H2 Optimizer Accuracy Noisy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "374b58b1-9ddb-4687-badb-f13a3772553b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Importing standard Qiskit libraries\n",
    "from qiskit import QuantumCircuit, transpile\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from ibm_quantum_widgets import *\n",
    "\n",
    "# qiskit-ibmq-provider has been deprecated.\n",
    "# Please see the Migration Guides in https://ibm.biz/provider_migration_guide for more detail.\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Estimator, Session, Options\n",
    "\n",
    "# Loading your IBM Quantum account(s)\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "\n",
    "# Invoke a primitive. For more details see https://qiskit.org/documentation/partners/qiskit_ibm_runtime/tutorials.html\n",
    "# result = Sampler(\"ibmq_qasm_simulator\").run(circuits).result()\n",
    "import qiskit_nature\n",
    "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver, VQE\n",
    "from qiskit_nature.second_q.transformers import FreezeCoreTransformer\n",
    "from qiskit_nature.second_q.formats.molecule_info import MoleculeInfo\n",
    "from qiskit_nature.second_q.mappers import ParityMapper\n",
    "from qiskit_nature.second_q.circuit.library import UCCSD, HartreeFock\n",
    "from qiskit_nature.second_q.mappers import JordanWignerMapper\n",
    "from qiskit_nature.units import DistanceUnit\n",
    "qiskit_nature.settings.use_pauli_sum_op = False\n",
    "from qiskit_nature.second_q.drivers import PySCFDriver\n",
    "import matplotlib.pyplot as plt\n",
    "from qiskit.circuit.library import EfficientSU2\n",
    "import numpy as np\n",
    "from qiskit.algorithms.optimizers import COBYLA, L_BFGS_B, SLSQP,SPSA,NFT\n",
    "from qiskit_aer.primitives import Estimator\n",
    "#from qiskit.chemistry.drivers import PySCFDriver, UnitsType, Molecule\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "from qiskit import Aer\n",
    "from qiskit.opflow import X, Z, I\n",
    "from qiskit.utils import QuantumInstance, algorithm_globals\n",
    "from qiskit.algorithms.optimizers import COBYLA, L_BFGS_B, SLSQP,SPSA,NFT\n",
    "from qiskit.circuit.library import TwoLocal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e6d1d06a-ac69-40d9-b6c0-436ad4aece6d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NoiseModel:\n",
      "  Basis gates: ['cx', 'id', 'rz', 'sx', 'x']\n",
      "  Instructions with noise: ['id', 'sx', 'x', 'cx', 'measure']\n",
      "  Qubits with noise: [0, 1, 2, 3, 4]\n",
      "  Specific qubit errors: [('id', (0,)), ('id', (1,)), ('id', (2,)), ('id', (3,)), ('id', (4,)), ('sx', (0,)), ('sx', (1,)), ('sx', (2,)), ('sx', (3,)), ('sx', (4,)), ('x', (0,)), ('x', (1,)), ('x', (2,)), ('x', (3,)), ('x', (4,)), ('cx', (3, 4)), ('cx', (4, 3)), ('cx', (3, 1)), ('cx', (1, 3)), ('cx', (1, 2)), ('cx', (2, 1)), ('cx', (0, 1)), ('cx', (1, 0)), ('measure', (0,)), ('measure', (1,)), ('measure', (2,)), ('measure', (3,)), ('measure', (4,))]\n"
     ]
    }
   ],
   "source": [
    "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,\n",
    "# and are useful for extracting realistic noise models.\n",
    "device = FakeVigo()\n",
    "\n",
    "coupling_map = device.configuration().coupling_map\n",
    "noise_model = NoiseModel.from_backend(device)\n",
    "seed = 170\n",
    "print(noise_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f052c434-7c11-4ef0-be56-9e368dcb1881",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def get_qubit_op_jw(dist):\n",
    "    # Define Molecule\n",
    "    driver = PySCFDriver(\n",
    "    atom=\"H 0 0 0; H 0 0 \"+str(dist),\n",
    "    basis=\"sto3g\",\n",
    "    charge=0,\n",
    "    spin=0,\n",
    "    unit=DistanceUnit.ANGSTROM,\n",
    "    )\n",
    "    # Get properties\n",
    "    problem = driver.run()\n",
    "\n",
    "    num_particles = problem.num_particles\n",
    "    num_spatial_orbitals = problem.num_spatial_orbitals\n",
    "    \n",
    "    mapper = ParityMapper()\n",
    "    #tapered_mapper = problem.get_tapered_mapper(mapper)\n",
    "    qubit_op = mapper.map(problem.second_q_ops()[0])\n",
    "    return qubit_op, num_particles, num_spatial_orbitals, problem, mapper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6ffe232e-a890-49ab-aa3c-25daca524957",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def exact_solver_jw(qubit_op, problem):\n",
    "    sol = NumPyMinimumEigensolver().compute_minimum_eigenvalue(qubit_op)\n",
    "    result = problem.interpret(sol)\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8d824a39-5ae0-4c1f-a47d-6d146c107ec2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interatomic Distance: 0.1 VQE Result: 3.63404 Exact Energy: 2.70996\n",
      "Interatomic Distance: 0.2 VQE Result: 1.00318 Exact Energy: 0.15748\n",
      "Interatomic Distance: 0.3 VQE Result: 0.14145 Exact Energy: -0.60180\n",
      "Interatomic Distance: 0.4 VQE Result: -0.27917 Exact Energy: -0.91415\n",
      "Interatomic Distance: 0.5 VQE Result: -0.51086 Exact Energy: -1.05516\n",
      "Interatomic Distance: 0.6 VQE Result: -0.64993 Exact Energy: -1.11629\n",
      "Interatomic Distance: 0.7 VQE Result: -0.73410 Exact Energy: -1.13619\n",
      "Interatomic Distance: 0.8 VQE Result: -0.78652 Exact Energy: -1.13415\n",
      "Interatomic Distance: 0.9 VQE Result: -0.81379 Exact Energy: -1.12056\n",
      "Interatomic Distance: 1.0 VQE Result: -0.83087 Exact Energy: -1.10115\n",
      "Interatomic Distance: 1.1 VQE Result: -0.84042 Exact Energy: -1.07919\n",
      "Interatomic Distance: 1.2 VQE Result: -0.80848 Exact Energy: -1.05674\n",
      "Interatomic Distance: 1.3 VQE Result: -0.82880 Exact Energy: -1.03519\n",
      "Interatomic Distance: 1.4 VQE Result: -0.82308 Exact Energy: -1.01547\n",
      "Interatomic Distance: 1.5 VQE Result: -0.81676 Exact Energy: -0.99815\n",
      "Interatomic Distance: 1.6 VQE Result: -0.80150 Exact Energy: -0.98347\n",
      "Interatomic Distance: 1.7 VQE Result: -0.80683 Exact Energy: -0.97143\n",
      "Interatomic Distance: 1.8 VQE Result: -0.79473 Exact Energy: -0.96182\n",
      "Interatomic Distance: 1.9 VQE Result: -0.79689 Exact Energy: -0.95434\n",
      "Interatomic Distance: 2.0 VQE Result: -0.79095 Exact Energy: -0.94864\n",
      "Interatomic Distance: 2.1 VQE Result: -0.78277 Exact Energy: -0.94437\n",
      "Interatomic Distance: 2.2 VQE Result: -0.79071 Exact Energy: -0.94122\n",
      "Interatomic Distance: 2.3 VQE Result: -0.78733 Exact Energy: -0.93892\n",
      "Interatomic Distance: 2.4 VQE Result: -0.78275 Exact Energy: -0.93725\n",
      "Interatomic Distance: 2.5 VQE Result: -0.78054 Exact Energy: -0.93605\n",
      "Interatomic Distance: 2.6 VQE Result: -0.77945 Exact Energy: -0.93520\n",
      "Interatomic Distance: 2.7 VQE Result: -0.77337 Exact Energy: -0.93458\n",
      "Interatomic Distance: 2.8 VQE Result: -0.76926 Exact Energy: -0.93415\n",
      "Interatomic Distance: 2.9 VQE Result: -0.77717 Exact Energy: -0.93385\n",
      "Interatomic Distance: 3.0 VQE Result: -0.78271 Exact Energy: -0.93363\n",
      "Interatomic Distance: 3.1 VQE Result: -0.76038 Exact Energy: -0.93348\n",
      "Interatomic Distance: 3.2 VQE Result: -0.77375 Exact Energy: -0.93338\n",
      "Interatomic Distance: 3.3 VQE Result: -0.77223 Exact Energy: -0.93331\n",
      "Interatomic Distance: 3.4 VQE Result: -0.77898 Exact Energy: -0.93326\n",
      "Interatomic Distance: 3.5 VQE Result: -0.77793 Exact Energy: -0.93323\n",
      "Interatomic Distance: 3.6 VQE Result: -0.77816 Exact Energy: -0.93321\n",
      "Interatomic Distance: 3.7 VQE Result: -0.77374 Exact Energy: -0.93319\n",
      "Interatomic Distance: 3.8 VQE Result: -0.75967 Exact Energy: -0.93318\n",
      "Interatomic Distance: 3.9 VQE Result: -0.76044 Exact Energy: -0.93318\n",
      "All energies have been calculated\n"
     ]
    }
   ],
   "source": [
    "distances = np.arange(0.1, 4.0, 0.1)\n",
    "exact_energies_cobyla = []\n",
    "vqe_energies_cobyla = []\n",
    "error_cobyla = []\n",
    "optimizer = COBYLA(maxiter=100)\n",
    "#noiseless_estimator = Estimator(approximation=True)\n",
    "noisy_estimator = Estimator(\n",
    "    backend_options={\n",
    "        \"method\": \"density_matrix\",\n",
    "        \"coupling_map\": coupling_map,\n",
    "        \"noise_model\": noise_model,\n",
    "    },\n",
    "    run_options={\"seed\": seed, \"shots\": 1024},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")\n",
    "for dist in distances:\n",
    "    (qubit_op, num_particles, num_spatial_orbitals, problem, mapper) = get_qubit_op_jw(\n",
    "        dist\n",
    "    )\n",
    "\n",
    "    result = exact_solver_jw(qubit_op, problem)\n",
    "    exact_energies_cobyla.append(result.total_energies[0].real)\n",
    "    init_state = HartreeFock(num_spatial_orbitals, num_particles, mapper)\n",
    "    var_form = UCCSD(\n",
    "        num_spatial_orbitals, num_particles, mapper, initial_state=init_state\n",
    "    )\n",
    "    vqe = VQE(\n",
    "        noisy_estimator,\n",
    "        var_form,\n",
    "        optimizer,\n",
    "        initial_point=[0] * var_form.num_parameters,\n",
    "    )\n",
    "    \n",
    "    vqe_calc = vqe.compute_minimum_eigenvalue(qubit_op)\n",
    "    vqe_result = problem.interpret(vqe_calc).total_energies[0].real\n",
    "    vqe_energies_cobyla.append(vqe_result)\n",
    "    error_cobyla.append(abs(vqe_result - (-1.13619)))\n",
    "    print(\n",
    "        f\"Interatomic Distance: {np.round(dist, 2)}\",\n",
    "        f\"VQE Result: {vqe_result:.5f}\",\n",
    "        f\"Exact Energy: {exact_energies_cobyla[-1]:.5f}\",)\n",
    "\n",
    "print(\"All energies have been calculated\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "54d6b10a-993e-4e10-a205-65f3d0694ae0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interatomic Distance: 0.1 VQE Result: 3.67258 Exact Energy: 2.70996\n",
      "Interatomic Distance: 0.2 VQE Result: 1.03761 Exact Energy: 0.15748\n",
      "Interatomic Distance: 0.3 VQE Result: 0.61865 Exact Energy: -0.60180\n",
      "Interatomic Distance: 0.4 VQE Result: -0.25321 Exact Energy: -0.91415\n",
      "Interatomic Distance: 0.5 VQE Result: -0.50578 Exact Energy: -1.05516\n",
      "Interatomic Distance: 0.6 VQE Result: -0.62411 Exact Energy: -1.11629\n",
      "Interatomic Distance: 0.7 VQE Result: -0.71308 Exact Energy: -1.13619\n",
      "Interatomic Distance: 0.8 VQE Result: -0.76466 Exact Energy: -1.13415\n",
      "Interatomic Distance: 0.9 VQE Result: -0.78428 Exact Energy: -1.12056\n",
      "Interatomic Distance: 1.0 VQE Result: -0.82679 Exact Energy: -1.10115\n",
      "Interatomic Distance: 1.1 VQE Result: -0.83206 Exact Energy: -1.07919\n",
      "Interatomic Distance: 1.2 VQE Result: -0.83341 Exact Energy: -1.05674\n",
      "Interatomic Distance: 1.3 VQE Result: -0.83099 Exact Energy: -1.03519\n",
      "Interatomic Distance: 1.4 VQE Result: -0.80400 Exact Energy: -1.01547\n",
      "Interatomic Distance: 1.5 VQE Result: -0.80378 Exact Energy: -0.99815\n",
      "Interatomic Distance: 1.6 VQE Result: -0.80776 Exact Energy: -0.98347\n",
      "Interatomic Distance: 1.7 VQE Result: -0.80713 Exact Energy: -0.97143\n",
      "Interatomic Distance: 1.8 VQE Result: -0.79772 Exact Energy: -0.96182\n",
      "Interatomic Distance: 1.9 VQE Result: -0.78307 Exact Energy: -0.95434\n",
      "Interatomic Distance: 2.0 VQE Result: -0.78939 Exact Energy: -0.94864\n",
      "Interatomic Distance: 2.1 VQE Result: -0.77974 Exact Energy: -0.94437\n",
      "Interatomic Distance: 2.2 VQE Result: -0.78356 Exact Energy: -0.94122\n",
      "Interatomic Distance: 2.3 VQE Result: -0.77615 Exact Energy: -0.93892\n",
      "Interatomic Distance: 2.4 VQE Result: -0.77320 Exact Energy: -0.93725\n",
      "Interatomic Distance: 2.5 VQE Result: -0.77606 Exact Energy: -0.93605\n",
      "Interatomic Distance: 2.6 VQE Result: -0.77065 Exact Energy: -0.93520\n",
      "Interatomic Distance: 2.7 VQE Result: -0.77464 Exact Energy: -0.93458\n",
      "Interatomic Distance: 2.8 VQE Result: -0.77938 Exact Energy: -0.93415\n",
      "Interatomic Distance: 2.9 VQE Result: -0.77422 Exact Energy: -0.93385\n",
      "Interatomic Distance: 3.0 VQE Result: -0.77905 Exact Energy: -0.93363\n",
      "Interatomic Distance: 3.1 VQE Result: -0.77795 Exact Energy: -0.93348\n",
      "Interatomic Distance: 3.2 VQE Result: -0.77144 Exact Energy: -0.93338\n",
      "Interatomic Distance: 3.3 VQE Result: -0.76951 Exact Energy: -0.93331\n",
      "Interatomic Distance: 3.4 VQE Result: -0.74133 Exact Energy: -0.93326\n",
      "Interatomic Distance: 3.5 VQE Result: -0.77417 Exact Energy: -0.93323\n",
      "Interatomic Distance: 3.6 VQE Result: -0.77142 Exact Energy: -0.93321\n",
      "Interatomic Distance: 3.7 VQE Result: -0.77278 Exact Energy: -0.93319\n",
      "Interatomic Distance: 3.8 VQE Result: -0.76849 Exact Energy: -0.93318\n",
      "Interatomic Distance: 3.9 VQE Result: -0.77192 Exact Energy: -0.93318\n",
      "All energies have been calculated\n"
     ]
    }
   ],
   "source": [
    "distances = np.arange(0.1, 4.0, 0.1)\n",
    "exact_energies_spsa = []\n",
    "vqe_energies_spsa = []\n",
    "error_spsa = []\n",
    "optimizer = SPSA(maxiter=100)\n",
    "#noiseless_estimator = Estimator(approximation=True)\n",
    "noisy_estimator = Estimator(\n",
    "    backend_options={\n",
    "        \"method\": \"density_matrix\",\n",
    "        \"coupling_map\": coupling_map,\n",
    "        \"noise_model\": noise_model,\n",
    "    },\n",
    "    run_options={\"seed\": seed, \"shots\": 1024},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")\n",
    "for dist in distances:\n",
    "    (qubit_op, num_particles, num_spatial_orbitals, problem, mapper) = get_qubit_op_jw(\n",
    "        dist\n",
    "    )\n",
    "\n",
    "    result = exact_solver_jw(qubit_op, problem)\n",
    "    exact_energies_spsa.append(result.total_energies[0].real)\n",
    "    init_state = HartreeFock(num_spatial_orbitals, num_particles, mapper)\n",
    "    var_form = UCCSD(\n",
    "        num_spatial_orbitals, num_particles, mapper, initial_state=init_state\n",
    "    )\n",
    "    vqe = VQE(\n",
    "        noisy_estimator,\n",
    "        var_form,\n",
    "        optimizer,\n",
    "        initial_point=[0] * var_form.num_parameters,\n",
    "    )\n",
    "    \n",
    "    vqe_calc = vqe.compute_minimum_eigenvalue(qubit_op)\n",
    "    vqe_result = problem.interpret(vqe_calc).total_energies[0].real\n",
    "    vqe_energies_spsa.append(vqe_result)\n",
    "    error_spsa.append(abs(vqe_result - (-1.13619)))\n",
    "    print(\n",
    "        f\"Interatomic Distance: {np.round(dist, 2)}\",\n",
    "        f\"VQE Result: {vqe_result:.5f}\",\n",
    "        f\"Exact Energy: {exact_energies_spsa[-1]:.5f}\",)\n",
    "\n",
    "print(\"All energies have been calculated\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "209f13c0-8a8f-4a61-a24a-cd13ed8a3d75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interatomic Distance: 0.1 VQE Result: 3.65657 Exact Energy: 2.70996\n",
      "Interatomic Distance: 0.2 VQE Result: 1.02073 Exact Energy: 0.15748\n",
      "Interatomic Distance: 0.3 VQE Result: 0.15645 Exact Energy: -0.60180\n",
      "Interatomic Distance: 0.4 VQE Result: -0.25921 Exact Energy: -0.91415\n",
      "Interatomic Distance: 0.5 VQE Result: -0.49123 Exact Energy: -1.05516\n",
      "Interatomic Distance: 0.6 VQE Result: -0.62855 Exact Energy: -1.11629\n",
      "Interatomic Distance: 0.7 VQE Result: -0.71062 Exact Energy: -1.13619\n",
      "Interatomic Distance: 0.8 VQE Result: -0.75865 Exact Energy: -1.13415\n",
      "Interatomic Distance: 0.9 VQE Result: -0.78526 Exact Energy: -1.12056\n",
      "Interatomic Distance: 1.0 VQE Result: -0.79809 Exact Energy: -1.10115\n",
      "Interatomic Distance: 1.1 VQE Result: -0.80180 Exact Energy: -1.07919\n",
      "Interatomic Distance: 1.2 VQE Result: -0.79933 Exact Energy: -1.05674\n",
      "Interatomic Distance: 1.3 VQE Result: -0.79266 Exact Energy: -1.03519\n",
      "Interatomic Distance: 1.4 VQE Result: -0.78324 Exact Energy: -1.01547\n",
      "Interatomic Distance: 1.5 VQE Result: -0.77213 Exact Energy: -0.99815\n",
      "Interatomic Distance: 1.6 VQE Result: -0.76011 Exact Energy: -0.98347\n",
      "Interatomic Distance: 1.7 VQE Result: -0.74777 Exact Energy: -0.97143\n",
      "Interatomic Distance: 1.8 VQE Result: -0.73551 Exact Energy: -0.96182\n",
      "Interatomic Distance: 1.9 VQE Result: -0.72363 Exact Energy: -0.95434\n",
      "Interatomic Distance: 2.0 VQE Result: -0.71233 Exact Energy: -0.94864\n",
      "Interatomic Distance: 2.1 VQE Result: -0.70171 Exact Energy: -0.94437\n",
      "Interatomic Distance: 2.2 VQE Result: -0.69186 Exact Energy: -0.94122\n",
      "Interatomic Distance: 2.3 VQE Result: -0.68278 Exact Energy: -0.93892\n",
      "Interatomic Distance: 2.4 VQE Result: -0.67447 Exact Energy: -0.93725\n",
      "Interatomic Distance: 2.5 VQE Result: -0.66691 Exact Energy: -0.93605\n",
      "Interatomic Distance: 2.6 VQE Result: -0.66006 Exact Energy: -0.93520\n",
      "Interatomic Distance: 2.7 VQE Result: -0.65387 Exact Energy: -0.93458\n",
      "Interatomic Distance: 2.8 VQE Result: -0.64829 Exact Energy: -0.93415\n",
      "Interatomic Distance: 2.9 VQE Result: -0.64329 Exact Energy: -0.93385\n",
      "Interatomic Distance: 3.0 VQE Result: -0.63880 Exact Energy: -0.93363\n",
      "Interatomic Distance: 3.1 VQE Result: -0.63479 Exact Energy: -0.93348\n",
      "Interatomic Distance: 3.2 VQE Result: -0.63120 Exact Energy: -0.93338\n",
      "Interatomic Distance: 3.3 VQE Result: -0.62799 Exact Energy: -0.93331\n",
      "Interatomic Distance: 3.4 VQE Result: -0.62512 Exact Energy: -0.93326\n",
      "Interatomic Distance: 3.5 VQE Result: -0.62256 Exact Energy: -0.93323\n",
      "Interatomic Distance: 3.6 VQE Result: -0.62025 Exact Energy: -0.93321\n",
      "Interatomic Distance: 3.7 VQE Result: -0.61818 Exact Energy: -0.93319\n",
      "Interatomic Distance: 3.8 VQE Result: -0.61631 Exact Energy: -0.93318\n",
      "Interatomic Distance: 3.9 VQE Result: -0.61462 Exact Energy: -0.93318\n",
      "All energies have been calculated\n"
     ]
    }
   ],
   "source": [
    "distances = np.arange(0.1, 4.0, 0.1)\n",
    "exact_energies_slsqp = []\n",
    "vqe_energies_slsqp = []\n",
    "error_slsqp = []\n",
    "optimizer = SLSQP(maxiter=100)\n",
    "#noiseless_estimator = Estimator(approximation=True)\n",
    "noisy_estimator = Estimator(\n",
    "    backend_options={\n",
    "        \"method\": \"density_matrix\",\n",
    "        \"coupling_map\": coupling_map,\n",
    "        \"noise_model\": noise_model,\n",
    "    },\n",
    "    run_options={\"seed\": seed, \"shots\": 1024},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")\n",
    "for dist in distances:\n",
    "    (qubit_op, num_particles, num_spatial_orbitals, problem, mapper) = get_qubit_op_jw(\n",
    "        dist\n",
    "    )\n",
    "\n",
    "    result = exact_solver_jw(qubit_op, problem)\n",
    "    exact_energies_slsqp.append(result.total_energies[0].real)\n",
    "    init_state = HartreeFock(num_spatial_orbitals, num_particles, mapper)\n",
    "    var_form = UCCSD(\n",
    "        num_spatial_orbitals, num_particles, mapper, initial_state=init_state\n",
    "    )\n",
    "    vqe = VQE(\n",
    "        noisy_estimator,\n",
    "        var_form,\n",
    "        optimizer,\n",
    "        initial_point=[0] * var_form.num_parameters,\n",
    "    )\n",
    "    \n",
    "    vqe_calc = vqe.compute_minimum_eigenvalue(qubit_op)\n",
    "    vqe_result = problem.interpret(vqe_calc).total_energies[0].real\n",
    "    vqe_energies_slsqp.append(vqe_result)\n",
    "    error_slsqp.append(abs(vqe_result - (-1.13619)))\n",
    "    print(\n",
    "        f\"Interatomic Distance: {np.round(dist, 2)}\",\n",
    "        f\"VQE Result: {vqe_result:.5f}\",\n",
    "        f\"Exact Energy: {exact_energies_slsqp[-1]:.5f}\",)\n",
    "\n",
    "print(\"All energies have been calculated\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f7b906c7-d591-4e8f-b87d-f399806bcc14",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interatomic Distance: 0.1 VQE Result: 3.65657 Exact Energy: 2.70996\n",
      "Interatomic Distance: 0.2 VQE Result: 1.02073 Exact Energy: 0.15748\n",
      "Interatomic Distance: 0.3 VQE Result: 0.15645 Exact Energy: -0.60180\n",
      "Interatomic Distance: 0.4 VQE Result: -0.25921 Exact Energy: -0.91415\n",
      "Interatomic Distance: 0.5 VQE Result: -0.49123 Exact Energy: -1.05516\n",
      "Interatomic Distance: 0.6 VQE Result: -0.62855 Exact Energy: -1.11629\n",
      "Interatomic Distance: 0.7 VQE Result: -0.71062 Exact Energy: -1.13619\n",
      "Interatomic Distance: 0.8 VQE Result: -0.75865 Exact Energy: -1.13415\n",
      "Interatomic Distance: 0.9 VQE Result: -0.78526 Exact Energy: -1.12056\n",
      "Interatomic Distance: 1.0 VQE Result: -0.79809 Exact Energy: -1.10115\n",
      "Interatomic Distance: 1.1 VQE Result: -0.81426 Exact Energy: -1.07919\n",
      "Interatomic Distance: 1.2 VQE Result: -0.81223 Exact Energy: -1.05674\n",
      "Interatomic Distance: 1.3 VQE Result: -0.80601 Exact Energy: -1.03519\n",
      "Interatomic Distance: 1.4 VQE Result: -0.79702 Exact Energy: -1.01547\n",
      "Interatomic Distance: 1.5 VQE Result: -0.78588 Exact Energy: -0.99815\n",
      "Interatomic Distance: 1.6 VQE Result: -0.77472 Exact Energy: -0.98347\n",
      "Interatomic Distance: 1.7 VQE Result: -0.76277 Exact Energy: -0.97143\n",
      "Interatomic Distance: 1.8 VQE Result: -0.75041 Exact Energy: -0.96182\n",
      "Interatomic Distance: 1.9 VQE Result: -0.73888 Exact Energy: -0.95434\n",
      "Interatomic Distance: 2.0 VQE Result: -0.72790 Exact Energy: -0.94864\n",
      "Interatomic Distance: 2.1 VQE Result: -0.71812 Exact Energy: -0.94437\n",
      "Interatomic Distance: 2.2 VQE Result: -0.70804 Exact Energy: -0.94122\n",
      "Interatomic Distance: 2.3 VQE Result: -0.69924 Exact Energy: -0.93892\n",
      "Interatomic Distance: 2.4 VQE Result: -0.69119 Exact Energy: -0.93725\n",
      "Interatomic Distance: 2.5 VQE Result: -0.68388 Exact Energy: -0.93605\n",
      "Interatomic Distance: 2.6 VQE Result: -0.67781 Exact Energy: -0.93520\n",
      "Interatomic Distance: 2.7 VQE Result: -0.70565 Exact Energy: -0.93458\n",
      "Interatomic Distance: 2.8 VQE Result: -0.66648 Exact Energy: -0.93415\n",
      "Interatomic Distance: 2.9 VQE Result: -0.69414 Exact Energy: -0.93385\n",
      "Interatomic Distance: 3.0 VQE Result: -0.70909 Exact Energy: -0.93363\n",
      "Interatomic Distance: 3.1 VQE Result: -0.70583 Exact Energy: -0.93348\n",
      "Interatomic Distance: 3.2 VQE Result: -0.70966 Exact Energy: -0.93338\n",
      "Interatomic Distance: 3.3 VQE Result: -0.68365 Exact Energy: -0.93331\n",
      "Interatomic Distance: 3.4 VQE Result: -0.70513 Exact Energy: -0.93326\n",
      "Interatomic Distance: 3.5 VQE Result: -0.69606 Exact Energy: -0.93323\n",
      "Interatomic Distance: 3.6 VQE Result: -0.70217 Exact Energy: -0.93321\n",
      "Interatomic Distance: 3.7 VQE Result: -0.67335 Exact Energy: -0.93319\n",
      "Interatomic Distance: 3.8 VQE Result: -0.69904 Exact Energy: -0.93318\n",
      "Interatomic Distance: 3.9 VQE Result: -0.67264 Exact Energy: -0.93318\n",
      "All energies have been calculated\n"
     ]
    }
   ],
   "source": [
    "distances = np.arange(0.1, 4.0, 0.1)\n",
    "exact_energies_nft = []\n",
    "vqe_energies_nft = []\n",
    "error_nft = []\n",
    "optimizer = NFT(maxiter=100)\n",
    "#noiseless_estimator = Estimator(approximation=True)\n",
    "noisy_estimator = Estimator(\n",
    "    backend_options={\n",
    "        \"method\": \"density_matrix\",\n",
    "        \"coupling_map\": coupling_map,\n",
    "        \"noise_model\": noise_model,\n",
    "    },\n",
    "    run_options={\"seed\": seed, \"shots\": 1024},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")\n",
    "for dist in distances:\n",
    "    (qubit_op, num_particles, num_spatial_orbitals, problem, mapper) = get_qubit_op_jw(\n",
    "        dist\n",
    "    )\n",
    "\n",
    "    result = exact_solver_jw(qubit_op, problem)\n",
    "    exact_energies_nft.append(result.total_energies[0].real)\n",
    "    init_state = HartreeFock(num_spatial_orbitals, num_particles, mapper)\n",
    "    var_form = UCCSD(\n",
    "        num_spatial_orbitals, num_particles, mapper, initial_state=init_state\n",
    "    )\n",
    "    vqe = VQE(\n",
    "        noisy_estimator,\n",
    "        var_form,\n",
    "        optimizer,\n",
    "        initial_point=[0] * var_form.num_parameters,\n",
    "    )\n",
    "    \n",
    "    vqe_calc = vqe.compute_minimum_eigenvalue(qubit_op)\n",
    "    vqe_result = problem.interpret(vqe_calc).total_energies[0].real\n",
    "    vqe_energies_nft.append(vqe_result)\n",
    "    error_nft.append(abs(vqe_result - (-1.13619)))\n",
    "    print(\n",
    "        f\"Interatomic Distance: {np.round(dist, 2)}\",\n",
    "        f\"VQE Result: {vqe_result:.5f}\",\n",
    "        f\"Exact Energy: {exact_energies_nft[-1]:.5f}\",)\n",
    "\n",
    "print(\"All energies have been calculated\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "59e85b8c-a188-4a8b-b001-f7ab03553e8d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interatomic Distance: 0.1 VQE Result: 3.65657 Exact Energy: 2.70996\n",
      "Interatomic Distance: 0.2 VQE Result: 1.02073 Exact Energy: 0.15748\n",
      "Interatomic Distance: 0.3 VQE Result: 0.15645 Exact Energy: -0.60180\n",
      "Interatomic Distance: 0.4 VQE Result: -0.25921 Exact Energy: -0.91415\n",
      "Interatomic Distance: 0.5 VQE Result: -0.49123 Exact Energy: -1.05516\n",
      "Interatomic Distance: 0.6 VQE Result: -0.62855 Exact Energy: -1.11629\n",
      "Interatomic Distance: 0.7 VQE Result: -0.71062 Exact Energy: -1.13619\n",
      "Interatomic Distance: 0.8 VQE Result: -0.75865 Exact Energy: -1.13415\n",
      "Interatomic Distance: 0.9 VQE Result: -0.78526 Exact Energy: -1.12056\n",
      "Interatomic Distance: 1.0 VQE Result: -0.79809 Exact Energy: -1.10115\n",
      "Interatomic Distance: 1.1 VQE Result: -0.80180 Exact Energy: -1.07919\n",
      "Interatomic Distance: 1.2 VQE Result: -0.79933 Exact Energy: -1.05674\n",
      "Interatomic Distance: 1.3 VQE Result: -0.79266 Exact Energy: -1.03519\n",
      "Interatomic Distance: 1.4 VQE Result: -0.78324 Exact Energy: -1.01547\n",
      "Interatomic Distance: 1.5 VQE Result: -0.77213 Exact Energy: -0.99815\n",
      "Interatomic Distance: 1.6 VQE Result: -0.76011 Exact Energy: -0.98347\n",
      "Interatomic Distance: 1.7 VQE Result: -0.74777 Exact Energy: -0.97143\n",
      "Interatomic Distance: 1.8 VQE Result: -0.73551 Exact Energy: -0.96182\n",
      "Interatomic Distance: 1.9 VQE Result: -0.72363 Exact Energy: -0.95434\n",
      "Interatomic Distance: 2.0 VQE Result: -0.71233 Exact Energy: -0.94864\n",
      "Interatomic Distance: 2.1 VQE Result: -0.70171 Exact Energy: -0.94437\n",
      "Interatomic Distance: 2.2 VQE Result: -0.69186 Exact Energy: -0.94122\n",
      "Interatomic Distance: 2.3 VQE Result: -0.68278 Exact Energy: -0.93892\n",
      "Interatomic Distance: 2.4 VQE Result: -0.67447 Exact Energy: -0.93725\n",
      "Interatomic Distance: 2.5 VQE Result: -0.66691 Exact Energy: -0.93605\n",
      "Interatomic Distance: 2.6 VQE Result: -0.66006 Exact Energy: -0.93520\n",
      "Interatomic Distance: 2.7 VQE Result: -0.65387 Exact Energy: -0.93458\n",
      "Interatomic Distance: 2.8 VQE Result: -0.64829 Exact Energy: -0.93415\n",
      "Interatomic Distance: 2.9 VQE Result: -0.64329 Exact Energy: -0.93385\n",
      "Interatomic Distance: 3.0 VQE Result: -0.63880 Exact Energy: -0.93363\n",
      "Interatomic Distance: 3.1 VQE Result: -0.63479 Exact Energy: -0.93348\n",
      "Interatomic Distance: 3.2 VQE Result: -0.63120 Exact Energy: -0.93338\n",
      "Interatomic Distance: 3.3 VQE Result: -0.62799 Exact Energy: -0.93331\n",
      "Interatomic Distance: 3.4 VQE Result: -0.62512 Exact Energy: -0.93326\n",
      "Interatomic Distance: 3.5 VQE Result: -0.62256 Exact Energy: -0.93323\n",
      "Interatomic Distance: 3.6 VQE Result: -0.62025 Exact Energy: -0.93321\n",
      "Interatomic Distance: 3.7 VQE Result: -0.61818 Exact Energy: -0.93319\n",
      "Interatomic Distance: 3.8 VQE Result: -0.61631 Exact Energy: -0.93318\n",
      "Interatomic Distance: 3.9 VQE Result: -0.61462 Exact Energy: -0.93318\n",
      "All energies have been calculated\n"
     ]
    }
   ],
   "source": [
    "distances = np.arange(0.1, 4.0, 0.1)\n",
    "exact_energies_bfgs = []\n",
    "vqe_energies_bfgs = []\n",
    "error_bfgs = []\n",
    "optimizer = L_BFGS_B(maxiter=100)\n",
    "#noiseless_estimator = Estimator(approximation=True)\n",
    "noisy_estimator = Estimator(\n",
    "    backend_options={\n",
    "        \"method\": \"density_matrix\",\n",
    "        \"coupling_map\": coupling_map,\n",
    "        \"noise_model\": noise_model,\n",
    "    },\n",
    "    run_options={\"seed\": seed, \"shots\": 1024},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")\n",
    "for dist in distances:\n",
    "    (qubit_op, num_particles, num_spatial_orbitals, problem, mapper) = get_qubit_op_jw(\n",
    "        dist\n",
    "    )\n",
    "\n",
    "    result = exact_solver_jw(qubit_op, problem)\n",
    "    exact_energies_bfgs.append(result.total_energies[0].real)\n",
    "    init_state = HartreeFock(num_spatial_orbitals, num_particles, mapper)\n",
    "    var_form = UCCSD(\n",
    "        num_spatial_orbitals, num_particles, mapper, initial_state=init_state\n",
    "    )\n",
    "    vqe = VQE(\n",
    "        noisy_estimator,\n",
    "        var_form,\n",
    "        optimizer,\n",
    "        initial_point=[0] * var_form.num_parameters,\n",
    "    )\n",
    "    \n",
    "    vqe_calc = vqe.compute_minimum_eigenvalue(qubit_op)\n",
    "    vqe_result = problem.interpret(vqe_calc).total_energies[0].real\n",
    "    vqe_energies_bfgs.append(vqe_result)\n",
    "    error_bfgs.append(abs(vqe_result - (-1.13619)))\n",
    "    print(\n",
    "        f\"Interatomic Distance: {np.round(dist, 2)}\",\n",
    "        f\"VQE Result: {vqe_result:.5f}\",\n",
    "        f\"Exact Energy: {exact_energies_bfgs[-1]:.5f}\",)\n",
    "\n",
    "print(\"All energies have been calculated\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "dba73dc3-4d05-43bc-b641-641b198d8204",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(distances, error_cobyla, label=\"COBYLA\")\n",
    "ci = 0.2 * np.std(error_cobyla) / np.mean(error_cobyla)\n",
    "plt.fill_between(distances, (error_cobyla-ci), (error_cobyla+ci), color='blue', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, error_spsa, label=\"SPSA\")\n",
    "ci_spsa = 0.2 * np.std(error_spsa) / np.mean(error_spsa)\n",
    "plt.fill_between(distances, (error_spsa-ci_spsa), (error_spsa+ci_spsa), color='gold', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, error_slsqp, label=\"SLSQP\")\n",
    "ci_slsqp = 0.2 * np.std(error_slsqp) / np.mean(error_slsqp)\n",
    "plt.fill_between(distances, (error_slsqp-ci_slsqp), (error_slsqp+ci_slsqp), color='green', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, error_nft, label=\"NFT\")\n",
    "ci_nft = 0.2 * np.std(error_nft) / np.mean(error_nft)\n",
    "plt.fill_between(distances, (error_nft-ci_nft), (error_nft+ci_nft), color='red', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, error_bfgs, label=\"L_BFGS_B\")\n",
    "ci_bfgs = 0.2 * np.std(error_bfgs) / np.mean(error_bfgs)\n",
    "plt.fill_between(distances, (error_bfgs-ci_nft), (error_bfgs+ci_nft), color='purple', alpha=0.1)\n",
    "\n",
    "#plt.ylim(0,0.000000000001)\n",
    "plt.xlabel(\"Atomic distance (Angstrom)\")\n",
    "plt.ylabel(\"Energy\")\n",
    "plt.legend()\n",
    "plt.savefig(\"H2_Error_Optimizer_Comparison_Noisy.jpeg\",dpi=300)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cd360af7-2798-4603-b0a1-192dc4a9c83a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.792755325084995, 2.1569182884475584, 1.2926370383660606, 0.8769793021389545, 0.6449621771198857, 0.5076385138800934, 0.4255729977434397, 0.37754384896453974, 0.350933520351316, 0.33809772196595367, 0.3343874384061174, 0.33686223264698345, 0.3435278438160694, 0.35294831050219844, 0.3640611344060296, 0.3760787971646562, 0.38842389628841456, 0.40068078956024833, 0.4125587039498777, 0.4238634940938808, 0.43447548462617935, 0.44433140730940424, 0.45340932561463454, 0.4617161705832623, 0.46927785045237047, 0.4761318776209378, 0.4823222601337791, 0.4878962124648728, 0.49290215498986933, 0.4973885081616327, 0.5014029052925344, 0.5049915908305919, 0.5081988952679771, 0.5110667619885727, 0.5136343437962937, 0.5159376973949328, 0.5180095959992443, 0.51987946509106, 0.5215734317591582]\n"
     ]
    }
   ],
   "source": [
    "print(error_bfgs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8ad2323d-7a48-4a91-92d9-290d56d928f6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.770230640404947, 2.1393746214417937, 1.2776356885803823, 0.8570220063111791, 0.6253254824717371, 0.486256209380701, 0.4020875339294263, 0.34966552941186624, 0.32239521513425884, 0.3053211040728593, 0.2957702504312232, 0.3277114876487599, 0.30738985691135934, 0.3131128941109538, 0.3194335136194111, 0.3346917611561264, 0.32935865539685705, 0.3414568400848462, 0.33930260736689033, 0.34523927611802874, 0.35342100457718906, 0.34548282148138276, 0.348862765492838, 0.35343960814109365, 0.3556489711015961, 0.35673575336817764, 0.3628247782503886, 0.3669343095612949, 0.3590187049807382, 0.3534835051738692, 0.37580660534307586, 0.3624353327100919, 0.3639610102869215, 0.35720821775350964, 0.3582585259405041, 0.35803365472797943, 0.36245280142112923, 0.37651684227866056, 0.375751587907717]\n"
     ]
    }
   ],
   "source": [
    "print(error_cobyla)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "65df50b1-d900-44dc-90af-d3fd8688b22c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.792755325084995, 2.1569182884475584, 1.2926370383660606, 0.8769793021389545, 0.6449621771198857, 0.5076385138800934, 0.4255729977434397, 0.37754384896453974, 0.350933520351316, 0.33809772196595367, 0.3343874384061174, 0.33686223264698345, 0.3435278438160694, 0.35294831050219844, 0.3640611344060296, 0.3760787971646562, 0.38842389628841456, 0.40068078956024833, 0.4125587039498777, 0.4238634940938808, 0.43447548462617935, 0.44433140730940424, 0.45340932561463454, 0.4617161705832623, 0.46927785045237047, 0.4761318776209378, 0.4823222601337791, 0.4878962124648728, 0.49290215498986933, 0.4973885081616327, 0.5014029052925344, 0.5049915908305919, 0.5081988952679771, 0.5110667619885727, 0.5136343437962937, 0.5159376973949328, 0.5180095959992443, 0.51987946509106, 0.5215734317591582]\n"
     ]
    }
   ],
   "source": [
    "print(error_slsqp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8ae54679-4fc9-4b5a-b9f9-c23b9644419b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.808771186859325, 2.173796305648917, 1.754842645330695, 0.8829798080336382, 0.6304123460042983, 0.5120804309433213, 0.42311355579887855, 0.3715258128954033, 0.35190523919863104, 0.3094003343465811, 0.3041337109613962, 0.3027845623154015, 0.3052015289420311, 0.33218668292211095, 0.33240893633337465, 0.32842863452808424, 0.3290581761993019, 0.338473556754736, 0.3531236032242955, 0.3468043774997722, 0.35645290717973244, 0.35263479513865925, 0.3600381428415862, 0.36299474389125663, 0.3601333426275134, 0.365538441792318, 0.3615548738045511, 0.35681395405456773, 0.36197415470629357, 0.357140316926605, 0.3582444590307071, 0.3647524152771381, 0.36667755740820185, 0.3948642965169398, 0.3620189741367602, 0.3647696583813633, 0.36340952766963963, 0.36769889579265713, 0.36426616237989773]\n"
     ]
    }
   ],
   "source": [
    "print(error_spsa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "fcb1418a-f9b5-4049-85fe-7e951e6d7eb9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(distances, vqe_energies_cobyla, label=\"COBYLA\")\n",
    "ci = 0.2 * np.std(vqe_energies_cobyla) / np.mean(vqe_energies_cobyla)\n",
    "plt.fill_between(distances, (vqe_energies_cobyla-ci), (vqe_energies_cobyla+ci), color='blue', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, vqe_energies_spsa, label=\"SPSA\")\n",
    "ci = 0.2 * np.std(vqe_energies_spsa) / np.mean(vqe_energies_spsa)\n",
    "plt.fill_between(distances, (vqe_energies_spsa-ci), (vqe_energies_spsa+ci), color='gold', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, vqe_energies_slsqp, label=\"SLSQP\")\n",
    "ci = 0.2 * np.std(vqe_energies_slsqp) / np.mean(vqe_energies_slsqp)\n",
    "plt.fill_between(distances, (vqe_energies_slsqp-ci), (vqe_energies_slsqp+ci), color='green', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, vqe_energies_nft, label=\"NFT\")\n",
    "ci = 0.2 * np.std(vqe_energies_nft) / np.mean(vqe_energies_nft)\n",
    "plt.fill_between(distances, (vqe_energies_nft-ci), (vqe_energies_nft+ci), color='red', alpha=0.1)\n",
    "\n",
    "plt.plot(distances, vqe_energies_bfgs, label=\"L_BFGS_B\")\n",
    "ci = 0.2 * np.std(vqe_energies_bfgs) / np.mean(vqe_energies_bfgs)\n",
    "plt.fill_between(distances, (vqe_energies_bfgs-ci), (vqe_energies_bfgs+ci), color='purple', alpha=0.1)\n",
    "#plt.ylim(0,0.000000000001)\n",
    "plt.xlabel(\"Atomic distance (Angstrom)\")\n",
    "plt.ylabel(\"Energy\")\n",
    "plt.legend()\n",
    "plt.savefig(\"H2_Optimizer_Comparison_noisy.jpeg\",dpi=300)\n",
    "plt.show()"
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