test_vqd.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6524bb19-3fb3-4862-92d2-6c29839027af",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b4f06b66-7f94-42f5-9ca4-5d439b7ebe42",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane as qml"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5a54aecd-24aa-4bce-9d40-25a2e55347da",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane.numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import vqd\n",
    "import json"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e40fd0e5-d334-4c20-bbd4-c3b8b8db2ebb",
   "metadata": {},
   "outputs": [],
   "source": [
    "large_width = 400\n",
    "np.set_printoptions(linewidth=large_width)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d8e96084-dd66-4cea-8faa-2ba65da9f5c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "total_time = 2.0\n",
    "#total_time = 0.5\n",
    "dt = 0.05\n",
    "max_iterations = 5000\n",
    "cost_threshold = 0.00002\n",
    "n_qubits = 3\n",
    "interface = 'autograd'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "29bee666-7ecd-418b-8693-e63af8ed52c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "vqdrunner = vqd.VQD(interface, total_time, dt, max_iterations, cost_threshold, n_qubits, shots=80, optimization_step_size=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "5ed701da-9747-44fd-b439-9f0e1556bc98",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n"
     ]
    }
   ],
   "source": [
    "results = vqdrunner.run_optimization()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "03347ed2-3882-4853-91ff-b4eb84b01d05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['final_costs_v_time', 'full_costs_v_time', 'final_params_v_time', 'full_params_v_time', 'failed_to_converge_times', 'number_of_iterations_to_converge', 'observables', 'variances', 'time'])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3f8ca436-46d7-44ed-8f1f-926d6c322784",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[57,\n",
       " 58,\n",
       " 58,\n",
       " 59,\n",
       " 62,\n",
       " 64,\n",
       " 66,\n",
       " 67,\n",
       " 67,\n",
       " 67,\n",
       " 69,\n",
       " 79,\n",
       " 193,\n",
       " 251,\n",
       " 235,\n",
       " 202,\n",
       " 168,\n",
       " 138,\n",
       " 113,\n",
       " 93,\n",
       " 81,\n",
       " 76,\n",
       " 74,\n",
       " 74,\n",
       " 76,\n",
       " 78,\n",
       " 80,\n",
       " 82,\n",
       " 83,\n",
       " 83,\n",
       " 82,\n",
       " 83,\n",
       " 88,\n",
       " 99,\n",
       " 120,\n",
       " 150,\n",
       " 186,\n",
       " 221,\n",
       " 239,\n",
       " 232,\n",
       " 213]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results['number_of_iterations_to_converge']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9f8404d9-86aa-4c4d-8bd2-d92483571818",
   "metadata": {},
   "outputs": [],
   "source": [
    "sig_x = np.tensor(results['observables'])[:,:3]\n",
    "sig_z = np.tensor(results['observables'])[:,3:]\n",
    "std_sig_x = np.sqrt(np.tensor(results['variances'])[:,:3]/vqdrunner.shots)\n",
    "std_sig_z = np.sqrt(np.tensor(results['variances'])[:,3:]/vqdrunner.shots)\n",
    "\n",
    "sum_sig_x = np.sum(sig_x, axis=1)\n",
    "sum_sig_z = np.sum(sig_z, axis=1)\n",
    "sum_sig_x_std = np.sqrt(np.sum(std_sig_x**2, axis=1))\n",
    "sum_sig_z_std = np.sqrt(np.sum(std_sig_z**2, axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "c7c46bf4-4dd0-4145-9ad0-dce10bc881d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Shots = 80')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(results['time'],sum_sig_x, sum_sig_x_std, fmt = '.', label='$\\Sigma_i <\\sigma_{x,i}>$')\n",
    "plt.errorbar(results['time'],sum_sig_z/3, sum_sig_z_std/3, fmt = '.', label='$\\Sigma_i <\\sigma_{z,i}>/3$')\n",
    "plt.legend()\n",
    "plt.title(f'Shots = {vqdrunner.shots}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bf9e95df-8e05-4847-8733-88f8a2d51f15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Shots = 80')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(results['time'],sum_sig_x/3, sum_sig_x_std/3, fmt = '.', label='$\\Sigma_i <\\sigma_{x,i}>/3$')\n",
    "plt.errorbar(results['time'],sum_sig_z/3, sum_sig_z_std/3, fmt = '.', label='$\\Sigma_i <\\sigma_{z,i}>/3$')\n",
    "plt.legend()\n",
    "plt.title(f'Shots = {vqdrunner.shots}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8c401253-f307-464a-9d31-f2262f222255",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Shots = 80')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(results['time'],sig_x[:,0], std_sig_x[:,0], fmt='.', label='$<\\sigma_{x0}$>')\n",
    "plt.errorbar(results['time'],sig_x[:,1], std_sig_x[:,1], fmt='.', label='$<\\sigma_{x1}$>')\n",
    "plt.errorbar(results['time'],sig_x[:,2], std_sig_x[:,2], fmt='.', label='$<\\sigma_{x2}$>')\n",
    "plt.legend()\n",
    "plt.title(f'Shots = {vqdrunner.shots}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cbbeb261-6259-44dd-a138-759bd1de7bcd",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting run for shots: 80\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n",
      "starting run for shots: 800\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n",
      "starting run for shots: 8000\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n",
      "starting run for shots: 80000\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n"
     ]
    }
   ],
   "source": [
    "shots_list = [80, 800, 8000, 80000]\n",
    "results_over_shots_with_observables = []\n",
    "for shots in shots_list:\n",
    "    print(f'starting run for shots: {shots}')\n",
    "    vqdrunner = vqd.VQD(interface, total_time, dt, max_iterations, cost_threshold, n_qubits, shots=shots, optimization_step_size=0.05)\n",
    "    results_over_shots_with_observables.append(vqdrunner.run_optimization())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b0022f93-d4fd-488b-82d4-0f0897b0d56d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_total_mag(results, shots):\n",
    "    sig_x = np.tensor(results['observables'])[:,:3]\n",
    "    sig_z = np.tensor(results['observables'])[:,3:]\n",
    "    std_sig_x = np.sqrt(np.tensor(results['variances'])[:,:3]/shots)\n",
    "    std_sig_z = np.sqrt(np.tensor(results['variances'])[:,3:]/shots)\n",
    "\n",
    "    sum_sig_x = np.sum(sig_x, axis=1)\n",
    "    sum_sig_z = np.sum(sig_z, axis=1)\n",
    "    sum_sig_x_std = np.sqrt(np.sum(std_sig_x**2, axis=1))\n",
    "    sum_sig_z_std = np.sqrt(np.sum(std_sig_z**2, axis=1))\n",
    "    \n",
    "    return sum_sig_x, sum_sig_z, sum_sig_x_std, sum_sig_z_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1616b567-0998-4a7a-97a4-2009b813e4eb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4c9484b5-8c01-4ab1-9f27-28b29b60dc91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f9fceafc700>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,4))\n",
    "for s, results in zip(shots_list,results_over_shots_with_observables):\n",
    "    sum_sig_x, sum_sig_z, sum_sig_x_std, sum_sig_z_std = get_total_mag(results, s)\n",
    "    ax.errorbar(results['time'],sum_sig_x/3, sum_sig_x_std/3, fmt = '.', label=f'{s} shots')\n",
    "    ax.set_ylabel('$\\Sigma_i <\\sigma_{x,i}>/3$')\n",
    "    \n",
    "exact = json.load(open('exact_solutions.dat'))\n",
    "ax.plot(exact['times'][:40],exact['Sx'][:40],label =\"Exact\",linestyle='dashed',linewidth=1.2,color='black')\n",
    "ax.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "f2fcd284-0464-4527-b530-3903482a21b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f9fce9aea70>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,4))\n",
    "for s, results in zip(shots_list,results_over_shots_with_observables):\n",
    "    sum_sig_x, sum_sig_z, sum_sig_x_std, sum_sig_z_std = get_total_mag(results, s)\n",
    "    ax.errorbar(results['time'],sum_sig_z/3, sum_sig_z_std/3, fmt = '.', label=f'{s} shots')\n",
    "    ax.set_ylabel('$\\Sigma_i <\\sigma_{z,i}>/3$')\n",
    "\n",
    "exact = json.load(open('exact_solutions.dat'))\n",
    "ax.plot(exact['times'][:40],exact['Sz'][:40],label =\"Exact\",linestyle='dashed',linewidth=1.2,color='black')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "925e882e-1040-400c-a2c6-9aeacc6d1920",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting run for shots: 80-0\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n",
      "starting run for shots: 80-1\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
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      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n",
      "starting run for shots: 80000-7\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n",
      "starting run for shots: 80000-8\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n",
      "starting run for shots: 80000-9\n",
      "0.0\n",
      "0.05\n",
      "0.1\n",
      "0.15000000000000002\n",
      "0.2\n",
      "0.25\n",
      "0.30000000000000004\n",
      "0.35000000000000003\n",
      "0.4\n",
      "0.45\n",
      "0.5\n",
      "0.55\n",
      "0.6000000000000001\n",
      "0.65\n",
      "0.7000000000000001\n",
      "0.75\n",
      "0.8\n",
      "0.8500000000000001\n",
      "0.9\n",
      "0.9500000000000001\n",
      "1.0\n",
      "1.05\n",
      "1.1\n",
      "1.1500000000000001\n",
      "1.2000000000000002\n",
      "1.25\n",
      "1.3\n",
      "1.35\n",
      "1.4000000000000001\n",
      "1.4500000000000002\n",
      "1.5\n",
      "1.55\n",
      "1.6\n",
      "1.6500000000000001\n",
      "1.7000000000000002\n",
      "1.75\n",
      "1.8\n",
      "1.85\n",
      "1.9000000000000001\n",
      "1.9500000000000002\n",
      "2.0\n"
     ]
    }
   ],
   "source": [
    "shots_list = [80, 800, 8000, 80000]\n",
    "results_over_shots = []\n",
    "for shots in shots_list:\n",
    "    results_stats = []\n",
    "    for i in range(10):\n",
    "        print(f'starting run for shots: {shots}-{i}')\n",
    "        vqdrunner = vqd.VQD(interface, total_time, dt, max_iterations, cost_threshold, n_qubits, shots=shots, optimization_step_size=0.05)\n",
    "        results_stats.append(vqdrunner.run_optimization(compute_observables=False))\n",
    "        \n",
    "    results_over_shots.append(results_stats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "id": "9a206d30-b8d7-43bb-84e0-b07fce626dec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(results_over_shots[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "54e62973-275e-4a39-8c75-ade96a626c5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "state_results = {}\n",
    "for results, shots in zip(results_over_shots, shots_list):\n",
    "    state_results[shots] = results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "03b8819a-f089-4d5c-bf8a-cd103682100d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys([80, 800, 8000, 80000])"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state_results.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "31865808-c630-42d0-a954-48ab63542b88",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = qml.data.Dataset(state_results = state_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "a0ddc49d-3c9e-4a3b-a417-4ba66e54d3ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "d.write('state_results.dat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "8de9c53c-c989-40d0-9d7a-563a9d5d176b",
   "metadata": {},
   "outputs": [],
   "source": [
    "observable_results = {}\n",
    "for results, shots in zip(results_over_shots_with_observables, shots_list):\n",
    "    observable_results[shots] = results\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "b4b6f615-8dd7-4b76-9323-3b76ec330b54",
   "metadata": {},
   "outputs": [],
   "source": [
    "d_observables = qml.data.Dataset(observable_results = observable_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "35496123-b26a-4337-b295-1164f259e113",
   "metadata": {},
   "outputs": [],
   "source": [
    "d_observables.write('observable_results_v2.dat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "b44d9492-9c36-413f-b640-96a10e07c60a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(state_results[80])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "id": "211a6e17-14b8-43ba-bc2e-9e58b97ecdf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "r = state_results[80][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "id": "48a88723-8107-4f0c-935a-2cbe88be710b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['final_costs_v_time', 'full_costs_v_time', 'final_params_v_time', 'full_params_v_time', 'failed_to_converge_times', 'number_of_iterations_to_converge', 'observables', 'variances', 'time'])"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "id": "55ce9c6c-e93f-4faa-ae17-e4dfea568d31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.169946285647601e-05,\n",
       " 9.169042804524352e-05,\n",
       " 9.178110701335562e-05,\n",
       " 9.216247878185424e-05,\n",
       " 9.288909701010706e-05,\n",
       " 9.378442521423835e-05,\n",
       " 9.454314951373721e-05,\n",
       " 9.492039157887877e-05,\n",
       " 9.490091882924379e-05,\n",
       " 9.480448011622844e-05,\n",
       " 9.531562065712151e-05,\n",
       " 9.741391996942461e-05,\n",
       " 9.383505758542299e-05,\n",
       " 9.451705902285834e-05,\n",
       " 9.904022820450553e-05,\n",
       " 9.99167597194317e-05,\n",
       " 9.662366417539925e-05,\n",
       " 9.925327105064774e-05,\n",
       " 9.677407755770417e-05,\n",
       " 9.848498439946063e-05,\n",
       " 9.87825893883354e-05,\n",
       " 9.969458703884548e-05,\n",
       " 9.64499087862114e-05,\n",
       " 9.521016417601835e-05,\n",
       " 9.595111835658532e-05,\n",
       " 9.806963775160771e-05,\n",
       " 9.448038282033888e-05,\n",
       " 9.626915124349988e-05,\n",
       " 9.642420165334453e-05,\n",
       " 9.436586661615287e-05,\n",
       " 9.606171543952158e-05,\n",
       " 9.702885695850316e-05,\n",
       " 9.90790630381877e-05,\n",
       " 9.665296808281099e-05,\n",
       " 9.70279522591877e-05,\n",
       " 9.992868444130831e-05,\n",
       " 9.836041192778922e-05,\n",
       " 9.46024477513907e-05,\n",
       " 9.74695193528552e-05,\n",
       " 9.960440202094745e-05,\n",
       " 9.896783481633253e-05]"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r['final_costs_v_time']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "id": "bd75f685-4f1f-4d53-b185-0edd71a2a3ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.169946285647601e-05,\n",
       " 9.169042804524352e-05,\n",
       " 9.178110701335562e-05,\n",
       " 9.216247878185424e-05,\n",
       " 9.288909701010706e-05,\n",
       " 9.378442521423835e-05,\n",
       " 9.454314951373721e-05,\n",
       " 9.492039157887877e-05,\n",
       " 9.490091882924379e-05,\n",
       " 9.480448011622844e-05,\n",
       " 9.531562065712151e-05,\n",
       " 9.741391996942461e-05,\n",
       " 9.383505758542299e-05,\n",
       " 9.451705902285834e-05,\n",
       " 9.904022820450553e-05,\n",
       " 9.99167597194317e-05,\n",
       " 9.662366417539925e-05,\n",
       " 9.925327105064774e-05,\n",
       " 9.677407755770417e-05,\n",
       " 9.848498439946063e-05,\n",
       " 9.87825893883354e-05,\n",
       " 9.969458703884548e-05,\n",
       " 9.64499087862114e-05,\n",
       " 9.521016417601835e-05,\n",
       " 9.595111835658532e-05,\n",
       " 9.806963775160771e-05,\n",
       " 9.448038282033888e-05,\n",
       " 9.626915124349988e-05,\n",
       " 9.642420165334453e-05,\n",
       " 9.436586661615287e-05,\n",
       " 9.606171543952158e-05,\n",
       " 9.702885695850316e-05,\n",
       " 9.90790630381877e-05,\n",
       " 9.665296808281099e-05,\n",
       " 9.70279522591877e-05,\n",
       " 9.992868444130831e-05,\n",
       " 9.836041192778922e-05,\n",
       " 9.46024477513907e-05,\n",
       " 9.74695193528552e-05,\n",
       " 9.960440202094745e-05,\n",
       " 9.896783481633253e-05]"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r['final_costs_v_time']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "1ac9d687-1aca-41c7-8ec1-fa8005b5b286",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80\n",
      "0.03944832045221114\n",
      "0.00015561699865003392\n",
      "800\n",
      "0.03944832045221114\n",
      "0.00015561699865003392\n",
      "8000\n",
      "0.03944832045221114\n",
      "0.00015561699865003392\n",
      "80000\n",
      "0.03944832045221114\n",
      "0.00015561699865003392\n"
     ]
    }
   ],
   "source": [
    "total_final_costs = []\n",
    "\n",
    "for shots, results in state_results.items():\n",
    "    sum_costs = 0\n",
    "    sum_costs_sq = 0\n",
    "    for i in range(10):\n",
    "        sum_costs += np.sum(results[i]['final_costs_v_time'])\n",
    "        sum_costs_sq += np.sum(results[i]['final_costs_v_time'])**2\n",
    "        \n",
    "    print(shots)\n",
    "    print(sum_costs)\n",
    "    print(sum_costs_sq)\n",
    "    mean_costs = sum_costs/10\n",
    "    var_costs = sum_costs_sq/10 - mean_costs**2\n",
    "    std_mean_costs = np.sqrt(var_costs)\n",
    "    total_final_costs.append([shots, mean_costs, std_mean_costs])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cb71150-91e3-47e2-b1d6-fbba88630e3d",
   "metadata": {},
   "source": [
    "Doh! The state vector simulator does not depend on number of shots because it does not simulate shots. It returns the same state estimate every time. Therefore, we will not see any change in the sum of final costs or variance of that value!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "id": "c5dab28c-4e64-4a0d-92ab-3859091a3737",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['final_costs_v_time', 'full_costs_v_time', 'final_params_v_time', 'full_params_v_time', 'failed_to_converge_times', 'number_of_iterations_to_converge', 'observables', 'variances', 'time'])\n",
      "dict_keys(['final_costs_v_time', 'full_costs_v_time', 'final_params_v_time', 'full_params_v_time', 'failed_to_converge_times', 'number_of_iterations_to_converge', 'observables', 'variances', 'time'])\n",
      "dict_keys(['final_costs_v_time', 'full_costs_v_time', 'final_params_v_time', 'full_params_v_time', 'failed_to_converge_times', 'number_of_iterations_to_converge', 'observables', 'variances', 'time'])\n",
      "dict_keys(['final_costs_v_time', 'full_costs_v_time', 'final_params_v_time', 'full_params_v_time', 'failed_to_converge_times', 'number_of_iterations_to_converge', 'observables', 'variances', 'time'])\n"
     ]
    }
   ],
   "source": [
    "for shots, results in d_observables.observable_results.items():\n",
    "    print(results.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "54c7e862-c21a-49a1-a46d-433f70d97882",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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