preparing the quantum state.\n",
    "            operator: The operator whose energy to evaluate.\n",
    "\n",
    "        Returns:\n",
    "            A callable that computes and returns the energy of the hamiltonian of each parameter.\n",
    "\n",
    "        Raises:\n",
    "            AlgorithmError: If the primitive job to evaluate the energy fails.\n",
    "        \"\"\"\n",
    "        num_parameters = ansatz.num_parameters\n",
    "\n",
    "        # avoid creating an instance variable to remain stateless regarding results\n",
    "        eval_count = 0\n",
    "\n",
    "        def evaluate_energy(parameters: np.ndarray) -> np.ndarray | float:\n",
    "            nonlocal eval_count\n",
    "\n",
    "            # handle broadcasting: ensure parameters is of shape [array, array, ...]\n",
    "            parameters = np.reshape(parameters, (-1, num_parameters)).tolist()\n",
    "            batch_size = len(parameters)\n",
    "\n",
    "            try:\n",
    "                job = self.estimator.run(batch_size * [ansatz], batch_size * [operator], parameters)\n",
    "                estimator_result = job.result()\n",
    "            except Exception as exc:\n",
    "                raise AlgorithmError(\"The primitive job to evaluate the energy failed!\") from exc\n",
    "\n",
    "            values = estimator_result.values\n",
    "\n",
    "            if self.callback is not None:\n",
    "                metadata = estimator_result.metadata\n",
    "                for params, value, meta in zip(parameters, values, metadata):\n",
    "                    eval_count += 1\n",
    "                    self.callback(eval_count, params, value, meta)\n",
    "\n",
    "            energy = values[0] if len(values) == 1 else values\n",
    "\n",
    "            return energy\n",
    "\n",
    "        return evaluate_energy\n",
    "\n",
    "    def _get_evaluate_gradient(\n",
    "        self,\n",
    "        ansatz: QuantumCircuit,\n",
    "        operator: BaseOperator | PauliSumOp,\n",
    "    ) -> Callable[[np.ndarray], np.ndarray]:\n",
    "        \"\"\"Get a function handle to evaluate the gradient at given parameters for the ansatz.\n",
    "\n",
    "        Args:\n",
    "            ansatz: The ansatz preparing the quantum state.\n",
    "            operator: The operator whose energy to evaluate.\n",
    "\n",
    "        Returns:\n",
    "            A function handle to evaluate the gradient at given parameters for the ansatz.\n",
    "\n",
    "        Raises:\n",
    "            AlgorithmError: If the primitive job to evaluate the gradient fails.\n",
    "        \"\"\"\n",
    "\n",
    "        def evaluate_gradient(parameters: np.ndarray) -> np.ndarray:\n",
    "            # broadcasting not required for the estimator gradients\n",
    "            try:\n",
    "                job = self.gradient.run([ansatz], [operator], [parameters])\n",
    "                gradients = job.result().gradients\n",
    "            except Exception as exc:\n",
    "                raise AlgorithmError(\"The primitive job to evaluate the gradient failed!\") from exc\n",
    "\n",
    "            return gradients[0]\n",
    "\n",
    "        return evaluate_gradient\n",
    "\n",
    "    def _check_operator_ansatz(self, operator: BaseOperator | PauliSumOp):\n",
    "        \"\"\"Check that the number of qubits of operator and ansatz match and that the ansatz is\n",
    "        parameterized.\n",
    "        \"\"\"\n",
    "        if operator.num_qubits != self.ansatz.num_qubits:\n",
    "            try:\n",
    "                logger.info(\n",
    "                    \"Trying to resize ansatz to match operator on %s qubits.\", operator.num_qubits\n",
    "                )\n",
    "                self.ansatz.num_qubits = operator.num_qubits\n",
    "            except AttributeError as error:\n",
    "                raise AlgorithmError(\n",
    "                    \"The number of qubits of the ansatz does not match the \"\n",
    "                    \"operator, and the ansatz does not allow setting the \"\n",
    "                    \"number of qubits using `num_qubits`.\"\n",
    "                ) from error\n",
    "\n",
    "        if self.ansatz.num_parameters == 0:\n",
    "            raise AlgorithmError(\"The ansatz must be parameterized, but has no free parameters.\")\n",
    "\n",
    "    def _build_vqe_result(\n",
    "        self,\n",
    "        ansatz: QuantumCircuit,\n",
    "        optimizer_result: OptimizerResult,\n",
    "        aux_operators_evaluated: ListOrDict[tuple[complex, tuple[complex, int]]],\n",
    "        optimizer_time: float,\n",
    "    ) -> VQEResult:\n",
    "        result = VQEResult()\n",
    "        result.optimal_circuit = ansatz.copy()\n",
    "        result.eigenvalue = optimizer_result.fun\n",
    "        result.cost_function_evals = optimizer_result.nfev\n",
    "        result.optimal_point = optimizer_result.x\n",
    "        result.optimal_parameters = dict(zip(self.ansatz.parameters, optimizer_result.x))\n",
    "        result.optimal_value = optimizer_result.fun\n",
    "        result.optimizer_time = optimizer_time\n",
    "        result.aux_operators_evaluated = aux_operators_evaluated\n",
    "        result.optimizer_result = optimizer_result\n",
    "        return result\n",
    "\n",
    "\n",
    "\n",
    "class VQEResult(VariationalResult, MinimumEigensolverResult):\n",
    "    \"\"\"Variational quantum eigensolver result.\"\"\"\n",
    "\n",
    "    def __init__(self) -> None:\n",
    "        super().__init__()\n",
    "        self._cost_function_evals = None\n",
    "\n",
    "    @property\n",
    "    def cost_function_evals(self) -> int | None:\n",
    "        \"\"\"The number of cost optimizer evaluations.\"\"\"\n",
    "        return self._cost_function_evals\n",
    "\n",
    "    @cost_function_evals.setter\n",
    "    def cost_function_evals(self, value: int) -> None:\n",
    "        self._cost_function_evals = value\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1b7660ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_nature.second_q.mappers import BravyiKitaevMapper, BravyiKitaevSuperFastMapper, ParityMapper, JordanWignerMapper, QubitConverter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "75faef2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fermion_to_qubit(fermion_op, second_q_op, mapper, truncate=20, two_qubit_reduction=False, z2symmetry_reduction=None, show=True): \n",
    "    if show: \n",
    "        print(\"Qubit Hamiltonian operator\")\n",
    "    dmap = {\"Jordan-Wigner\": JordanWignerMapper(), \"Parity\": ParityMapper(), \"Bravyi-Kitaev\": BravyiKitaevMapper()}\n",
    "    qubit_op = None\n",
    "    qubit_converter = None \n",
    "    mapper_func = None\n",
    "    for label,function in dmap.items(): \n",
    "        if label == mapper: \n",
    "            if show: \n",
    "                print(\"{} transformation \". format(mapper))\n",
    "            qubit_converter = QubitConverter(function, two_qubit_reduction=two_qubit_reduction, z2symmetry_reduction=z2symmetry_reduction)\n",
    "            if two_qubit_reduction: \n",
    "                qubit_op = qubit_converter.convert(second_q_op, num_particles=fermion_op.num_particles)\n",
    "            else: \n",
    "                qubit_op = qubit_converter.convert(second_q_op)\n",
    "            n_items = len(qubit_op)\n",
    "            if show: \n",
    "                print(\"Number of items in the Pauli list:\", n_items)\n",
    "                if n_items <= truncate: \n",
    "                    print(qubit_op)\n",
    "                else: \n",
    "                    print(qubit_op[0:truncate])\n",
    "    return qubit_op, qubit_converter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fbfd3862",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<qiskit_nature.second_q.problems.electronic_structure_problem.ElectronicStructureProblem object at 0x124c21790>\n"
     ]
    }
   ],
   "source": [
    "from qiskit_nature.units import DistanceUnit\n",
    "from qiskit_nature.second_q.drivers import PySCFDriver\n",
    "from qiskit_nature.second_q.transformers import FreezeCoreTransformer\n",
    "\n",
    "LiH_driver = PySCFDriver(\n",
    "    atom=\"Li 0 0 0; H 0 0 1.5949\",\n",
    "    basis=\"sto3g\",\n",
    "    charge=0,\n",
    "    spin=0,\n",
    "    unit=DistanceUnit.ANGSTROM,\n",
    ")\n",
    "\n",
    "LiH_hamiltonian = LiH_driver.run()\n",
    "print(LiH_hamiltonian)\n",
    "transformers = FreezeCoreTransformer(freeze_core=True, remove_orbitals=[4, 3])\n",
    "LiH_hamiltonian = transformers.transform(LiH_hamiltonian)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fb1185ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fermionic Operator\n",
      "number spin orbitals=6, number terms=342\n",
      "  0.24383238270778604 * ( +_0 +_0 -_0 -_0 )\n",
      "+ -0.02424663124312874 * ( +_0 +_0 -_0 -_1 )\n",
      "+ 0.06352872063592943 * ( +_0 +_0 -_0 -_2 )\n",
      "+ -0.024246631243128747 * ( +_0 +_0 -_1 -_0 )\n",
      "+ 0.006506486652329654 * ( +_0 +_0 -_1 -_1 )\n",
      "+ -0.017269906433599266 * ( +_0 +_0 -_1 -_2 )\n",
      "+ 0.06352872063592944 * ( +_0 +_0 -_2 -_0 )\n",
      "+ -0.017269906433599224 * ( +_0 +_0 -_2 -_1 )\n",
      "+ 0.06193562404867832 * ( +_0 +_0 -_2 -_2 )\n",
      "+ -0.024246631243128737 * ( +_0 +_1 -_0 -_0 )\n",
      "+ 0.006506486652329656 * ( +_0 +_1 -_0 -_1 )\n",
      "+ -0.01726990643359925 * ( +_0 +_1 -_0 -_2 )\n",
      "+ 0.11187797311553374 * ( +_0 +_1 -_1 -_0 )\n",
      "+ 0.0037084406488361982 * ( +_0 +_1 -_1 -_1 )\n",
      "+ -0.006140759576282037 * ( +_0 +_1 -_1 -_2 )\n",
      "+ -0.025670133324871156 * ( +_0 +_1 -_2 -_0 )\n",
      "+ 0.004678216820684089 * ( +_0 +_1 -_2 -_1 )\n",
      "+ -0.015928052340327924 * ( +_0 +_1 -_2 -_2 )\n",
      "+ 0.06352872063592944 * ( +_0 +_2 -_0 -_0 )\n",
      "+ -0.017269906433599245 * ( +_0 +_2 -_0 -_1 )\n",
      "+ 0.06193562404867841 * ( +_0 +_2 -_0 -_2 )\n",
      "+ -0.025670133324871162 * ( +_0 +_2 -_1 -_0 )\n",
      "+ 0.004678216820684092 * ( +_0 +_2 -_1 -_1 )\n",
      "+ -0.015928052340328014 * ( +_0 +_2 -_1 -_2 )\n",
      "+ 0.22702294277714777 * ( +_0 +_2 -_2 -_0 )\n",
      "+ -0.021646459870939775 * ( +_0 +_2 -_2 -_1 )\n",
      "+ 0.06726759455797143 * ( +_0 +_2 -_2 -_2 )\n",
      "+ 0.24383238270778604 * ( +_0 +_3 -_3 -_0 )\n",
      "+ -0.024246631243128737 * ( +_0 +_3 -_3 -_1 )\n",
      "+ 0.06352872063592944 * ( +_0 +_3 -_3 -_2 )\n",
      "+ -0.024246631243128737 * ( +_0 +_3 -_4 -_0 )\n",
      "+ 0.006506486652329658 * ( +_0 +_3 -_4 -_1 )\n",
      "+ -0.01726990643359924 * ( +_0 +_3 -_4 -_2 )\n",
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      "+ 0.22698094784842193 * ( +_5 +_2 -_2 -_5 )\n",
      "+ 0.06352872063592944 * ( +_5 +_3 -_3 -_3 )\n",
      "+ -0.02567013332487114 * ( +_5 +_3 -_3 -_4 )\n",
      "+ 0.22702294277714777 * ( +_5 +_3 -_3 -_5 )\n",
      "+ -0.017269906433599266 * ( +_5 +_3 -_4 -_3 )\n",
      "+ 0.004678216820684105 * ( +_5 +_3 -_4 -_4 )\n",
      "+ -0.02164645987093974 * ( +_5 +_3 -_4 -_5 )\n",
      "+ 0.061935624048678334 * ( +_5 +_3 -_5 -_3 )\n",
      "+ -0.015928052340327962 * ( +_5 +_3 -_5 -_4 )\n",
      "+ 0.0672675945579714 * ( +_5 +_3 -_5 -_5 )\n",
      "+ -0.017269906433599245 * ( +_5 +_4 -_3 -_3 )\n",
      "+ 0.004678216820684114 * ( +_5 +_4 -_3 -_4 )\n",
      "+ -0.02164645987093968 * ( +_5 +_4 -_3 -_5 )\n",
      "+ -0.006140759576282011 * ( +_5 +_4 -_4 -_3 )\n",
      "+ 0.017990975523311643 * ( +_5 +_4 -_4 -_4 )\n",
      "+ 0.12073423553556059 * ( +_5 +_4 -_4 -_5 )\n",
      "+ -0.015928052340327927 * ( +_5 +_4 -_5 -_3 )\n",
      "+ 0.013218234104963249 * ( +_5 +_4 -_5 -_4 )\n",
      "+ -0.022025875848649384 * ( +_5 +_4 -_5 -_5 )\n",
      "+ 0.06193562404867838 * ( +_5 +_5 -_3 -_3 )\n",
      "+ -0.015928052340327944 * ( +_5 +_5 -_3 -_4 )\n",
      "+ 0.06726759455797145 * ( +_5 +_5 -_3 -_5 )\n",
      "+ -0.015928052340327993 * ( +_5 +_5 -_4 -_3 )\n",
      "+ 0.013218234104963252 * ( +_5 +_5 -_4 -_4 )\n",
      "+ -0.022025875848649568 * ( +_5 +_5 -_4 -_5 )\n",
      "+ 0.06726759455797143 * ( +_5 +_5 -_5 -_3 )\n",
      "+ -0.02202587584864946 * ( +_5 +_5 -_5 -_4 )\n",
      "+ 0.22698094784842193 * ( +_5 +_5 -_5 -_5 )\n",
      "+ -0.7733695074853202 * ( +_0 -_0 )\n",
      "+ 0.04849327476205081 * ( +_0 -_1 )\n",
      "+ -0.12705744053712398 * ( +_0 -_2 )\n",
      "+ 0.04849327476205082 * ( +_1 -_0 )\n",
      "+ -0.35623706999508264 * ( +_1 -_1 )\n",
      "+ 0.0681407150800552 * ( +_1 -_2 )\n",
      "+ -0.1270574405371236 * ( +_2 -_0 )\n",
      "+ 0.06814071508005524 * ( +_2 -_1 )\n",
      "+ -0.23509124917853763 * ( +_2 -_2 )\n",
      "+ -0.7733695074853202 * ( +_3 -_3 )\n",
      "+ 0.04849327476205081 * ( +_3 -_4 )\n",
      "+ -0.12705744053712398 * ( +_3 -_5 )\n",
      "+ 0.04849327476205082 * ( +_4 -_3 )\n",
      "+ -0.35623706999508264 * ( +_4 -_4 )\n",
      "+ 0.0681407150800552 * ( +_4 -_5 )\n",
      "+ -0.1270574405371236 * ( +_5 -_3 )\n",
      "+ 0.06814071508005524 * ( +_5 -_4 )\n",
      "+ -0.23509124917853763 * ( +_5 -_5 )\n"
     ]
    }
   ],
   "source": [
    "LiH_second_q_op = LiH_hamiltonian.second_q_ops()\n",
    "print(LiH_second_q_op[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "31a1e8fe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lithin hydride molecule\n",
      "Qubit Hamiltonian operator\n",
      "Parity transformation \n",
      "Number of items in the Pauli list: 100\n",
      "-0.20719719190633393 * IIII\n",
      "- 0.09366929886870892 * IIIZ\n",
      "- 0.0031543121484092955 * IIZX\n",
      "+ 0.0031543121484092955 * IIIX\n",
      "- 0.0012009424597524635 * IIXX\n",
      "+ 0.0012009424597524696 * IIYY\n",
      "- 0.21165898406312897 * IIZZ\n",
      "+ 0.3588108418024316 * IIZI\n",
      "+ 0.019217840714923103 * IIXZ\n",
      "+ 0.019217840714923103 * IIXI\n",
      "+ 0.09366929886870887 * IZII\n",
      "- 0.12191619135389295 * IZIZ\n",
      "+ 0.012123315621564367 * IZZX\n",
      "- 0.012123315621564367 * IZIX\n",
      "+ 0.03176436031796471 * IZXX\n",
      "- 0.03176436031796471 * IZYY\n",
      "+ 0.0031543121484092504 * ZXII\n",
      "+ 0.012123315621564363 * ZXIZ\n",
      "+ 0.0031543121484092504 * IXII\n",
      "+ 0.012123315621564363 * IXIZ\n"
     ]
    }
   ],
   "source": [
    "LiH_qubit_op, qubit_converter = fermion_to_qubit(LiH_hamiltonian, LiH_second_q_op[0] ,\"Parity\", two_qubit_reduction=True, z2symmetry_reduction=\"auto\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "3db18663",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.20719719190633393 * IIII - 0.09366929886870892 * IIIZ - 0.0031543121484092955 * IIZX + 0.0031543121484092955 * IIIX - 0.0012009424597524635 * IIXX + 0.0012009424597524696 * IIYY - 0.21165898406312897 * IIZZ + 0.3588108418024316 * IIZI + 0.019217840714923103 * IIXZ + 0.019217840714923103 * IIXI + 0.09366929886870887 * IZII - 0.12191619135389295 * IZIZ + 0.012123315621564367 * IZZX - 0.012123315621564367 * IZIX + 0.03176436031796471 * IZXX - 0.03176436031796471 * IZYY + 0.0031543121484092504 * ZXII + 0.012123315621564363 * ZXIZ + 0.0031543121484092504 * IXII + 0.012123315621564363 * IXIZ - 0.0032532433261648268 * ZXZX - 0.0032532433261648268 * IXZX + 0.0032532433261648268 * ZXIX + 0.0032532433261648268 * IXIX - 0.008634953216799614 * ZXXX - 0.008634953216799614 * IXXX + 0.008634953216799614 * ZXYY + 0.008634953216799614 * IXYY - 0.0012009424597524635 * XXII - 0.0317643603179647 * XXIZ + 0.0012009424597524635 * YYII + 0.0317643603179647 * YYIZ + 0.008634953216799626 * XXZX - 0.008634953216799626 * YYZX - 0.008634953216799626 * XXIX + 0.008634953216799626 * YYIX + 0.030967812024339174 * XXXX - 0.030967812024339174 * YYXX - 0.030967812024339174 * XXYY + 0.030967812024339174 * YYYY - 0.21165898406312902 * ZZII + 0.05593898655776685 * ZZIZ + 0.0018542203244181126 * ZZZX - 0.0018542203244181126 * ZZIX + 0.0030703797881410063 * ZZXX - 0.0030703797881410063 * ZZYY - 0.01921784071492313 * XZII - 0.012835066662435566 * XZIZ + 0.01921784071492313 * XIII + 0.012835066662435566 * XIIZ + 0.0023391084103420528 * XZZX - 0.0023391084103420528 * XIZX - 0.0023391084103420528 * XZIX + 0.0023391084103420528 * XIIX + 0.007964026170163972 * XZXX - 0.007964026170163972 * XIXX - 0.007964026170163972 * XZYY + 0.007964026170163972 * XIYY - 0.3588108418024315 * ZIII + 0.11351147138857383 * ZIIZ - 0.010823229935469853 * ZIZX + 0.010823229935469853 * ZIIX - 0.033633797278985696 * ZIXX + 0.033633797278985696 * ZIYY - 0.05593898655776685 * IZZZ - 0.012835066662435576 * IZXZ - 0.012835066662435576 * IZXI - 0.001854220324418099 * ZXZZ - 0.001854220324418099 * IXZZ + 0.002339108410342043 * ZXXZ + 0.002339108410342043 * IXXZ + 0.002339108410342043 * ZXXI + 0.002339108410342043 * IXXI + 0.003070379788141011 * XXZZ - 0.003070379788141011 * YYZZ - 0.00796402617016398 * XXXZ + 0.00796402617016398 * YYXZ - 0.00796402617016398 * XXXI + 0.00796402617016398 * YYXI + 0.08448401142398787 * ZZZZ - 0.008995487761655811 * ZZXZ - 0.008995487761655811 * ZZXI + 0.008995487761655816 * XZZZ - 0.008995487761655816 * XIZZ - 0.006609117052481622 * XZXZ + 0.006609117052481622 * XIXZ - 0.006609117052481622 * XZXI + 0.006609117052481622 * XIXI + 0.06036711776778028 * ZIZZ + 0.011012937924324735 * ZIXZ + 0.011012937924324735 * ZIXI + 0.11351147138857383 * IZZI - 0.01082322993546989 * ZXZI - 0.01082322993546989 * IXZI + 0.0336337972789857 * XXZI - 0.0336337972789857 * YYZI - 0.060367117767780254 * ZZZI + 0.011012937924324725 * XZZI - 0.011012937924324725 * XIZI - 0.11349047392421092 * ZIZI\n"
     ]
    }
   ],
   "source": [
    "print(str(LiH_qubit_op).replace(\"\\n\", \" \"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "30aca7b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_qubit_op_from_molecule(driver): \n",
    "    hamiltonian = driver.run()\n",
    "    transformers = FreezeCoreTransformer(freeze_core=True, remove_orbitals=[4, 3])\n",
    "    hamiltonian = transformers.transform(hamiltonian)\n",
    "    second_q_op = hamiltonian.second_q_ops()\n",
    "    qubit_op, qubit_converter = fermion_to_qubit(hamiltonian, second_q_op[0] ,\"Parity\", two_qubit_reduction=True, z2symmetry_reduction=\"auto\", show=False )\n",
    "    return qubit_op, qubit_converter, hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c714913b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== GROUND STATE ENERGY ===\n",
      " \n",
      "* Electronic ground state energy (Hartree): -8.876526512881\n",
      "  - computed part:      -1.078193758676\n",
      "  - FreezeCoreTransformer extracted energy part: -7.798332754205\n",
      "~ Nuclear repulsion energy (Hartree): 0.995380044366\n",
      "> Total ground state energy (Hartree): -7.881146468515\n",
      " \n",
      "=== MEASURED OBSERVABLES ===\n",
      " \n",
      "  0:  # Particles: 2.000 S: 0.000 S^2: 0.000 M: 0.000\n",
      " \n",
      "=== DIPOLE MOMENTS ===\n",
      " \n",
      "~ Nuclear dipole moment (a.u.): [0.0  0.0  3.0139242]\n",
      " \n",
      "  0: \n",
      "  * Electronic dipole moment (a.u.): [0.0  0.0  4.850322]\n",
      "    - computed part:      [0.0  0.0  4.85436625]\n",
      "    - FreezeCoreTransformer extracted energy part: [0.0  0.0  -0.00404424]\n",
      "  > Dipole moment (a.u.): [0.0  0.0  -1.8363978]  Total: 1.8363978\n",
      "                 (debye): [0.0  0.0  -4.66765719]  Total: 4.66765719\n",
      " \n"
     ]
    }
   ],
   "source": [
    "npme = NumPyMinimumEigensolverFactory()\n",
    "calc = GroundStateEigensolver(qubit_converter, npme)\n",
    "res = calc.solve(LiH_hamiltonian)\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9caf2c75",
   "metadata": {},
   "source": [
    "Now that we have the hamiltonian in the form of the sum of pauli strings, we move on to working on the VQE. The first step is state preparation. We need 2 things for this. \n",
    "- An easy to prepare initial state \n",
    "- A parameterised Unitary \n",
    "\n",
    "Using an arbitrary or unstructured ansatz will lead to poor convergence of the optimization routine due to the abundance of barren plateaus, as shown by McClean et al. \n",
    "\n",
    "Physically motivated ansatz that have a measurable gradient, can be used to better guide the optimizer. Another requirement is implementing it with a high-fidelity and low-depth circuit. \n",
    "\n",
    "Here I am beginning with Hardware efficient ansatz. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "b856e8b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 1) 6 <qiskit_nature.second_q.mappers.qubit_converter.QubitConverter object at 0x124c45c90>\n",
      "     ┌───┐\n",
      "q_0: ┤ X ├\n",
      "     ├───┤\n",
      "q_1: ┤ X ├\n",
      "     └───┘\n",
      "q_2: ─────\n",
      "          \n",
      "q_3: ─────\n",
      "          \n",
      "     ┌───┐┌───────────────────────────────────┐»\n",
      "q_0: ┤ X ├┤0                                  ├»\n",
      "     ├───┤│                                   │»\n",
      "q_1: ┤ X ├┤1                                  ├»\n",
      "     └───┘│  exp(-it (IIIY + IIZY))(1.0*t[0]) │»\n",
      "q_2: ─────┤2                                  ├»\n",
      "          │                                   │»\n",
      "q_3: ─────┤3                                  ├»\n",
      "          └───────────────────────────────────┘»\n",
      "«     ┌───────────────────────────────────┐»\n",
      "«q_0: ┤0                                  ├»\n",
      "«     │                                   │»\n",
      "«q_1: ┤1                                  ├»\n",
      "«     │  exp(-it (IIYX + IIXY))(1.0*t[1]) │»\n",
      "«q_2: ┤2                                  ├»\n",
      "«     │                                   │»\n",
      "«q_3: ┤3                                  ├»\n",
      "«     └───────────────────────────────────┘»\n",
      "«     ┌───────────────────────────────────┐»\n",
      "«q_0: ┤0                                  ├»\n",
      "«     │                                   │»\n",
      "«q_1: ┤1                                  ├»\n",
      "«     │  exp(-it (IYII + ZYII))(1.0*t[2]) │»\n",
      "«q_2: ┤2                                  ├»\n",
      "«     │                                   │»\n",
      "«q_3: ┤3                                  ├»\n",
      "«     └───────────────────────────────────┘»\n",
      "«     ┌───────────────────────────────────┐»\n",
      "«q_0: ┤0                                  ├»\n",
      "«     │                                   │»\n",
      "«q_1: ┤1                                  ├»\n",
      "«     │  exp(-it (YXII + XYII))(1.0*t[3]) │»\n",
      "«q_2: ┤2                                  ├»\n",
      "«     │                                   │»\n",
      "«q_3: ┤3                                  ├»\n",
      "«     └───────────────────────────────────┘»\n",
      "«     ┌─────────────────────────────────────────────────────────────────────────────┐»\n",
      "«q_0: ┤0                                                                            ├»\n",
      "«     │                                                                             │»\n",
      "«q_1: ┤1                                                                            ├»\n",
      "«     │  exp(-it (ZXIY + IXIY + IYZX + ZYZX + IYIX + ZYIX + ZXZY + IXZY))(1.0*t[4]) │»\n",
      "«q_2: ┤2                                                                            ├»\n",
      "«     │                                                                             │»\n",
      "«q_3: ┤3                                                                            ├»\n",
      "«     └─────────────────────────────────────────────────────────────────────────────┘»\n",
      "«     ┌─────────────────────────────────────────────────────────────────────────────┐»\n",
      "«q_0: ┤0                                                                            ├»\n",
      "«     │                                                                             │»\n",
      "«q_1: ┤1                                                                            ├»\n",
      "«     │  exp(-it (XXIY + YYIY + YXZX + XYZX + YXIX + XYIX + XXZY + YYZY))(1.0*t[5]) │»\n",
      "«q_2: ┤2                                                                            ├»\n",
      "«     │                                                                             │»\n",
      "«q_3: ┤3                                                                            ├»\n",
      "«     └─────────────────────────────────────────────────────────────────────────────┘»\n",
      "«     ┌─────────────────────────────────────────────────────────────────────────────┐»\n",
      "«q_0: ┤0                                                                            ├»\n",
      "«     │                                                                             │»\n",
      "«q_1: ┤1                                                                            ├»\n",
      "«     │  exp(-it (ZXYX + IXYX + IYXX + ZYXX + IYYY + ZYYY + ZXXY + IXXY))(1.0*t[6]) │»\n",
      "«q_2: ┤2                                                                            ├»\n",
      "«     │                                                                             │»\n",
      "«q_3: ┤3                                                                            ├»\n",
      "«     └─────────────────────────────────────────────────────────────────────────────┘»\n",
      "«     ┌─────────────────────────────────────────────────────────────────────────────┐\n",
      "«q_0: ┤0                                                                            ├\n",
      "«     │                                                                             │\n",
      "«q_1: ┤1                                                                            ├\n",
      "«     │  exp(-it (XXYX + YYYX + YXXX + XYXX + YXYY + XYYY + XXXY + YYXY))(1.0*t[7]) │\n",
      "«q_2: ┤2                                                                            ├\n",
      "«     │                                                                             │\n",
      "«q_3: ┤3                                                                            ├\n",
      "«     └─────────────────────────────────────────────────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "from qiskit.circuit.library import EfficientSU2\n",
    "from qiskit_nature.circuit.library import UCC, UCCSD \n",
    "from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD\n",
    "\n",
    "num_qubits = LiH_qubit_op.num_qubits\n",
    "num_particles = LiH_hamiltonian.num_particles \n",
    "num_spin_orbitals = LiH_hamiltonian.num_spin_orbitals\n",
    "num_spatial_orbitals = LiH_hamiltonian.num_spatial_orbitals\n",
    "print(num_particles, num_spin_orbitals, qubit_converter)\n",
    "initial_state = HartreeFock(num_particles=num_particles, num_spatial_orbitals=num_spatial_orbitals,qubit_converter=qubit_converter)\n",
    "print(initial_state)\n",
    "hha_ansatz = EfficientSU2(num_qubits,entanglement='circular', reps=1)\n",
    "uccsd_ansatz = UCC(\n",
    "    qubit_converter=qubit_converter,\n",
    "    num_particles=num_particles, \n",
    "    num_spin_orbitals=num_spin_orbitals,\n",
    "    excitations='sd',\n",
    "    initial_state=initial_state\n",
    ")\n",
    "print(uccsd_ansatz.decompose(reps=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "94ea50d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from qiskit_aer.noise import NoiseModel\n",
    "from qiskit.providers.fake_provider import FakeVigo\n",
    "\n",
    "# fake providers contain data from real IBM Quantum devices stored in Qiskit Terra,\n",
    "# and are useful for extracting realistic noise models.\n",
    "device = FakeVigo()\n",
    "\n",
    "coupling_map = device.configuration().coupling_map\n",
    "noise_model_device = NoiseModel.from_backend(device)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "20751525",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.utils import algorithm_globals\n",
    "from qiskit_aer.primitives import Estimator as AerEstimator\n",
    "from qiskit.algorithms.gradients import FiniteDiffEstimatorGradient\n",
    "from qiskit_ibm_runtime import Options, Estimator \n",
    "\n",
    "seed = 150\n",
    "algorithm_globals.random_seed = seed\n",
    "shots = 1024\n",
    "options = Options()\n",
    "options.resilience_level = 0 \n",
    "noiseless_estimator = AerEstimator(\n",
    "    run_options={\"seed\": seed, \"shots\": shots},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")\n",
    "\n",
    "\n",
    "gradient = FiniteDiffEstimatorGradient(noiseless_estimator, epsilon=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "29d5146e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_aer.noise import (NoiseModel, QuantumError, ReadoutError,\n",
    "    pauli_error, depolarizing_error, reset_error, thermal_relaxation_error)\n",
    "    \n",
    "# Example error probabilities\n",
    "p_reset = 0.1\n",
    "p_meas = 0.2\n",
    "p_gate1 = [0.05, 0.1, 0.15, 0.2, 0.25, 0.3] \n",
    "p1Q = [0.05, 0.10, 0.15, 0.20, 0.25, 0.30]\n",
    "p2Q = [0.30, 0.40, 0.50, 0.60, 0.70, 0.80]\n",
    "\n",
    "noisy_estimators = [] \n",
    "noise_model = NoiseModel() \n",
    "for (p_gate, p1q, p2q) in zip(p_gate1, p1Q, p2Q): \n",
    "    noise_model_device = NoiseModel.from_backend(device)\n",
    "    noise_model = NoiseModel() \n",
    "    error_meas = pauli_error([('X',p_meas), ('I', 1 - p_meas)])\n",
    "    error_gate1 = pauli_error([('X',p_gate), ('I', 1 - p_gate)])\n",
    "    error_gate2 = error_gate1.tensor(error_gate1)\n",
    "    error_reset = reset_error(p_reset, 1-p_reset)\n",
    "    noise_model.add_all_qubit_quantum_error(error_gate1, ['sx', 'u1', 'u2', 'u3', 'rz'])\n",
    "    noise_model.add_all_qubit_quantum_error(depolarizing_error(p1q, 1),  ['x'])\n",
    "    noise_model.add_all_qubit_quantum_error(error_meas, \"measure\")\n",
    "    noisy_estimator = AerEstimator(\n",
    "            backend_options={\n",
    "                # \"method\": \"density_matrix\",\n",
    "                # \"coupling_map\": coupling_map,\n",
    "                \"noise_model\": noise_model,\n",
    "            },\n",
    "            run_options={\"seed\": seed, \"shots\": shots},\n",
    "            transpile_options={\"seed_transpiler\": seed},\n",
    "        )\n",
    "    noisy_estimators.append(noisy_estimator)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "83eed8f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.algorithms.optimizers import SPSA, SLSQP\n",
    "optimizer = SPSA(maxiter=1024, last_avg=1)\n",
    "from qiskit.algorithms.optimizers import COBYLA\n",
    "optimizer = COBYLA(maxiter=2048, tol=0.0001)\n",
    "optimizer= SLSQP(maxiter=1024)\n",
    "optimizer = SPSA(maxiter=1024, last_avg=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "dc127f6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_nature.second_q.algorithms.initial_points import HFInitialPoint \n",
    "hf_initial_point = HFInitialPoint()\n",
    "hf_initial_point.ansatz = uccsd_ansatz\n",
    "initial_point = hf_initial_point.to_numpy_array()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "b80ebdd9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "ansatz = uccsd_ansatz \n",
    "print(ansatz.num_parameters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "71521bea",
   "metadata": {},
   "outputs": [],
   "source": [
    "counts = [] \n",
    "values = [] \n",
    "def store_intermediate_result(eval_count, parameters, mean, std):\n",
    "    counts.append(eval_count)\n",
    "    values.append(mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "c124a5cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def get_noise_probability(number_of_runs, circuit_dict, error_gate1, polarization_error1, polarization_error2, measurement_error, number_of_qubits):\n",
    "    noise_probability = 0 \n",
    "    for key in circuit_dict:\n",
    "        for j in range(circuit_dict[key]): \n",
    "            if key in ['sx', 'u1', 'u2', 'u3']: \n",
    "                noise_probability = noise_probability + error_gate1\n",
    "            elif key in ['x', 'rz']: \n",
    "                noise_probability = noise_probability + polarization_error1\n",
    "    noise_probability += measurement_error * number_of_runs * number_of_qubits\n",
    "    return noise_probability "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "c902a311",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import transpile\n",
    "\n",
    "def get_circuit_gate_counts(result): \n",
    "    final_circ = result.optimal_circuit\n",
    "    transpiled = transpile(final_circ, basis_gates=['cx', 'id', 'rz', 'sx', 'x', 'u1', 'u2', 'u3'])\n",
    "    return dict(transpiled.count_ops())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "5f5bc9fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'cx': 172, 'rz': 114, 'sx': 65, 'x': 2}\n",
      "VQE on Aer qasm simulator (no noise): -1.20959\n",
      "6\n",
      "     ┌──────────────────────────────────────────────────────┐\n",
      "q_0: ┤0                                                     ├\n",
      "     │                                                      │\n",
      "q_1: ┤1                                                     ├\n",
      "     │  EvolvedOps(t[0],t[1],t[2],t[3],t[4],t[5],t[6],t[7]) │\n",
      "q_2: ┤2                                                     ├\n",
      "     │                                                      │\n",
      "q_3: ┤3                                                     ├\n",
      "     └──────────────────────────────────────────────────────┘\n",
      "{'cx': 172, 'u3': 62, 'rz': 38, 'u2': 5, 'x': 2}\n",
      "1684.55\n",
      "VQE on Aer qasm simulator (device noise): -0.32482\n",
      "1689.9\n",
      "VQE on Aer qasm simulator (device noise): -0.24749\n",
      "1695.25\n",
      "VQE on Aer qasm simulator (device noise): -0.21036\n",
      "1700.6\n",
      "VQE on Aer qasm simulator (device noise): -0.21048\n",
      "1705.95\n",
      "VQE on Aer qasm simulator (device noise): -0.21053\n",
      "1711.3000000000002\n",
      "VQE on Aer qasm simulator (device noise): -0.21053\n"
     ]
    }
   ],
   "source": [
    "# from qiskit.algorithms.minimum_eigensolvers import VQE\n",
    "from qiskit import Aer\n",
    "noiseless_counts = []\n",
    "noiseless_values = [] \n",
    "noisy_counts = []\n",
    "noisy_values = [] \n",
    "counts = [] \n",
    "values = []\n",
    "backend = Aer.get_backend('aer_simulator')\n",
    "vqe = VQE(noiseless_estimator, ansatz, optimizer, callback=store_intermediate_result, gradient=gradient, initial_point=initial_point)\n",
    "# vqe.construct_circuit()\n",
    "vqe_circuits = vqe.estimator.circuits\n",
    "# print(vqe_circuits[0].decompose(reps=3))\n",
    "if(len(vqe_circuits)) > 0: \n",
    "    circ = vqe_circuits[0]\n",
    "    transpiled = transpile(circ, basis_gates=['cx', 'id', 'rz', 'sx', 'x'])\n",
    "    # print(transpiled.draw())\n",
    "    print(dict(transpiled.count_ops()))\n",
    "# ensure that the optimizer starts in the all-zero state which corresponds to\n",
    "# the Hartree-Fock starting point\n",
    "# vqe.initial_point = [0] * ansatz.num_parameters\n",
    "noiseless_result = vqe.compute_minimum_eigenvalue(LiH_qubit_op)\n",
    "noiseless_counts = counts \n",
    "noiseless_values = values \n",
    "counts = [] \n",
    "values = [] \n",
    "print(f\"VQE on Aer qasm simulator (no noise): {noiseless_result.eigenvalue.real:.5f}\")\n",
    "print(len(noisy_estimators))\n",
    "print(noiseless_result.optimal_circuit)\n",
    "final_circ = noiseless_result.optimal_circuit\n",
    "transpiled = transpile(final_circ, basis_gates=['cx', 'id', 'rz', 'sx', 'x', 'u1', 'u2', 'u3'])\n",
    "# print(transpiled.draw())\n",
    "print(dict(transpiled.count_ops()))\n",
    "results = []\n",
    "probabilities = [] \n",
    "for index, noisy_estimator in enumerate(noisy_estimators): \n",
    "    vqe = VQE(noisy_estimator, ansatz, optimizer, callback=store_intermediate_result, gradient=gradient, initial_point=initial_point)\n",
    "    noisy_result = vqe.compute_minimum_eigenvalue(LiH_qubit_op)\n",
    "    noisy_counts.append(counts)\n",
    "    noisy_values.append(values) \n",
    "    noise_probability = get_noise_probability(len(counts), get_circuit_gate_counts(noisy_result), p_gate1[index], p1Q[index], p2Q[index], p_meas, num_qubits)\n",
    "    print(noise_probability)\n",
    "    probabilities.append(noise_probability)\n",
    "    counts = [] \n",
    "    values = [] \n",
    "    calc = GroundStateEigensolver(qubit_converter, vqe)\n",
    "    print(f\"VQE on Aer qasm simulator (device noise): {noisy_result.eigenvalue.real:.5f}\")\n",
    "    results.append(noisy_result.eigenvalue.real)\n",
    "# print(f\"Reference energy value is {(ref_value):.5f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "80a6c672",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.7721273281232683\n",
      "-0.7721273281232683\n",
      "[-0.45249741486812617, -0.26792146257982236, -0.21570136633933, -0.20992431249410537, -0.21050873513019555, -0.21053263595673347]\n"
     ]
    }
   ],
   "source": [
    "mitigated_result = get_error_mitigated_value(results, probabilities)\n",
    "print(mitigated_result)\n",
    "print(results)\n",
    "data = np.array(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "835c7af1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16ad22590>"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pylab as pylab\n",
    "import matplotlib.patches as mpatches\n",
    "\n",
    "colors = [\"red\", \"black\", \"green\", \"orange\", \"magenta\", \"cyan\"]\n",
    "\n",
    "pylab.rcParams[\"figure.figsize\"] = (12, 4)\n",
    "pylab.plot(noiseless_counts, noiseless_values, color = \"blue\", label=\"No noise\")\n",
    "patches = []\n",
    "patch1 = mpatches.Patch(color=\"blue\", label='No noise') \n",
    "patches.append(patch1)\n",
    "for index, noisy_count in enumerate(noisy_counts): \n",
    "    pylab.plot(noisy_count, noisy_values[index], color = colors[index], label=\"Noise Level \" + str(index))\n",
    "    patch = mpatches.Patch(color = colors[index], label=\"Noise Level \" + str(index)) \n",
    "    patches.append(patch)\n",
    "pylab.xlabel(\"Eval count\")\n",
    "pylab.ylabel(\"Energy\")\n",
    "pylab.title(\"Convergence\")\n",
    "pylab.legend(handles=patches)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "c16a0b7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def get_error_mitigated_value(results, probabilities): \n",
    "    arr = []\n",
    "    for res, prob in zip(results,probabilities): \n",
    "        arr.append([prob, res]) \n",
    "\n",
    "    # data = np.array(arr)\n",
    "    data = np.array(arr)\n",
    "\n",
    "    # Extract the two columns as separate arrays\n",
    "    x = data[:, 0]\n",
    "    y = data[:, 1]\n",
    "    z = np.polyfit(x, y, 3)\n",
    "    p = np.poly1d(z)\n",
    "    y0 = p(0)\n",
    "    print(y0)\n",
    "    return y0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "473067ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def LiH_VQE(distance, noise, mitigated):\n",
    "    molecule = 'H .0 .0 -{0}; Li .0 .0 {0}'\n",
    "    LiH_driver = PySCFDriver(\n",
    "    atom=molecule.format(distance/2),\n",
    "    basis=\"sto3g\",\n",
    "    # charge=0,\n",
    "    # spin=0,\n",
    "    unit=DistanceUnit.ANGSTROM,\n",
    "    )\n",
    "    LiH_qubit_op, qubit_converter, LiH_hamiltonian = get_qubit_op_from_molecule(LiH_driver)\n",
    "    num_qubits = LiH_qubit_op.num_qubits\n",
    "    num_particles = LiH_hamiltonian.num_particles \n",
    "    num_spin_orbitals = LiH_hamiltonian.num_spin_orbitals\n",
    "    num_spatial_orbitals = LiH_hamiltonian.num_spatial_orbitals\n",
    "    initial_state = HartreeFock(num_particles=num_particles, num_spatial_orbitals=num_spatial_orbitals,qubit_converter=qubit_converter)\n",
    "    # hha_ansatz = EfficientSU2(num_qubits,entanglement='circular', reps=1)\n",
    "    ansatz = UCC(\n",
    "        qubit_converter=qubit_converter,\n",
    "        num_particles=num_particles, \n",
    "        num_spin_orbitals=num_spin_orbitals,\n",
    "        excitations='sd',\n",
    "        initial_state=initial_state\n",
    "    )\n",
    "    optimizer = SPSA(maxiter=500, last_avg=1)\n",
    "    seed = 150\n",
    "    algorithm_globals.random_seed = seed\n",
    "    shots = 1024\n",
    "    gradient = FiniteDiffEstimatorGradient(noiseless_estimator, epsilon=0.01)\n",
    "    if not noise: \n",
    "        estimator = AerEstimator(\n",
    "            run_options={\"seed\": seed, \"shots\": shots},\n",
    "            transpile_options={\"seed_transpiler\": seed},\n",
    "        )\n",
    "    else:\n",
    "        p_reset = 0.1\n",
    "        p_meas = 0.4\n",
    "        p_gate1 = 0.05 \n",
    "        p1Q = 0.05 \n",
    "        p2Q = 0.30 \n",
    "        noise_model = NoiseModel() \n",
    "        error_meas = pauli_error([('X',p_meas), ('I', 1 - p_meas)])\n",
    "        error_gate1 = pauli_error([('X',p_gate1), ('I', 1 - p_gate1)])\n",
    "        error_gate2 = error_gate1.tensor(error_gate1)\n",
    "        error_reset = reset_error(p_reset, 1-p_reset)\n",
    "        noise_model.add_all_qubit_quantum_error(error_gate1, ['rz', 'sx', 'u1', 'u2', 'u3'])\n",
    "        noise_model.add_all_qubit_quantum_error(depolarizing_error(p1Q, 1),  ['x'])\n",
    "        estimator = AerEstimator(\n",
    "                backend_options={\n",
    "                    \"noise_model\": noise_model,\n",
    "                },\n",
    "                run_options={\"seed\": seed, \"shots\": shots},\n",
    "                transpile_options={\"seed_transpiler\": seed},\n",
    "            )\n",
    "    if not mitigated: \n",
    "        gradient = FiniteDiffEstimatorGradient(noiseless_estimator, epsilon=0.01)\n",
    "        backend = Aer.get_backend('aer_simulator')\n",
    "        vqe = VQE(estimator, ansatz, optimizer,gradient=gradient, initial_point=initial_point)\n",
    "        result = vqe.compute_minimum_eigenvalue(LiH_qubit_op)\n",
    "        return result.eigenvalue.real\n",
    "\n",
    "    else: \n",
    "        p_reset = 0.1\n",
    "        p_meas = 0.4\n",
    "        p_gate1 = [0.05, 0.1, 0.15, 0.2, 0.25, 0.3] \n",
    "        p1Q = [0.05, 0.10, 0.15, 0.20, 0.25, 0.30]\n",
    "        p2Q = [0.30, 0.40, 0.50, 0.60, 0.70, 0.80]\n",
    "\n",
    "        noisy_estimators = [] \n",
    "\n",
    "        for (p_gate, p1q, p2q) in zip(p_gate1, p1Q, p2Q): \n",
    "            noise_model_device = NoiseModel.from_backend(device)\n",
    "            noise_model = NoiseModel() \n",
    "            error_meas = pauli_error([('X',p_meas), ('I', 1 - p_meas)])\n",
    "            error_gate1 = pauli_error([('X',p_gate), ('I', 1 - p_gate)])\n",
    "            error_gate2 = error_gate1.tensor(error_gate1)\n",
    "            error_reset = reset_error(p_reset, 1-p_reset)\n",
    "            noise_model.add_all_qubit_quantum_error(error_gate1, ['rz', 'sx', 'u1', 'u2', 'u3'])\n",
    "            noise_model.add_all_qubit_quantum_error(depolarizing_error(p1q, 1),  ['x'])\n",
    "            noisy_estimator = AerEstimator(\n",
    "                    backend_options={\n",
    "                        # \"method\": \"density_matrix\",\n",
    "                        # \"coupling_map\": coupling_map,\n",
    "                        \"noise_model\": noise_model,\n",
    "                    },\n",
    "                    run_options={\"seed\": seed, \"shots\": shots},\n",
    "                    transpile_options={\"seed_transpiler\": seed},\n",
    "                )\n",
    "            noisy_estimators.append(noisy_estimator)\n",
    "        results = []\n",
    "        probabilities = [] \n",
    "        for index, noisy_estimator in enumerate(noisy_estimators): \n",
    "            vqe = VQE(noisy_estimator, ansatz, optimizer, gradient=gradient, initial_point=initial_point)\n",
    "            noisy_result = vqe.compute_minimum_eigenvalue(LiH_qubit_op)\n",
    "            noise_probability = get_noise_probability(len(counts), get_circuit_gate_counts(noisy_result), p_gate1[index], p1Q[index], p2Q[index])\n",
    "            probabilities.append(noise_probability)\n",
    "            calc = GroundStateEigensolver(qubit_converter, vqe)\n",
    "            results.append(noisy_result.eigenvalue.real)\n",
    "        mitigated_result = get_error_mitigated_value(results, probabilities)\n",
    "        return mitigated_result\n",
    "         \n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "a9768512",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing step  0\n",
      "NoNoise -1.335636155817891\n",
      "Noise -0.8009491476844295\n",
      "-0.9942320780614156\n",
      "Mitigated -0.9942320780614156\n",
      " 1\n",
      "NoNoise -1.1869544301584898\n",
      "Noise -0.7877986882695883\n",
      "-0.9291940275278737\n",
      "Mitigated -0.9291940275278737\n",
      " 2\n",
      "NoNoise -1.131512900401683\n",
      "Noise -0.80506332174862\n",
      "-0.9483551178171933\n",
      "Mitigated -0.9483551178171933\n",
      " 3\n",
      "NoNoise -1.1078894368264867\n",
      "Noise -0.829479396260281\n",
      "-1.0173085647883842\n",
      "Mitigated -1.0173085647883842\n",
      " 4\n",
      "NoNoise -1.1925236901495129\n",
      "Noise -0.8182223488714666\n",
      "-1.0138277260888189\n",
      "Mitigated -1.0138277260888189\n",
      " 5\n",
      "NoNoise -1.1103040656791967\n",
      "Noise -0.7942776536899113\n",
      "-0.9770512925534048\n",
      "Mitigated -0.9770512925534048\n",
      " 6\n",
      "NoNoise -1.2090263566191544\n",
      "Noise -0.778873099067693\n",
      "-0.9567088003105648\n",
      "Mitigated -0.9567088003105648\n",
      " 7\n",
      "NoNoise -1.0735518735776768\n",
      "Noise -0.7606469179705678\n",
      "-0.9184409604303029\n",
      "Mitigated -0.9184409604303029\n",
      " 8\n",
      "NoNoise -1.022980234185112\n",
      "Noise -0.7488416687148183\n",
      "-1.0510331914248117\n",
      "Mitigated -1.0510331914248117\n",
      " 9\n",
      "NoNoise -1.006826371837744\n",
      "Noise -0.5828153037886931\n",
      "-0.4715867060595203\n",
      "Mitigated -0.4715867060595203\n",
      "10\n",
      "NoNoise -1.0254176933865258\n",
      "Noise -0.7487438204062737\n",
      "-0.9407330746460577\n",
      "Mitigated -0.9407330746460577\n",
      "11\n",
      "NoNoise -1.004571299394549\n",
      "Noise -0.7232935771328173\n",
      "-1.00905253025755\n",
      "Mitigated -1.00905253025755\n",
      "12\n",
      "NoNoise -0.9899793048751081\n",
      "Noise -0.7133693151333929\n",
      "-0.8575446373608858\n",
      "Mitigated -0.8575446373608858\n",
      "13\n",
      "NoNoise -0.9750957855860618\n",
      "Noise -0.7119350759488963\n",
      "-0.8488696103047879\n",
      "Mitigated -0.8488696103047879\n",
      "14\n",
      "NoNoise -0.9556903930147774\n",
      "Noise -0.692714555618901\n",
      "-0.8289224147399896\n",
      "Mitigated -0.8289224147399896\n",
      "15\n",
      "NoNoise -1.0152940450640713\n",
      "Noise -0.6018199580632363\n",
      "-0.6265985622543342\n",
      "Mitigated -0.6265985622543342\n",
      "16\n",
      "NoNoise -1.0327053038759078\n",
      "Noise -0.5238086096977429\n",
      "-0.42958157911187034\n",
      "Mitigated -0.42958157911187034\n",
      "17\n",
      "NoNoise -0.9816599609093896\n",
      "Noise -0.621176265751003\n",
      "-0.7415307599941345\n",
      "Mitigated -0.7415307599941345\n",
      "18\n",
      "NoNoise -0.9413974988198802\n",
      "Noise -0.6010452786523273\n",
      "-0.7029588441340169\n",
      "Mitigated -0.7029588441340169\n",
      "19\n",
      "NoNoise -0.894674495439571\n",
      "Noise -0.5561206686642132\n",
      "-0.5851933225152492\n",
      "Mitigated -0.5851933225152492\n",
      "20\n",
      "NoNoise -0.9049298789324147\n",
      "Noise -0.521262555039358\n",
      "-0.5278366635660425\n",
      "Mitigated -0.5278366635660425\n",
      "21\n",
      "NoNoise -0.8984245316438715\n",
      "Noise -0.5251803617424325\n",
      "-0.5444899211660125\n",
      "Mitigated -0.5444899211660125\n",
      "22\n",
      "NoNoise -0.8983316582685063\n",
      "Noise -0.5126631308420206\n",
      "-0.5230309891472934\n",
      "Mitigated -0.5230309891472934\n",
      " --- complete\n",
      "Distances:  [0.6  0.7  0.8  0.9  1.   1.1  1.2  1.3  1.4  1.5  1.6  1.7  1.8  1.9\n",
      " 2.   2.25 2.5  2.75 3.   3.25 3.5  3.75 4.  ]\n",
      "Energies: [[-1.33563616 -1.18695443 -1.1315129  -1.10788944 -1.19252369 -1.11030407\n",
      "  -1.20902636 -1.07355187 -1.02298023 -1.00682637 -1.02541769 -1.0045713\n",
      "  -0.9899793  -0.97509579 -0.95569039 -1.01529405 -1.0327053  -0.98165996\n",
      "  -0.9413975  -0.8946745  -0.90492988 -0.89842453 -0.89833166]\n",
      " [-0.80094915 -0.78779869 -0.80506332 -0.8294794  -0.81822235 -0.79427765\n",
      "  -0.7788731  -0.76064692 -0.74884167 -0.5828153  -0.74874382 -0.72329358\n",
      "  -0.71336932 -0.71193508 -0.69271456 -0.60181996 -0.52380861 -0.62117627\n",
      "  -0.60104528 -0.55612067 -0.52126256 -0.52518036 -0.51266313]\n",
      " [-0.99423208 -0.92919403 -0.94835512 -1.01730856 -1.01382773 -0.97705129\n",
      "  -0.9567088  -0.91844096 -1.05103319 -0.47158671 -0.94073307 -1.00905253\n",
      "  -0.85754464 -0.84886961 -0.82892241 -0.62659856 -0.42958158 -0.74153076\n",
      "  -0.70295884 -0.58519332 -0.52783666 -0.54448992 -0.52303099]]\n",
      "VQE num evaluations: [0.00000000e+000 2.75204642e-314 6.42285340e-323 2.78134232e-309\n",
      " 1.48219694e-323 1.48219694e-323 1.18575755e-322 5.56268465e-309\n",
      " 9.88131292e-324 9.88131292e-324 7.90505033e-323 3.95252517e-323\n",
      " 0.00000000e+000 2.75204922e-314 1.00000000e+000 1.11253693e-308\n",
      " 1.48219694e-323 1.48219694e-323 1.18575755e-322 1.39067116e-308\n",
      " 0.00000000e+000 9.88131292e-324 0.00000000e+000]\n"
     ]
    }
   ],
   "source": [
    "algorithms = ['NoNoise', 'Noise', 'Mitigated']\n",
    "\n",
    "pts  = [x * 0.1  for x in range(6, 20)]\n",
    "pts += [x * 0.25 for x in range(8, 16)]\n",
    "pts += [4.0]\n",
    "energies = np.empty([len(algorithms), len(pts)])\n",
    "hf_energies = np.empty(len(pts))\n",
    "distances = np.empty(len(pts))\n",
    "dipoles     = np.empty([len(algorithms), len(pts)])\n",
    "eval_counts = np.empty(len(pts))\n",
    "\n",
    "print('Processing step __', end='')\n",
    "for i, d in enumerate(pts):\n",
    "    print('\\b\\b{:2d}'.format(i), flush=True)\n",
    "    for j in range(len(algorithms)):   \n",
    "        # driver = PySCFDriver(molecule.format(d/2), basis='sto3g')\n",
    "        # qmolecule = driver.run()\n",
    "        # operator =  Hamiltonian(qubit_mapping=QubitMappingType.PARITY,\n",
    "        #                         two_qubit_reduction=True, freeze_core=True,\n",
    "        #                         orbital_reduction=[-3, -2])\n",
    "        # qubit_op, aux_ops = operator.run(qmolecule)\n",
    "        if algorithms[j] == 'NoNoise':\n",
    "            result = LiH_VQE(d, False, False)\n",
    "        elif algorithms[j] == 'Noise':\n",
    "            result = LiH_VQE(d, True, False)\n",
    "        else: \n",
    "            result = LiH_VQE(d, True, True)\n",
    "        print(algorithms[j], result)\n",
    "        \n",
    "            # optimizer = SLSQP(maxiter=1000)\n",
    "            # initial_state = HartreeFock(operator.molecule_info['num_orbitals'],\n",
    "            #                             operator.molecule_info['num_particles'],\n",
    "            #                             qubit_mapping=operator._qubit_mapping,\n",
    "            #                             two_qubit_reduction=operator._two_qubit_reduction)\n",
    "            # var_form = UCCSD(num_orbitals=operator.molecule_info['num_orbitals'],\n",
    "            #                 num_particles=operator.molecule_info['num_particles'],\n",
    "            #                 initial_state=initial_state,\n",
    "            #                 qubit_mapping=operator._qubit_mapping,\n",
    "            #                 two_qubit_reduction=operator._two_qubit_reduction)\n",
    "            # algo = VQE(qubit_op, var_form, optimizer, aux_operators=aux_ops)\n",
    "            # result = algo.run(QuantumInstance(BasicAer.get_backend('statevector_simulator')))\n",
    "            # eval_counts[i] = result.optimizer_evals\n",
    "            \n",
    "        # result = operator.process_algorithm_result(result)\n",
    "        energies[j][i] = result\n",
    "        # hf_energies[i] = result.hartree_fock_energy\n",
    "        # dipoles[j][i]  = result.total_dipole_moment / 0.393430307\n",
    "\n",
    "    distances[i] = d\n",
    "print(' --- complete')\n",
    "\n",
    "print('Distances: ', distances)\n",
    "print('Energies:', energies)\n",
    "# print('Hartree-Fock energies:', hf_energies)\n",
    "print('VQE num evaluations:', eval_counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "9a848481",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pylab.plot(distances, hf_energies, label='Hartree-Fock')\n",
    "for j in range(len(algorithms)):\n",
    "    pylab.plot(distances, energies[j], label=algorithms[j])\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.title('LiH Ground State Energy')\n",
    "pylab.legend(loc='upper right');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.2"
  },
  "vscode": {
   "interpreter": {
    "hash": "7ff51084057887e9731447a8205f6b556069c70827513c9ff86fe23630979031"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}