test_circuit.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "29a3fb1b-afd7-45b7-ae7a-9506012b7f52",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "88f68364-f1ed-4bcd-a213-5badb4168efd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane as qml\n",
    "import pennylane.numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "12f61e32-a630-4874-b7d2-710acea76b9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ecd30b72-95f8-4d30-83ed-d5dc5cd7f4eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "interface = 'autograd'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "db78c73e-49bf-4420-9a9e-03854cdb7f45",
   "metadata": {},
   "outputs": [],
   "source": [
    "if interface == 'autograd':\n",
    "    import pennylane.numpy as np\n",
    "    dev = qml.device(\"default.qubit\", wires=range(3))\n",
    "    def reset_params():\n",
    "        return 0.05 * np.ones(18)\n",
    "\n",
    "elif interface == 'jax':\n",
    "    import jax\n",
    "    import jax.numpy as jnp\n",
    "    # next line raises TypeError with default.qubit.jax\n",
    "    # dev = qml.device(\"default.qubit.jax\", wires=range(3))\n",
    "    dev = qml.device(\"default.qubit\", wires=range(3))\n",
    "    def reset_params():\n",
    "        return jnp.array([0.05] * 18)\n",
    "elif interface == 'torch':\n",
    "    import torch\n",
    "    dev = qml.device(\"default.qubit\", wires=range(3))\n",
    "    def reset_params():\n",
    "        return torch.tensor([0.05] * 18, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2c078cf3-7549-47de-95ae-f955d9440b76",
   "metadata": {},
   "outputs": [],
   "source": [
    "@qml.qnode(dev, interface=interface)\n",
    "def three_spins_forward_state(params, delta_time, n=10):\n",
    "    three_spins_circuit(params)\n",
    "    qml.ApproxTimeEvolution(hamiltonian(), delta_time, n)\n",
    "    return qml.state()\n",
    "\n",
    "@qml.qnode(dev, interface=interface)\n",
    "def three_spins_current_state(params):\n",
    "    three_spins_circuit(params)\n",
    "    return qml.state()\n",
    "\n",
    "@qml.qnode(dev, interface=interface)\n",
    "def three_spins_obvservables(params):\n",
    "    three_spins_circuit(params)\n",
    "    return [qml.expval(qml.PauliX(i)) for i in range(3)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "24bbc7fc-3cb5-4dd6-a6ed-74a7479bef2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9724868837244939"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test this works\n",
    "params = reset_params()\n",
    "dt = 0.1\n",
    "original_state = three_spins_current_state(params)\n",
    "forward_state = three_spins_forward_state(params + 0.01, dt)\n",
    "\n",
    "qml.math.fidelity(original_state, forward_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "ec9a90a2-42e5-45e4-b9fb-62113ec70849",
   "metadata": {},
   "outputs": [],
   "source": [
    "prev_params = params\n",
    "\n",
    "def cost_function(params):\n",
    "    \n",
    "    original_state = three_spins_current_state(prev_params)\n",
    "    forward_state = three_spins_forward_state(params, dt)\n",
    "\n",
    "    fidelity = qml.math.fidelity(original_state, forward_state)\n",
    "    return 1 - fidelity\n",
    "\n",
    "\n",
    "recorded_costs = [cost_function(params)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "88db5fe1-3761-4a7b-9015-eb62747117ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7087283866669527"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prev_params = params\n",
    "cost_function(np.random.random(18))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "39f3c3ae-a6ad-4974-939c-c1d12e59cbf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "total_time = 2.0\n",
    "#total_time = 0.5\n",
    "dt = 0.05\n",
    "max_iterations = 500\n",
    "cost_threshold = 0.0001\n",
    "n_qubits = 3\n",
    "\n",
    "prev_params = reset_params()\n",
    "params = reset_params()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "b8b7d5dd-d91f-4057-b8ac-c9ec374257df",
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = qml.GradientDescentOptimizer(stepsize=0.1)\n",
    "\n",
    "final_costs_v_time = []\n",
    "full_costs_v_time = []\n",
    "final_params_v_time = []\n",
    "full_params_v_time = []\n",
    "failed_to_converge_times = {}\n",
    "number_of_iterations_to_converge = []\n",
    "observables = []\n",
    "time = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "a58da732-66bd-40a3-8ba9-e85eeef03f13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "21 iterations to converge\n",
      "0.05\n",
      "21 iterations to converge\n",
      "0.1\n",
      "21 iterations to converge\n",
      "0.15000000000000002\n",
      "21 iterations to converge\n",
      "0.2\n",
      "21 iterations to converge\n",
      "0.25\n",
      "21 iterations to converge\n",
      "0.30000000000000004\n",
      "21 iterations to converge\n",
      "0.35000000000000003\n",
      "21 iterations to converge\n",
      "0.4\n",
      "21 iterations to converge\n",
      "0.45\n",
      "21 iterations to converge\n",
      "0.5\n",
      "21 iterations to converge\n",
      "0.55\n",
      "20 iterations to converge\n",
      "0.6000000000000001\n",
      "20 iterations to converge\n",
      "0.65\n",
      "20 iterations to converge\n",
      "0.7000000000000001\n",
      "20 iterations to converge\n",
      "0.75\n",
      "20 iterations to converge\n",
      "0.8\n",
      "21 iterations to converge\n",
      "0.8500000000000001\n",
      "21 iterations to converge\n",
      "0.9\n",
      "21 iterations to converge\n",
      "0.9500000000000001\n",
      "21 iterations to converge\n",
      "1.0\n",
      "21 iterations to converge\n",
      "1.05\n",
      "21 iterations to converge\n",
      "1.1\n",
      "22 iterations to converge\n",
      "1.1500000000000001\n",
      "22 iterations to converge\n",
      "1.2000000000000002\n",
      "22 iterations to converge\n",
      "1.25\n",
      "23 iterations to converge\n",
      "1.3\n",
      "24 iterations to converge\n",
      "1.35\n",
      "25 iterations to converge\n",
      "1.4000000000000001\n",
      "27 iterations to converge\n",
      "1.4500000000000002\n",
      "29 iterations to converge\n",
      "1.5\n",
      "31 iterations to converge\n",
      "1.55\n",
      "34 iterations to converge\n",
      "1.6\n",
      "37 iterations to converge\n",
      "1.6500000000000001\n",
      "38 iterations to converge\n",
      "1.7000000000000002\n",
      "39 iterations to converge\n",
      "1.75\n",
      "40 iterations to converge\n",
      "1.8\n",
      "41 iterations to converge\n",
      "1.85\n",
      "43 iterations to converge\n",
      "1.9000000000000001\n",
      "47 iterations to converge\n",
      "1.9500000000000002\n",
      "51 iterations to converge\n",
      "2.0\n",
      "53 iterations to converge\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for current_time in np.arange(0, total_time+dt, dt):\n",
    "    print(current_time)\n",
    "    \n",
    "    prev_params = params\n",
    "    recorded_params = [params]\n",
    "\n",
    "    recorded_costs = [cost_function(params)]\n",
    "\n",
    "    for n in range(max_iterations):\n",
    "        params, prev_cost = opt.step_and_cost(cost_function, params)\n",
    "\n",
    "        recorded_costs.append(cost_function(params))\n",
    "        recorded_params.append(params)\n",
    "\n",
    "        if recorded_costs[-1] <= cost_threshold:\n",
    "            break\n",
    "\n",
    "    print(f'{n} iterations to converge')\n",
    "    if recorded_costs[-1] > cost_threshold:\n",
    "        failed_to_converge_times[current_time] = recorded_costs[-1]\n",
    "        \n",
    "    time.append(current_time)\n",
    "    observables.append(three_spins_obvservables(params))\n",
    "    final_costs_v_time.append(recorded_costs[-1])\n",
    "    full_costs_v_time.append(recorded_costs)\n",
    "    final_params_v_time.append(recorded_params[-1])\n",
    "    full_params_v_time.append(recorded_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "240c7985-a7e0-4640-9a8c-5dd77beb7b7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8.534379615643406e-05,\n",
       " 8.667242128646002e-05,\n",
       " 8.876092307064098e-05,\n",
       " 9.091856832754708e-05,\n",
       " 9.261565155893603e-05,\n",
       " 9.352678952878613e-05,\n",
       " 9.348102833117711e-05,\n",
       " 9.241832097139913e-05,\n",
       " 9.039041656722091e-05,\n",
       " 8.75980686279032e-05,\n",
       " 8.443131202739984e-05,\n",
       " 9.894863084991545e-05,\n",
       " 9.676568034766575e-05,\n",
       " 9.597131249272639e-05,\n",
       " 9.67639465283554e-05,\n",
       " 9.888165880111988e-05,\n",
       " 8.395080583423198e-05,\n",
       " 8.660930468407102e-05,\n",
       " 8.896338784925018e-05,\n",
       " 9.10748030287234e-05,\n",
       " 9.330826443443296e-05,\n",
       " 9.618292579050003e-05,\n",
       " 8.359517447065201e-05,\n",
       " 8.89659204499349e-05,\n",
       " 9.658740016971201e-05,\n",
       " 9.146477016375165e-05,\n",
       " 9.066145654379465e-05,\n",
       " 9.395956918012427e-05,\n",
       " 9.075883866360712e-05,\n",
       " 9.269475771700453e-05,\n",
       " 9.754434868647355e-05,\n",
       " 9.647609828444814e-05,\n",
       " 9.510174832694229e-05,\n",
       " 9.976661648258833e-05,\n",
       " 9.963122868028584e-05,\n",
       " 9.778948621630423e-05,\n",
       " 9.778726478948396e-05,\n",
       " 9.888968625482164e-05,\n",
       " 9.859160616576546e-05,\n",
       " 9.821308443869192e-05,\n",
       " 9.849099214298551e-05]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_costs_v_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "50e757e2-c862-470e-bc82-9d55b0053894",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{}"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "failed_to_converge_times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "9f6454f8-3128-402e-ae04-bf4e3991ce81",
   "metadata": {},
   "outputs": [
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       "         0.04803393, 0.0456511 , 0.04803393], requires_grad=True),\n",
       " tensor([0.14055842, 0.1394524 , 0.14055842, 0.04514624, 0.04514624,\n",
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       " tensor([0.23116305, 0.22914746, 0.23116305, 0.03705965, 0.03705965,\n",
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       " tensor([ 0.32180003,  0.31891801,  0.32180003,  0.0271963 ,  0.0271963 ,\n",
       "          0.02127263, -0.01457752,  0.02127263,  0.01409703,  0.01409703,\n",
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       "          0.03877394,  0.01612105,  0.03877394], requires_grad=True),\n",
       " tensor([ 0.41242088,  0.40848127,  0.41242088,  0.01647426,  0.01647426,\n",
       "          0.0168641 , -0.02876833,  0.0168641 ,  0.00368518,  0.00368518,\n",
       "          0.41470279,  0.42007749,  0.41470279, -0.01670865, -0.01670865,\n",
       "          0.03752533,  0.01031955,  0.03752533], requires_grad=True),\n",
       " tensor([ 0.45770564,  0.45310477,  0.45770564,  0.01087832,  0.01087832,\n",
       "          0.01533364, -0.03536458,  0.01533364, -0.00122534, -0.00122534,\n",
       "          0.46001782,  0.46506856,  0.46001782, -0.02622285, -0.02622285,\n",
       "          0.03622975,  0.00402046,  0.03622975], requires_grad=True),\n",
       " tensor([ 0.50296208,  0.49759534,  0.50296208,  0.0050768 ,  0.0050768 ,\n",
       "          0.01411348, -0.04201415,  0.01411348, -0.00604986, -0.00604986,\n",
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       "          0.03484485, -0.00282299,  0.03484485], requires_grad=True),\n",
       " tensor([ 0.54818187,  0.5419483 ,  0.54818187, -0.00102364, -0.00102364,\n",
       "          0.01309165, -0.04902018,  0.01309165, -0.0109106 , -0.0109106 ,\n",
       "          0.5504444 ,  0.55410559,  0.5504444 , -0.04631419, -0.04631419,\n",
       "          0.03334559, -0.01019614,  0.03334559], requires_grad=True),\n",
       " tensor([ 0.59280798,  0.58563551,  0.59280798, -0.00753174, -0.00753174,\n",
       "          0.012092  , -0.05667077,  0.012092  , -0.01595177, -0.01595177,\n",
       "          0.59500292,  0.59761096,  0.59500292, -0.05672344, -0.05672344,\n",
       "          0.03171678, -0.01795094,  0.03171678], requires_grad=True),\n",
       " tensor([ 0.63738504,  0.62923585,  0.63738504, -0.01459922, -0.01459922,\n",
       "          0.01107446, -0.06517621,  0.01107446, -0.02131196, -0.02131196,\n",
       "          0.63949543,  0.64081989,  0.63949543, -0.06736667, -0.06736667,\n",
       "          0.03000451, -0.02593594,  0.03000451], requires_grad=True),\n",
       " tensor([ 0.6819098 ,  0.67280849,  0.6819098 , -0.02235433, -0.02235433,\n",
       "          0.0099633 , -0.07469432,  0.0099633 , -0.02712016, -0.02712016,\n",
       "          0.68393214,  0.68376785,  0.68393214, -0.07810518, -0.07810518,\n",
       "          0.02826853, -0.03387078,  0.02826853], requires_grad=True),\n",
       " tensor([ 0.72638278,  0.71643734,  0.72638278, -0.03088541, -0.03088541,\n",
       "          0.00871377, -0.08527694,  0.00871377, -0.03346303, -0.03346303,\n",
       "          0.72833078,  0.72651197,  0.72833078, -0.08876775, -0.08876775,\n",
       "          0.02659133, -0.04140216,  0.02659133], requires_grad=True),\n",
       " tensor([ 0.77080924,  0.76022591,  0.77080924, -0.04021417, -0.04021417,\n",
       "          0.00731618, -0.09685314,  0.00731618, -0.04036143, -0.04036143,\n",
       "          0.77271541,  0.76912773,  0.77271541, -0.09918326, -0.09918326,\n",
       "          0.02506352, -0.04814518,  0.02506352], requires_grad=True),\n",
       " tensor([ 0.81574287,  0.80484687,  0.81574287, -0.05035332, -0.05035332,\n",
       "          0.00585993, -0.10939747,  0.00585993, -0.04780231, -0.04780231,\n",
       "          0.81766297,  0.81222814,  0.81766297, -0.10933701, -0.10933701,\n",
       "          0.02375822, -0.05376787,  0.02375822], requires_grad=True),\n",
       " tensor([ 0.86065525,  0.84986331,  0.86065525, -0.06111134, -0.06111134,\n",
       "          0.00432315, -0.1224846 ,  0.00432315, -0.05562752, -0.05562752,\n",
       "          0.86264771,  0.85536784,  0.86264771, -0.11904201, -0.11904201,\n",
       "          0.02274223, -0.05790397,  0.02274223], requires_grad=True),\n",
       " tensor([ 0.90556724,  0.89536238,  0.90556724, -0.07228726, -0.07228726,\n",
       "          0.00275262, -0.13577328,  0.00275262, -0.06365065, -0.06365065,\n",
       "          0.90768088,  0.89859989,  0.90768088, -0.12831832, -0.12831832,\n",
       "          0.02204361, -0.06036959,  0.02204361], requires_grad=True),\n",
       " tensor([ 0.95050272,  0.94139586,  0.95050272, -0.08365251, -0.08365251,\n",
       "          0.00118921, -0.14892086,  0.00118921, -0.07166685, -0.07166685,\n",
       "          0.9527567 ,  0.94193812,  0.9527567 , -0.13725637, -0.13725637,\n",
       "          0.02166932, -0.0611007 ,  0.02166932], requires_grad=True),\n",
       " tensor([ 9.95486920e-01,  9.87976024e-01,  9.95486920e-01,\n",
       "         -9.49794947e-02, -9.49794947e-02, -3.35069322e-04,\n",
       "         -1.61617059e-01, -3.35069322e-04, -7.94832750e-02,\n",
       "         -7.94832750e-02,  9.97850431e-01,  9.85351533e-01,\n",
       "          9.97850431e-01, -1.45991839e-01, -1.45991839e-01,\n",
       "          2.16168329e-02, -6.01366726e-02,  2.16168329e-02], requires_grad=True),\n",
       " tensor([ 1.04054488,  1.03507901,  1.04054488, -0.10606135, -0.10606135,\n",
       "         -0.001794  , -0.17360148, -0.001794  , -0.08694031, -0.08694031,\n",
       "          1.04291956,  1.0287659 ,  1.04291956, -0.15467677, -0.15467677,\n",
       "          0.02188331, -0.05759311,  0.02188331], requires_grad=True),\n",
       " tensor([ 1.08619844,  1.08325894,  1.08619844, -0.11681013, -0.11681013,\n",
       "         -0.0030992 , -0.18478577, -0.0030992 , -0.09396442, -0.09396442,\n",
       "          1.08840076,  1.07255456,  1.08840076, -0.16368056, -0.16368056,\n",
       "          0.02237845, -0.05359464,  0.02237845], requires_grad=True),\n",
       " tensor([ 1.13198006,  1.13186322,  1.13198006, -0.12699266, -0.12699266,\n",
       "         -0.0042867 , -0.19486114, -0.0042867 , -0.10043805, -0.10043805,\n",
       "          1.13372568,  1.1160826 ,  1.13372568, -0.17293216, -0.17293216,\n",
       "          0.02318439, -0.04837715,  0.02318439], requires_grad=True),\n",
       " tensor([ 1.17791109,  1.18081328,  1.17791109, -0.13649097, -0.13649097,\n",
       "         -0.00532042, -0.20371112, -0.00532042, -0.1063313 , -0.1063313 ,\n",
       "          1.17881755,  1.15918399,  1.17881755, -0.18250126, -0.18250126,\n",
       "          0.0242967 , -0.0421599 ,  0.0242967 ], requires_grad=True),\n",
       " tensor([ 1.22448743,  1.23064032,  1.22448743, -0.14529531, -0.14529531,\n",
       "         -0.00611341, -0.21130936, -0.00611341, -0.11168193, -0.11168193,\n",
       "          1.22402356,  1.20208521,  1.22402356, -0.1927035 , -0.1927035 ,\n",
       "          0.02555838, -0.03521602,  0.02555838], requires_grad=True),\n",
       " tensor([ 1.27171033,  1.28126939,  1.27171033, -0.1533226 , -0.1533226 ,\n",
       "         -0.00663094, -0.21755596, -0.00663094, -0.11652257, -0.11652257,\n",
       "          1.26920415,  1.24453116,  1.26920415, -0.20350866, -0.20350866,\n",
       "          0.02691862, -0.02784377,  0.02691862], requires_grad=True),\n",
       " tensor([ 1.31958595,  1.3326409 ,  1.31958595, -0.16049614, -0.16049614,\n",
       "         -0.00683939, -0.22238963, -0.00683939, -0.12091076, -0.12091076,\n",
       "          1.31423147,  1.28628333,  1.31423147, -0.21476459, -0.21476459,\n",
       "          0.02832098, -0.02033879,  0.02832098], requires_grad=True),\n",
       " tensor([ 1.36849338,  1.38522523,  1.36849338, -0.16679925, -0.16679925,\n",
       "         -0.00667417, -0.22577877, -0.00667417, -0.1249485 , -0.1249485 ,\n",
       "          1.35925546,  1.32735469,  1.35925546, -0.22647845, -0.22647845,\n",
       "          0.02951908, -0.01317533,  0.02951908], requires_grad=True),\n",
       " tensor([ 1.41837801,  1.43893997,  1.41837801, -0.17211774, -0.17211774,\n",
       "         -0.00611635, -0.22769823, -0.00611635, -0.12871697, -0.12871697,\n",
       "          1.40411328,  1.36751917,  1.40411328, -0.238153  , -0.238153  ,\n",
       "          0.03047472, -0.00661568,  0.03047472], requires_grad=True),\n",
       " tensor([ 1.46915960e+00,  1.49368167e+00,  1.46915960e+00,\n",
       "         -1.76307172e-01, -1.76307172e-01, -5.14573208e-03,\n",
       "         -2.28145427e-01, -5.14573208e-03, -1.32287473e-01,\n",
       "         -1.32287473e-01,  1.44872682e+00,  1.40670675e+00,\n",
       "          1.44872682e+00, -2.49124577e-01, -2.49124577e-01,\n",
       "          3.12240076e-02, -7.24180326e-04,  3.12240076e-02], requires_grad=True),\n",
       " tensor([ 1.52096483,  1.54969315,  1.52096483, -0.17920341, -0.17920341,\n",
       "         -0.00369678, -0.22705828, -0.00369678, -0.13572884, -0.13572884,\n",
       "          1.49322588,  1.44509715,  1.49322588, -0.25884301, -0.25884301,\n",
       "          0.0316909 ,  0.00437312,  0.0316909 ], requires_grad=True),\n",
       " tensor([ 1.57349475,  1.60659912,  1.57349475, -0.18057681, -0.18057681,\n",
       "         -0.00169848, -0.22431325, -0.00169848, -0.13903459, -0.13903459,\n",
       "          1.53769344,  1.48297127,  1.53769344, -0.26661084, -0.26661084,\n",
       "          0.0321372 ,  0.00918784,  0.0321372 ], requires_grad=True),\n",
       " tensor([ 1.62591528e+00,  1.66312783e+00,  1.62591528e+00,\n",
       "         -1.80325744e-01, -1.80325744e-01,  8.93848512e-04,\n",
       "         -2.19774332e-01,  8.93848512e-04, -1.42109341e-01,\n",
       "         -1.42109341e-01,  1.58223459e+00,  1.52077425e+00,\n",
       "          1.58223459e+00, -2.72037656e-01, -2.72037656e-01,\n",
       "          3.32704334e-02,  1.51584369e-02,  3.32704334e-02], requires_grad=True),\n",
       " tensor([ 1.67786175,  1.71875394,  1.67786175, -0.17843467, -0.17843467,\n",
       "          0.00422654, -0.21309109,  0.00422654, -0.14484649, -0.14484649,\n",
       "          1.62714709,  1.55903794,  1.62714709, -0.27566494, -0.27566494,\n",
       "          0.03531327,  0.02295261,  0.03531327], requires_grad=True),\n",
       " tensor([ 1.72904037,  1.77306082,  1.72904037, -0.17496996, -0.17496996,\n",
       "          0.00846006, -0.20385728,  0.00846006, -0.14708477, -0.14708477,\n",
       "          1.67266833,  1.59815661,  1.67266833, -0.27852242, -0.27852242,\n",
       "          0.03830987,  0.03284549,  0.03830987], requires_grad=True),\n",
       " tensor([ 1.77928872,  1.82584723,  1.77928872, -0.17005233, -0.17005233,\n",
       "          0.01373384, -0.19171338,  0.01373384, -0.14860346, -0.14860346,\n",
       "          1.71893568,  1.63832592,  1.71893568, -0.28183378, -0.28183378,\n",
       "          0.04207756,  0.04458801,  0.04207756], requires_grad=True),\n",
       " tensor([ 1.82869863,  1.87735752,  1.82869863, -0.1637217 , -0.1637217 ,\n",
       "          0.02021387, -0.17625939,  0.02021387, -0.14911328, -0.14911328,\n",
       "          1.76604606,  1.67960588,  1.76604606, -0.28671002, -0.28671002,\n",
       "          0.04606725,  0.0571949 ,  0.04606725], requires_grad=True),\n",
       " tensor([ 1.87746266,  1.92806006,  1.87746266, -0.15593093, -0.15593093,\n",
       "          0.02809423, -0.15701372,  0.02809423, -0.14820681, -0.14820681,\n",
       "          1.81407213,  1.72200912,  1.81407213, -0.29404577, -0.29404577,\n",
       "          0.0494234 ,  0.06911338,  0.0494234 ], requires_grad=True),\n",
       " tensor([ 1.92558395,  1.9781224 ,  1.92558395, -0.14682388, -0.14682388,\n",
       "          0.03728355, -0.1339967 ,  0.03728355, -0.14530178, -0.14530178,\n",
       "          1.86293627,  1.76545792,  1.86293627, -0.30440307, -0.30440307,\n",
       "          0.05149811,  0.07915394,  0.05149811], requires_grad=True),\n",
       " tensor([ 1.97303654,  2.02761146,  1.97303654, -0.13664454, -0.13664454,\n",
       "          0.04735052, -0.10778297,  0.04735052, -0.13974802, -0.13974802,\n",
       "          1.91244617,  1.80976988,  1.91244617, -0.31788458, -0.31788458,\n",
       "          0.0520037 ,  0.08681627,  0.0520037 ], requires_grad=True)]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_params_v_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "a4a6bfb6-6235-48d3-b891-f8aaf1ae6e05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([0.10688482, 0.11366758, 0.10688482], requires_grad=True),\n",
       " tensor([0.10229813, 0.10444212, 0.10229813], requires_grad=True),\n",
       " tensor([0.09556866, 0.09081447, 0.09556866], requires_grad=True),\n",
       " tensor([0.08693481, 0.07329239, 0.08693481], requires_grad=True),\n",
       " tensor([0.07669762, 0.05252368, 0.07669762], requires_grad=True),\n",
       " tensor([0.06520128, 0.02925855, 0.06520128], requires_grad=True),\n",
       " tensor([0.0528177 , 0.00432046, 0.0528177 ], requires_grad=True),\n",
       " tensor([ 0.03993448, -0.02141604,  0.03993448], requires_grad=True),\n",
       " tensor([ 0.02694465, -0.04704444,  0.02694465], requires_grad=True),\n",
       " tensor([ 0.01423659, -0.07164656,  0.01423659], requires_grad=True),\n",
       " tensor([ 0.00218289, -0.09431818,  0.00218289], requires_grad=True),\n",
       " tensor([-0.00887496, -0.11418142, -0.00887496], requires_grad=True),\n",
       " tensor([-0.01867233, -0.13057695, -0.01867233], requires_grad=True),\n",
       " tensor([-0.02697515, -0.14290357, -0.02697515], requires_grad=True),\n",
       " tensor([-0.0336206 , -0.15075064, -0.0336206 ], requires_grad=True),\n",
       " tensor([-0.0385232 , -0.15393266, -0.0385232 ], requires_grad=True),\n",
       " tensor([-0.04158278, -0.15235682, -0.04158278], requires_grad=True),\n",
       " tensor([-0.04289914, -0.14633948, -0.04289914], requires_grad=True),\n",
       " tensor([-0.04257133, -0.13632542, -0.04257133], requires_grad=True),\n",
       " tensor([-0.0407441 , -0.12290022, -0.0407441 ], requires_grad=True),\n",
       " tensor([-0.0376121 , -0.10675861, -0.0376121 ], requires_grad=True),\n",
       " tensor([-0.03342829, -0.08868194, -0.03342829], requires_grad=True),\n",
       " tensor([-0.02826033, -0.069136  , -0.02826033], requires_grad=True),\n",
       " tensor([-0.02270398, -0.04936505, -0.02270398], requires_grad=True),\n",
       " tensor([-0.01720534, -0.03032075, -0.01720534], requires_grad=True),\n",
       " tensor([-0.01192738, -0.0124761 , -0.01192738], requires_grad=True),\n",
       " tensor([-0.0073488 ,  0.00325787, -0.0073488 ], requires_grad=True),\n",
       " tensor([-0.00395048,  0.01602866, -0.00395048], requires_grad=True),\n",
       " tensor([-0.00185241,  0.02555878, -0.00185241], requires_grad=True),\n",
       " tensor([-0.00143009,  0.03125751, -0.00143009], requires_grad=True),\n",
       " tensor([-0.00291998,  0.03280584, -0.00291998], requires_grad=True),\n",
       " tensor([-0.00610181,  0.03057546, -0.00610181], requires_grad=True),\n",
       " tensor([-0.01089883,  0.02477005, -0.01089883], requires_grad=True),\n",
       " tensor([-0.01754595,  0.01520655, -0.01754595], requires_grad=True),\n",
       " tensor([-0.02568511,  0.0025329 , -0.02568511], requires_grad=True),\n",
       " tensor([-0.03501804, -0.0126938 , -0.03501804], requires_grad=True),\n",
       " tensor([-0.04534671, -0.03005372, -0.04534671], requires_grad=True),\n",
       " tensor([-0.05642465, -0.04907029, -0.05642465], requires_grad=True),\n",
       " tensor([-0.06801751, -0.0692925 , -0.06801751], requires_grad=True),\n",
       " tensor([-0.08012158, -0.09047542, -0.08012158], requires_grad=True),\n",
       " tensor([-0.09272524, -0.11221931, -0.09272524], requires_grad=True)]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "f45144ae-4dd4-470c-975f-2392fc80484d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "14dff892-c476-48ec-825d-c97bd55b2dc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.32743721,  0.30903838,  0.28195178,  0.24716201,  0.20591892,\n",
       "         0.1596611 ,  0.10995585,  0.05845293,  0.00684486, -0.04317338,\n",
       "        -0.0899524 , -0.13193135, -0.1679216 , -0.19685386, -0.21799184,\n",
       "        -0.23097906, -0.23552238, -0.23213776, -0.22146808, -0.20438842,\n",
       "        -0.18198281, -0.15553852, -0.12565665, -0.094773  , -0.06473144,\n",
       "        -0.03633086, -0.01143973,  0.0081277 ,  0.02185396,  0.02839732,\n",
       "         0.02696588,  0.01837184,  0.00297239, -0.01988535, -0.04883732,\n",
       "        -0.08272988, -0.12074715, -0.16191959, -0.20532752, -0.25071857,\n",
       "        -0.2976698 ], requires_grad=True)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(observables, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "76d61832-e191-4da3-b05b-463eea0c88ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor(0., requires_grad=True),\n",
       " tensor(0.05, requires_grad=True),\n",
       " tensor(0.1, requires_grad=True),\n",
       " tensor(0.15, requires_grad=True),\n",
       " tensor(0.2, requires_grad=True),\n",
       " tensor(0.25, requires_grad=True),\n",
       " tensor(0.3, requires_grad=True),\n",
       " tensor(0.35, requires_grad=True),\n",
       " tensor(0.4, requires_grad=True),\n",
       " tensor(0.45, requires_grad=True),\n",
       " tensor(0.5, requires_grad=True),\n",
       " tensor(0.55, requires_grad=True),\n",
       " tensor(0.6, requires_grad=True),\n",
       " tensor(0.65, requires_grad=True),\n",
       " tensor(0.7, requires_grad=True),\n",
       " tensor(0.75, requires_grad=True),\n",
       " tensor(0.8, requires_grad=True),\n",
       " tensor(0.85, requires_grad=True),\n",
       " tensor(0.9, requires_grad=True),\n",
       " tensor(0.95, requires_grad=True),\n",
       " tensor(1., requires_grad=True),\n",
       " tensor(1.05, requires_grad=True),\n",
       " tensor(1.1, requires_grad=True),\n",
       " tensor(1.15, requires_grad=True),\n",
       " tensor(1.2, requires_grad=True),\n",
       " tensor(1.25, requires_grad=True),\n",
       " tensor(1.3, requires_grad=True),\n",
       " tensor(1.35, requires_grad=True),\n",
       " tensor(1.4, requires_grad=True),\n",
       " tensor(1.45, requires_grad=True),\n",
       " tensor(1.5, requires_grad=True),\n",
       " tensor(1.55, requires_grad=True),\n",
       " tensor(1.6, requires_grad=True),\n",
       " tensor(1.65, requires_grad=True),\n",
       " tensor(1.7, requires_grad=True),\n",
       " tensor(1.75, requires_grad=True),\n",
       " tensor(1.8, requires_grad=True),\n",
       " tensor(1.85, requires_grad=True),\n",
       " tensor(1.9, requires_grad=True),\n",
       " tensor(1.95, requires_grad=True),\n",
       " tensor(2., requires_grad=True)]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "1b82ed23-1201-4be3-b575-114a83191493",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbd00881420>]"
      ]
     },
     "execution_count": 78,
     "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": [
    "# expectation value of pauliX on qubit 0, 1 and 2 versus time.\n",
    "\n",
    "plt.plot(time,np.sum(observables, axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "b6e86bc9-9887-4577-9e59-38debf98f9c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.003820548064922269"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(final_costs_v_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "57315fa9-18b6-4e38-ad0b-6012838262a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbd01621750>]"
      ]
     },
     "execution_count": 79,
     "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.plot(time, final_costs_v_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50a6e7d4-ceb8-4a34-9c5a-9b6078551973",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}