IEEE_molecular_simulation_runtime_entry.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aa9b1827-d7ac-4c62-9d8c-8c56c3e7a6af",
   "metadata": {},
   "source": [
    "In this project my goal is to find the optimal angle and bond length of $H_\\mathrm{2}O$. $H_\\mathrm{2}O$ is a non collinear molecule so that the bond angle of $H-O-H$ is not $180^{o}$, so it is more difficult to find the optimal angle. Here i first using the Numpy function to obtain the value of the optimized bond angle and bond length by fitting a 3D potential energy surface of H2O, then i use VQE runtime to benchmark my ansatz to determine if my variational circuit can also produce simular minimal energy as the Numpy result. The runtime process is used to run the VQE process multiple times at different starting angle to understand which initial angle can result in the best VQE energy matching the exact diagnoalization using Numpy result. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "414ded0f-46f7-41cf-852c-456a86ee6c0c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[<IBMQSimulator('ibmq_qasm_simulator') from IBMQ(hub='ibm-q', group='open', project='main')>]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import copy\n",
    "# Importing standard Qiskit libraries\n",
    "from qiskit import QuantumCircuit, transpile, Aer, IBMQ\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from ibm_quantum_widgets import *\n",
    "\n",
    "# Loading your IBM Quantum account(s) and check with backend can use runtime. Here the qasm simulator is used because it can run runtime\n",
    "provider = IBMQ.load_account()\n",
    "backend = provider.get_backend('ibmq_qasm_simulator')\n",
    "runtime_backends = provider.backends(input_allowed='runtime')\n",
    "print(runtime_backends)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eba1ab0f-8912-4c9a-bffb-cec7e23add0b",
   "metadata": {},
   "source": [
    "Set up the water molecule so that we can vary the bond distance and bond angle to calculate a 3D potential energy suface to find the optimal values\n",
    "for bond angle and bond length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f3bf553b-8201-406f-a078-4486ca294155",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/pyscf/lib/misc.py:47: H5pyDeprecationWarning: Using default_file_mode other than 'r' is deprecated. Pass the mode to h5py.File() instead.\n",
      "  h5py.get_config().default_file_mode = 'a'\n"
     ]
    }
   ],
   "source": [
    "# Loading the relevant libraries and define the molecular structure of H2O in Z-matrix format.Here we vary the two bond legnth at equal distances\n",
    "# and the bond angle. The bond angle is varied from 30 degree to 180 degree\n",
    "\n",
    "from qiskit import Aer\n",
    "from qiskit_nature.drivers import PySCFDriver, UnitsType, Molecule\n",
    "from qiskit_nature.problems.second_quantization.electronic import ElectronicStructureProblem\n",
    "from qiskit_nature.transformers import FreezeCoreTransformer\n",
    "from qiskit_nature.mappers.second_quantization import JordanWignerMapper, ParityMapper\n",
    "from qiskit_nature.converters.second_quantization import QubitConverter\n",
    "from qiskit.algorithms import NumPyMinimumEigensolver\n",
    "from qiskit_nature.algorithms import GroundStateEigensolver\n",
    "\n",
    "H2O = 'H; O 1 {}; H 2 {} 1 {}'\n",
    "distance = [i * 0.1 + 0.3 for i in range(20)]\n",
    "angle = [j * 30 for j in range(1,7,1)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "a392974d-1b48-4c49-b7e6-4bef5eb65945",
   "metadata": {},
   "outputs": [],
   "source": [
    "# In this step we calculate the minimum energy of the H2O molecule at different angle and bond lengths using the Numpy exact diagnolization\n",
    "# The hamiltonian is mapped to qubit basis using the Parity mapper from the intial second quantization format\n",
    "# The core elevtrons are frozen to reduce the number of qubits for calculation\n",
    "\n",
    "converter = QubitConverter(mapper=JordanWignerMapper(), two_qubit_reduction=True)\n",
    "numpy_solver = NumPyMinimumEigensolver()\n",
    "energies_exact = []\n",
    "for a in angle:\n",
    "    for d in distance:\n",
    "        driver = PySCFDriver(H2O.format(d,d,a),unit=UnitsType.ANGSTROM, basis='sto3g')\n",
    "        problem = ElectronicStructureProblem(driver, q_molecule_transformers=[FreezeCoreTransformer(remove_orbitals=[4,5,6])])\n",
    "        second_q_ops = problem.second_q_ops()\n",
    "        main_op = second_q_ops[0]\n",
    "        num_particles = (problem.molecule_data_transformed.num_alpha,problem.molecule_data_transformed.num_beta)\n",
    "        qubit_op = converter.convert(main_op, num_particles=num_particles)\n",
    "        calc_exact = GroundStateEigensolver(converter,numpy_solver)\n",
    "        res_exact = calc_exact.solve(problem)\n",
    "        energies_exact.append(res_exact.total_energies[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "9b4dd4db-a0fe-4f97-a41e-affc13e98cf1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here we plot the data points of the minimum energy based on exact diagnolization for different angles and distances\n",
    " \n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "X = np.array(np.repeat(angle,len(distance)))\n",
    "Y = np.array(distance*len(angle))\n",
    "Z = np.array(energies_exact)\n",
    "fig = plt.figure(figsize =(16, 9))  \n",
    "ax = plt.axes(projection ='3d')\n",
    "ax.view_init(20, -10)\n",
    "ax.set_xlabel('angle ', fontsize=12, rotation=150)\n",
    "ax.set_ylabel('O-H bond',fontsize=12, rotation=150)\n",
    "ax.set_zlabel('Energy (Ha)', fontsize=15, rotation=60)\n",
    "surf = ax.scatter(X, Y, Z, color='red')  \n",
    "fig = plt.figure()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "1f03e591-7107-4b9b-be9e-55ba6ab7d651",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficients of equation of plane, (a1, a2, a3, a4, a5, a6):  [-2.45146825e+04 -4.13495495e+00  3.70121505e+06  4.64129647e+00\n",
      " -2.55000591e+08 -2.12934816e+00  9.09173837e+08  6.41499652e-01]\n",
      "value of intercept, c: -73.58769341533467\n"
     ]
    }
   ],
   "source": [
    "# To determine the optimal bond angle and distances in the potential energy surface, the 3D data ponints are fitted to a 3D function using linear regression\n",
    "# The 3D function has the format of a1/(X^2) + a2/(Y^2) + a3/(X^3) + a4/(Y^3) + a5/(x^4.5) + a6/(y^4.5)\n",
    "\n",
    "from sklearn import linear_model\n",
    "x1, y1, z1 = X.flatten(), Y.flatten(), Z.flatten()\n",
    "x11, y11, x12, y12, x13, y13, x14, y14 = 1/(x1**2), 1/(y1**2), 1/(x1**3), 1/(y1**3), 1/(x1**4), 1/(y1**4), 1/(x1**4.5), 1/(y1**4.5)\n",
    "X_data = np.array([x11, y11, x12, y12, x13, y13, x14, y14]).T  \n",
    "Y_data = z1\n",
    "reg = linear_model.LinearRegression().fit(X_data, Y_data)\n",
    "print(\"coefficients of equation of plane, (a1, a2, a3, a4, a5, a6): \", reg.coef_)\n",
    "print(\"value of intercept, c:\", reg.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "92d989c5-f8a3-4fea-a613-0e09e3a4a1da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the 3D function and the data points of minimum energy at different bond length and angles \n",
    "\n",
    "import matplotlib as mpl\n",
    "fig = plt.figure(figsize =(16, 9))  \n",
    "ax = plt.axes(projection ='3d')\n",
    "ax.view_init(20, -10)\n",
    "ax.set_xlabel('angle ', fontsize=12, rotation=150)\n",
    "ax.set_ylabel('O-H bond',fontsize=12, rotation=150)\n",
    "ax.set_zlabel('Energy (Ha)', fontsize=15, rotation=60)\n",
    "def z_pred(x, y):\n",
    "    z_func = reg.coef_[0]*1/(X**2) + reg.coef_[1]*1/(Y**2) + reg.coef_[2]*1/(X**3) + reg.coef_[3]*1/(Y**3) + reg.coef_[4]*1/(X**4) + reg.coef_[5]*1/(Y**4) + reg.coef_[6]*1/(X**4.5) + reg.coef_[7]*1/(Y**4.5) + reg.intercept_\n",
    "    return z_func\n",
    "[x_grid, y_grid] = np.meshgrid(X, Y)\n",
    "z_grid = z_pred(X, Y)\n",
    "ax.plot_trisurf(X, Y, z_grid, linewidth = 0, antialiased = False,color='blue',edgecolor=None, label = 'prediction')\n",
    "ax.scatter(X, Y, Z, color = 'red', label='data')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "db48feaf-5627-4805-9781-66b55a21dcfa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      fun: -74.96417406426215\n",
      " hess_inv: array([[ 2.41277323e+03, -1.35401968e-01],\n",
      "       [-1.35401968e-01,  2.59194460e-01]])\n",
      "      jac: array([0.00000000e+00, 9.53674316e-07])\n",
      "  message: 'Optimization terminated successfully.'\n",
      "     nfev: 78\n",
      "      nit: 22\n",
      "     njev: 26\n",
      "   status: 0\n",
      "  success: True\n",
      "        x: array([108.74515985,   1.00569146])\n"
     ]
    }
   ],
   "source": [
    "# Find the optimal bond length and angle by finding the minimum of the 3D function\n",
    "# Compare the minium bond distance and the angle with the values from data array\n",
    "\n",
    "import scipy.optimize as optimize\n",
    "\n",
    "def fit(params):\n",
    "    x, y = params\n",
    "    return reg.coef_[0]*1/(x**2) + reg.coef_[1]*1/(y**2) + reg.coef_[2]*1/(x**3) + reg.coef_[3]*1/(y**3) + reg.coef_[4]*1/(x**4) + reg.coef_[5]*1/(y**4) + reg.coef_[6]*1/(x**4.5) + reg.coef_[7]*1/(y**4.5) + reg.intercept_\n",
    "\n",
    "initial_guess = [100,0.9]\n",
    "result = optimize.minimize(fit, initial_guess)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "e235fd43-2d62-411c-9d1d-2c6454396f0d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "108.85417513665914\n",
      "1.005102450580927\n"
     ]
    }
   ],
   "source": [
    "# Set the optimized angle and bond length\n",
    "# Here the optimized angle and bond length match the experimental value of H2O with bon angle = 104.5 and legnth of O-H bond = 0.945\n",
    "\n",
    "optimized_angle = result['x'][0]\n",
    "optimized_distance = result['x'][1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "331b95f8-46a1-49d8-9c45-c4fe66970c1c",
   "metadata": {},
   "source": [
    "After obtaining the minimal theoretical values for bond angle and bond legnths through classical approach using Numpy, we begin our quantum run with $runtime$ $VQE$. Here to determine the initial optimal starting angles, we used runtime for different random starting angle. To determine the best starting angles of our variational circuit in the $VQE$ run, we benchmark the result against classical values obtained from exact diagnolization using Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "f47e3d18-d604-4b90-9cc2-8248d984bf64",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== GROUND STATE ENERGY ===\n",
      " \n",
      "* Electronic ground state energy (Hartree): -83.709197933496\n",
      "  - computed part:      -13.60601137269\n",
      "  - FreezeCoreTransformer extracted energy part: -70.103186560806\n",
      "~ Nuclear repulsion energy (Hartree): 8.747498538596\n",
      "> Total ground state energy (Hartree): -74.961699394901\n",
      " \n",
      "=== MEASURED OBSERVABLES ===\n",
      " \n",
      "  0:  # Particles: 6.000 S: 0.000 S^2: 0.000 M: 0.000\n",
      " \n",
      "=== DIPOLE MOMENTS ===\n",
      " \n",
      "~ Nuclear dipole moment (a.u.): [17.70811632  0.0  1.79745608]\n",
      " \n",
      "  0: \n",
      "  * Electronic dipole moment (a.u.): [18.0827398  0.0  1.27366455]\n",
      "    - computed part:      [10.48572279  0.0  1.27302639]\n",
      "    - FreezeCoreTransformer extracted energy part: [7.59701701  0.0  0.00063816]\n",
      "  > Dipole moment (a.u.): [-0.37462348  0.0  0.52379153]  Total: 0.6439723\n",
      "                 (debye): [-0.95219783  0.0  1.33134515]  Total: 1.63681417\n",
      " \n"
     ]
    }
   ],
   "source": [
    "# Compute the minimum energy using the optimized angle and bond length with exact diagnolization using Numpy\n",
    "# Here we remove the orbitals 4,5, and 6 to reduce the number of qubits during computation\n",
    "\n",
    "driver_optimized = PySCFDriver(H2O.format(optimized_distance,optimized_distance,optimized_angle),unit=UnitsType.ANGSTROM, basis='sto3g')\n",
    "problem_optimized = ElectronicStructureProblem(driver_optimized, q_molecule_transformers=[FreezeCoreTransformer(remove_orbitals=[4,5,6])])\n",
    "second_q_ops_optimized = problem_optimized.second_q_ops()\n",
    "main_op_optimized = second_q_ops_optimized[0]\n",
    "num_particles_optimized = (problem_optimized.molecule_data_transformed.num_alpha,problem_optimized.molecule_data_transformed.num_beta)\n",
    "qubit_op_optimized = converter.convert(main_op_optimized, num_particles=num_particles_optimized)\n",
    "calc_exact_optimized = GroundStateEigensolver(converter,numpy_solver)\n",
    "res_exact_optimized = calc_exact_optimized.solve(problem_optimized)\n",
    "print(res_exact_optimized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "ef620fc7-c566-44ac-96a3-c88af2e7de51",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     ┌───┐┌──────────┐ ┌──────────┐ ░       ░ ┌───────────┐┌───────────┐\n",
      "q_0: ┤ X ├┤ Ry(θ[0]) ├─┤ Rz(θ[6]) ├─░───■───░─┤ Ry(θ[12]) ├┤ Rz(θ[18]) ├\n",
      "     ├───┤├──────────┤ ├──────────┤ ░ ┌─┴─┐ ░ ├───────────┤├───────────┤\n",
      "q_1: ┤ X ├┤ Ry(θ[1]) ├─┤ Rz(θ[7]) ├─░─┤ X ├─░─┤ Ry(θ[13]) ├┤ Rz(θ[19]) ├\n",
      "     ├───┤├──────────┤ ├──────────┤ ░ └───┘ ░ ├───────────┤├───────────┤\n",
      "q_2: ┤ X ├┤ Ry(θ[2]) ├─┤ Rz(θ[8]) ├─░───■───░─┤ Ry(θ[14]) ├┤ Rz(θ[20]) ├\n",
      "     ├───┤├──────────┤ ├──────────┤ ░ ┌─┴─┐ ░ ├───────────┤├───────────┤\n",
      "q_3: ┤ X ├┤ Ry(θ[3]) ├─┤ Rz(θ[9]) ├─░─┤ X ├─░─┤ Ry(θ[15]) ├┤ Rz(θ[21]) ├\n",
      "     ├───┤├──────────┤┌┴──────────┤ ░ └───┘ ░ ├───────────┤├───────────┤\n",
      "q_4: ┤ X ├┤ Ry(θ[4]) ├┤ Rz(θ[10]) ├─░───■───░─┤ Ry(θ[16]) ├┤ Rz(θ[22]) ├\n",
      "     ├───┤├──────────┤├───────────┤ ░ ┌─┴─┐ ░ ├───────────┤├───────────┤\n",
      "q_5: ┤ X ├┤ Ry(θ[5]) ├┤ Rz(θ[11]) ├─░─┤ X ├─░─┤ Ry(θ[17]) ├┤ Rz(θ[23]) ├\n",
      "     └───┘└──────────┘└───────────┘ ░ └───┘ ░ └───────────┘└───────────┘\n"
     ]
    }
   ],
   "source": [
    "# Create an ansatz with initial condition from Hartree Fock state\n",
    "\n",
    "from qiskit_nature.circuit.library import HartreeFock\n",
    "\n",
    "init_state = HartreeFock(qubit_op_optimized.num_qubits, num_particles_optimized, converter)\n",
    "\n",
    "from qiskit.algorithms import VQE\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "ansatz= TwoLocal(qubit_op.num_qubits, ['ry','rz'],['cx'], entanglement= [[0,1],[2,3],[4,5]],\n",
    "                    reps= 1,insert_barriers=True)\n",
    "ansatz.compose(init_state, front=True, inplace=True)\n",
    "print(ansatz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "4ce35489-5074-4091-8a35-557e38c76021",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using runtime program to compute the minimum eigenvalue using the customized anstaz over 4 iterations to obtain the best eigenvalue\n",
    "\n",
    "from qiskit_nature.runtime import VQEProgram\n",
    "runtime = []\n",
    "for i in range(0,4,1):\n",
    "    intermediate_info = {\n",
    "        'nfev': [],\n",
    "        'parameters': [],\n",
    "        'energy': [],\n",
    "        'stddev': []\n",
    "    }\n",
    "    def callback(nfev, parameters, energy, stddev):\n",
    "        intermediate_info['nfev'].append(nfev)\n",
    "        intermediate_info['parameters'].append(parameters)\n",
    "        intermediate_info['energy'].append(energy)\n",
    "        intermediate_info['stddev'].append(stddev)\n",
    "    np.random.seed(10)  # seed for reproducibility\n",
    "    initial_point = np.random.random(ansatz.num_parameters)\n",
    "    measurement_error_mitigation = True\n",
    "    optimizer = {'name': 'SPSA','maxiter': 300}\n",
    "    runtime_vqe = VQEProgram(ansatz=ansatz,\n",
    "                         optimizer=optimizer,\n",
    "                         initial_point=initial_point,\n",
    "                         provider=provider,\n",
    "                         backend=backend,\n",
    "                         shots=8192,\n",
    "                         measurement_error_mitigation=measurement_error_mitigation,\n",
    "                         callback=callback)\n",
    "    runtime_result = runtime_vqe.compute_minimum_eigenvalue(qubit_op_optimized)\n",
    "    runtime.append(runtime_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "59348383-faa5-4787-acb4-4083e629f61f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-13.600194341155728, -13.499524432416639, -13.586526255117697, -13.5997952233699]\n"
     ]
    }
   ],
   "source": [
    "# Obtain the list of eigenvalues, eiegenstates,and statevectors for the different iteration\n",
    "\n",
    "qubit_list = []\n",
    "eigenstate_list = []\n",
    "eigenvalue_list = []\n",
    "for l in runtime:\n",
    "    qubit_number = list(l.eigenstate.keys())\n",
    "    qubit_list.append(qubit_number)\n",
    "    eigenstate_value = list(l.eigenstate.values())\n",
    "    eigenstate_list.append(eigenstate_value)\n",
    "    eigen_value = l.eigenvalue.real\n",
    "    eigenvalue_list.append(eigen_value)\n",
    "print(eigenvalue_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "777499fb-741f-47a3-95f2-c60a312ebb1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the difference between reference value (the Numpy diagnolization) and the eigenvalue obtained from different VQE runs\n",
    "# The best value is selected based on the minimula energy difference between VQE and exact diagnolization\n",
    "\n",
    "reference_value = float(res_exact_optimized.eigenenergies.real)\n",
    "eigenvalue_difference = []\n",
    "for j in eigenvalue_list:\n",
    "    difference = j - reference_value\n",
    "    eigenvalue_difference.append(difference*1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "8a8dfcae-53f0-461c-9b45-5da149521f6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the energy difference and eigenvalues for different VQE run. The reference value is plotted as the red line on the graph on the left\n",
    "# The best VQE run result is the value which minimizes the energy difference between VQE and exact diagnolization\n",
    "iteration = range(1,5,1)\n",
    "figure = plt.figure(figsize=(16,4))\n",
    "ax0 = figure.add_subplot(121)\n",
    "ax1 = figure.add_subplot(122)\n",
    "ax0.plot(iteration,eigenvalue_list,'o',color='black')\n",
    "ax0.axhline(y=reference_value, color='r', linestyle='-')\n",
    "ax0.set_ylabel('Minimum energy (Ha)')\n",
    "ax0.set_xlabel('Iteration')\n",
    "ax1.plot(iteration,eigenvalue_difference,'-o',color='black')\n",
    "ax1.set_ylabel('Energy difference (mHa)')\n",
    "ax1.set_xlabel('Iteration')\n",
    "figure.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "70095d84-b04f-49e0-bdb1-0c71c66c7ab3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The max probability for the statevector of  iteration 1 is 0.4051969391326999\n",
      "The second max probability for the statevector of  iteration 1 is 0.3761375867983654\n",
      "The probability difference for the most probable and second most probable statevector of  iteration 1 is 0.029059352334334487\n",
      "The max probability for the statevector of  iteration 2 is 0.33602833242796554\n",
      "The second max probability for the statevector of  iteration 2 is 0.27621358757963654\n",
      "The probability difference for the most probable and second most probable statevector of  iteration 2 is 0.05981474484832899\n",
      "The max probability for the statevector of  iteration 3 is 0.5454221639194772\n",
      "The second max probability for the statevector of  iteration 3 is 0.4294743746715886\n",
      "The probability difference for the most probable and second most probable statevector of  iteration 3 is 0.11594778924788857\n",
      "The max probability for the statevector of  iteration 4 is 0.5550724875807165\n",
      "The second max probability for the statevector of  iteration 4 is 0.4308931935304892\n",
      "The probability difference for the most probable and second most probable statevector of  iteration 4 is 0.12417929405022726\n"
     ]
    }
   ],
   "source": [
    "for value_index in range(0,4,1):\n",
    "    Max_value = max(eigenstate_list[value_index])\n",
    "    Second_max_value = max(n for n in eigenstate_list[value_index] if n!=Max_value)\n",
    "    difference_probability = Max_value - Second_max_value\n",
    "    print('The max probability for the statevector of  iteration {} is {}'.format(value_index+1, Max_value))\n",
    "    print('The second max probability for the statevector of  iteration {} is {}'.format(value_index+1, Second_max_value))\n",
    "    print('The probability difference for the most probable and second most probable statevector of  iteration {} is {}'.format(value_index+1, difference_probability))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "914b8076-acd2-424c-bb86-23e55f5e03cd",
   "metadata": {},
   "source": [
    "Finally we check if the optimal initial starting points of our variational circuit is still optimal even when the molecule structure changes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "0c01965f-de96-4bef-a8ca-bcd2722b9f21",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rerun the potential energy surface but only varies the angle while keeping the bond-length the same\n",
    "\n",
    "angle_list = [k * 10 for k in range(1,19,1)]\n",
    "exact_energies_angle = []\n",
    "for degree in angle_list:\n",
    "    driver_angle = PySCFDriver(H2O.format(optimized_distance,optimized_distance,degree),unit=UnitsType.ANGSTROM, basis='sto3g')\n",
    "    problem_angle = ElectronicStructureProblem(driver_angle, q_molecule_transformers=[FreezeCoreTransformer(remove_orbitals=[4,5,6])])\n",
    "    second_q_ops_angle = problem_angle.second_q_ops()\n",
    "    main_op_angle = second_q_ops_angle[0]\n",
    "    num_particles_angle = (problem_angle.molecule_data_transformed.num_alpha,problem_angle.molecule_data_transformed.num_beta)\n",
    "    qubit_op_angle = converter.convert(main_op_angle, num_particles=num_particles_angle)\n",
    "    calc_exact_angle = GroundStateEigensolver(converter,numpy_solver)\n",
    "    res_exact_angle = calc_exact_angle.solve(problem_angle)\n",
    "    exact_energies_angle.append(res_exact_angle)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "5da9be22-0504-4ece-8069-9c1ebc501b69",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using the optimal point of iteration 1 in runtime VQE as the starting point to calculate the potential energy surface using VQE\n",
    "\n",
    "runtime_vqe_angle = []\n",
    "for vqe_angle in angle_list:\n",
    "    intermediate_info_angle = {\n",
    "        'nfev': [],\n",
    "        'parameters': [],\n",
    "        'energy': [],\n",
    "        'stddev': []\n",
    "    }\n",
    "    def callback_angle(nfev, parameters, energy, stddev):\n",
    "        intermediate_info_angle['nfev'].append(nfev)\n",
    "        intermediate_info_angle['parameters'].append(parameters)\n",
    "        intermediate_info_angle['energy'].append(energy)\n",
    "        intermediate_info_angle['stddev'].append(stddev)\n",
    "    optimizer = {'name': 'SPSA','maxiter': 500}\n",
    "    driver_vqe_angle = PySCFDriver(H2O.format(optimized_distance,optimized_distance,vqe_angle),unit=UnitsType.ANGSTROM, basis='sto3g')\n",
    "    problem_vqe_angle = ElectronicStructureProblem(driver_vqe_angle, q_molecule_transformers=[FreezeCoreTransformer(remove_orbitals=[4,5,6])])\n",
    "    second_q_ops_vqe_angle = problem_vqe_angle.second_q_ops()\n",
    "    main_op_vqe_angle = second_q_ops_vqe_angle[0]\n",
    "    qubit_op_vqe_angle = converter.convert(main_op_vqe_angle, num_particles=num_particles_optimized)\n",
    "    runtime_angle_vqe = VQEProgram(ansatz=ansatz,\n",
    "                         optimizer=optimizer,\n",
    "                         initial_point=runtime[0].optimal_point,\n",
    "                         provider=provider,\n",
    "                         backend=backend,\n",
    "                         shots=8192,\n",
    "                         measurement_error_mitigation=True,\n",
    "                         callback=callback_angle)\n",
    "    runtime_result_angle = runtime_angle_vqe.compute_minimum_eigenvalue(qubit_op_vqe_angle)\n",
    "    runtime_vqe_angle.append(runtime_result_angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "5090f7b0-0dc2-47c5-8a98-160596946031",
   "metadata": {},
   "outputs": [],
   "source": [
    "runtime_eigenenergies_angle = []\n",
    "exact_total_eigenenergies_angle = []\n",
    "frozen_orbital_energies = []\n",
    "nuclear_energies = []\n",
    "for i in range(len(runtime_vqe_angle)):\n",
    "    runtime_eigenenergies_angle.append(runtime_vqe_angle[i].eigenvalue.real)\n",
    "for j in range(len(exact_energies_angle)):\n",
    "    exact_total_eigenenergies_angle.append(exact_energies_angle[j].total_energies)\n",
    "    frozen_orbital_energies.append(exact_energies_angle[j].electronic_energies-exact_energies_angle[j].computed_energies)\n",
    "    nuclear_energies.append(exact_energies_angle[j].nuclear_repulsion_energy)\n",
    "runtime_total_energies_angle = [k+l+m for k, l, m in zip(runtime_eigenenergies_angle,frozen_orbital_energies,nuclear_energies)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "be309312-3883-46aa-aa03-8ae230049241",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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    "# Plotting the minimal total energies from VQE and Numpy run for water at different angles\n",
    "# The VQE results match the classical numput result \n",
    "\n",
    "plt.xlabel('Angle')\n",
    "plt.ylabel('Energy (Ha)')\n",
    "plt.plot(angle_list,exact_eigenenergies_angle,'-o', color='black')\n",
    "plt.plot(angle_list,runtime_total_energies_angle, '-o', color='blue')\n",
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   ]
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