variational_circuit_adhoc_data.ipynb

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  {
   "source": [
    "# Effect of Entanglement on Model Training in QML"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "### Importing the required libraries"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.ml.datasets import *\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.aqua.components.optimizers import COBYLA, AQGD, ADAM\n",
    "from qiskit.circuit.library import ZZFeatureMap, RealAmplitudes\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qiskit.quantum_info import Statevector, DensityMatrix, entropy\n",
    "from qiskit import execute\n",
    "%matplotlib inline"
   ]
  },
  {
   "source": [
    "### Loading the Ad Hoc dataset from `qiskit.ml.datasets`"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "['A', 'B']\n"
     ]
    }
   ],
   "source": [
    "training_size = 100\n",
    "# size of test data set\n",
    "test_size = 20\n",
    "# dimension of data sets\n",
    "n = 2\n",
    "# construct training and test data\n",
    "_, training_input, test_input, class_labels = \\\n",
    "ad_hoc_data(training_size=training_size, test_size=test_size, n=n, gap=0.3, plot_data=False)\n",
    "print(class_labels)"
   ]
  },
  {
   "source": [
    "### Preparing the Variational Quantum Classifier Circuit\n",
    "\n",
    "Use of the `ZZFeatureMap` as the Quantum Feature Map and `Real Amplitudes` as Variational circuit from `qiskit.circuit.library`"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "     ┌───┐┌─────────────┐                                          ┌──────────┐»\n",
       "q_0: ┤ H ├┤ P(2.0*x[0]) ├──■────────────────────────────────────■──┤ RY(θ[0]) ├»\n",
       "     ├───┤├─────────────┤┌─┴─┐┌──────────────────────────────┐┌─┴─┐├──────────┤»\n",
       "q_1: ┤ H ├┤ P(2.0*x[1]) ├┤ X ├┤ P(2.0*(π - x[0])*(π - x[1])) ├┤ X ├┤ RY(θ[1]) ├»\n",
       "     └───┘└─────────────┘└───┘└──────────────────────────────┘└───┘└──────────┘»\n",
       "«          ┌──────────┐\n",
       "«q_0: ──■──┤ RY(θ[2]) ├\n",
       "«     ┌─┴─┐├──────────┤\n",
       "«q_1: ┤ X ├┤ RY(θ[3]) ├\n",
       "«     └───┘└──────────┘"
      ],
      "text/html": "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌─────────────┐                                          ┌──────────┐»\nq_0: ┤ H ├┤ P(2.0*x[0]) ├──■────────────────────────────────────■──┤ RY(θ[0]) ├»\n     ├───┤├─────────────┤┌─┴─┐┌──────────────────────────────┐┌─┴─┐├──────────┤»\nq_1: ┤ H ├┤ P(2.0*x[1]) ├┤ X ├┤ P(2.0*(π - x[0])*(π - x[1])) ├┤ X ├┤ RY(θ[1]) ├»\n     └───┘└─────────────┘└───┘└──────────────────────────────┘└───┘└──────────┘»\n«          ┌──────────┐\n«q_0: ──■──┤ RY(θ[2]) ├\n«     ┌─┴─┐├──────────┤\n«q_1: ┤ X ├┤ RY(θ[3]) ├\n«     └───┘└──────────┘</pre>"
     },
     "metadata": {},
     "execution_count": 58
    }
   ],
   "source": [
    "sv = Statevector.from_label('0' * n)\n",
    "feature_map = ZZFeatureMap(n, reps=1)\n",
    "var_form = RealAmplitudes(n, reps=1)\n",
    "circuit = feature_map.combine(var_form)\n",
    "circuit.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Preparing the parameter dictionary\n",
    "\n",
    "def get_data_dict(params, x):\n",
    "    parameters = {}\n",
    "    for i, p in enumerate(feature_map.ordered_parameters):\n",
    "        parameters[p] = x[i]\n",
    "    for i, p in enumerate(var_form.ordered_parameters):\n",
    "        parameters[p] = params[i]\n",
    "    return parameters\n"
   ]
  },
  {
   "source": [
    "### Getting a Glimpse of the circuit with initialized parameters"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "     ┌───┐┌──────────────────────┐                                 »\n",
       "q_0: ┤ H ├┤ P(0.200000000000000) ├──■───────────────────────────■──»\n",
       "     ├───┤├─────────────────────┬┘┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
       "q_1: ┤ H ├┤ P(2.40000000000000) ├─┤ X ├┤ P(11.8110679028453) ├┤ X ├»\n",
       "     └───┘└─────────────────────┘ └───┘└─────────────────────┘└───┘»\n",
       "«     ┌───────────────────────┐     ┌────────────────────────┐\n",
       "«q_0: ┤ RY(0.100000000000000) ├──■──┤ RY(0.0200000000000000) ├\n",
       "«     └┬──────────────────────┤┌─┴─┐├───────────────────────┬┘\n",
       "«q_1: ─┤ RY(1.20000000000000) ├┤ X ├┤ RY(0.100000000000000) ├─\n",
       "«      └──────────────────────┘└───┘└───────────────────────┘ "
      ],
      "text/html": "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌──────────────────────┐                                 »\nq_0: ┤ H ├┤ P(0.200000000000000) ├──■───────────────────────────■──»\n     ├───┤├─────────────────────┬┘┌─┴─┐┌─────────────────────┐┌─┴─┐»\nq_1: ┤ H ├┤ P(2.40000000000000) ├─┤ X ├┤ P(11.8110679028453) ├┤ X ├»\n     └───┘└─────────────────────┘ └───┘└─────────────────────┘└───┘»\n«     ┌───────────────────────┐     ┌────────────────────────┐\n«q_0: ┤ RY(0.100000000000000) ├──■──┤ RY(0.0200000000000000) ├\n«     └┬──────────────────────┤┌─┴─┐├───────────────────────┬┘\n«q_1: ─┤ RY(1.20000000000000) ├┤ X ├┤ RY(0.100000000000000) ├─\n«      └──────────────────────┘└───┘└───────────────────────┘ </pre>"
     },
     "metadata": {},
     "execution_count": 60
    }
   ],
   "source": [
    "data = [0.1, 1.2]\n",
    "params = np.array([0.1, 1.2, 0.02, 0.1])\n",
    "circ_ = circuit.assign_parameters(get_data_dict(params, data))\n",
    "circ_.draw(plot_barriers=True)"
   ]
  },
  {
   "source": [
    "### Setting up the environment for Quantum Classification"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def assign_label(bit_string, class_labels):\n",
    "    hamming_weight = sum([int(k) for k in list(bit_string)])\n",
    "    is_odd_parity = hamming_weight & 1\n",
    "    if is_odd_parity:\n",
    "        return class_labels[1]\n",
    "    else:\n",
    "        return class_labels[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def return_probabilities(counts, class_labels):\n",
    "    shots = sum(counts.values())\n",
    "    result = {class_labels[0]: 0,\n",
    "        class_labels[1]: 0}\n",
    "    for key, item in counts.items():\n",
    "        label = assign_label(key, class_labels)\n",
    "        result[label] += counts[key]/shots\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "{'A': 0.75, 'B': 0.25}"
      ]
     },
     "metadata": {},
     "execution_count": 63
    }
   ],
   "source": [
    "return_probabilities({'00' : 10, '01': 10, '11': 20}, class_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def classify(x_list, params, class_labels):\n",
    "    qc_list = []\n",
    "    for x in x_list:\n",
    "        circ_ = circuit.assign_parameters(get_data_dict(params, x))\n",
    "        qc = sv.evolve(circ_)\n",
    "        qc_list += [qc]\n",
    "    probs = []\n",
    "    for qc in qc_list:\n",
    "        counts = qc.to_counts()\n",
    "        prob = return_probabilities(counts, class_labels)\n",
    "        probs += [prob]\n",
    "    return probs\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[{'A': 0.9058187060399014, 'B': 0.09418129396009857}]"
      ]
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "x = np.asarray([[0.5, 0.9]])\n",
    "classify(x, params=np.array([0.8, -0.5, 1.5, 0,5]), class_labels=class_labels)"
   ]
  },
  {
   "source": [
    "### Defining the Cost function estimate"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_estimate_sigmoid(probs, expected_label): # probability of labels vs actual labels\n",
    "    p = probs.get(expected_label)\n",
    "    sig = None\n",
    "    if np.isclose(p, 0.0):\n",
    "        sig = 1\n",
    "    elif np.isclose(p, 1.0):\n",
    "        sig = 0\n",
    "    else:\n",
    "        denominator = np.sqrt(2*p*(1-p))\n",
    "        x = np.sqrt(200)*(0.5-p)/denominator\n",
    "        sig = 1/(1+np.exp(-x))\n",
    "    return sig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "x = np.linspace(0, 1, 20)\n",
    "y = [cost_estimate_sigmoid({'A': x_, 'B': 1-x_}, 'A') for x_ in x]\n",
    "plt.plot(x, y)\n",
    "plt.xlabel('Probability of assigning the correct class')\n",
    "plt.ylabel('Cost value')\n",
    "plt.show()\n"
   ]
  },
  {
   "source": [
    "### Creating the cost function"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_function_values = []\n",
    "def cost_function(training_input, class_labels, params, shots=100, print_value=False):\n",
    "    # map training input to list of labels and list of samples\n",
    "    cost = 0\n",
    "    training_labels = []\n",
    "    training_samples = []\n",
    "    for label, samples in training_input.items():\n",
    "        for sample in samples:\n",
    "            training_labels += [label]\n",
    "            training_samples += [sample]\n",
    "    # classify all samples\n",
    "    probs = classify(training_samples, params, class_labels)\n",
    "    # evaluate costs for all classified samples\n",
    "    for i, prob in enumerate(probs):\n",
    "        cost += cost_estimate_sigmoid(prob, training_labels[i])\n",
    "    cost /= len(training_samples)\n",
    "    # print resulting objective function\n",
    "    if print_value:\n",
    "        loss_function_values.append(cost)\n",
    "        print('%.4f' % cost)\n",
    "    # return objective value\n",
    "    return cost\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0.2541554066388654"
      ]
     },
     "metadata": {},
     "execution_count": 112
    }
   ],
   "source": [
    "cost_function(training_input, class_labels, params)"
   ]
  },
  {
   "source": [
    "### Optimizer Setup\n",
    "\n",
    "We use the ADAM optimizer and save the parameter after every step in a file named `adam_params.csv` by specifying the `snapshot_dir` argument."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.6350\n",
      "0.6350\n",
      "0.6350\n",
      "0.6350\n",
      "0.6350\n",
      "0.6349\n",
      "0.6349\n",
      "0.6349\n",
      "0.6349\n",
      "0.6349\n",
      "0.6347\n",
      "0.6347\n",
      "0.6347\n",
      "0.6347\n",
      "0.6347\n",
      "0.6346\n",
      "0.6346\n",
      "0.6346\n",
      "0.6346\n",
      "0.6346\n",
      "0.6344\n",
      "0.6344\n",
      "0.6344\n",
      "0.6344\n",
      "0.6344\n",
      "0.6343\n",
      "0.6343\n",
      "0.6343\n",
      "0.6343\n",
      "0.6343\n",
      "0.6341\n",
      "0.6341\n",
      "0.6341\n",
      "0.6341\n",
      "0.6341\n",
      "0.6340\n",
      "0.6340\n",
      "0.6340\n",
      "0.6340\n",
      "0.6340\n",
      "0.6338\n",
      "0.6338\n",
      "0.6338\n",
      "0.6338\n",
      "0.6338\n",
      "0.6337\n",
      "0.6337\n",
      "0.6337\n",
      "0.6337\n",
      "0.6337\n",
      "0.6335\n",
      "0.6335\n",
      "0.6335\n",
      "0.6335\n",
      "0.6335\n",
      "0.6334\n",
      "0.6334\n",
      "0.6334\n",
      "0.6334\n",
      "0.6334\n",
      "0.6332\n",
      "0.6332\n",
      "0.6332\n",
      "0.6332\n",
      "0.6332\n",
      "0.6331\n",
      "0.6331\n",
      "0.6331\n",
      "0.6331\n",
      "0.6331\n",
      "0.6329\n",
      "0.6329\n",
      "0.6329\n",
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      "0.6276\n",
      "0.6274\n",
      "\n",
      "opt_params: [5.98091485 0.60635221 4.31953022 4.44815442]\n",
      "opt_value:  0.6274423518977522\n"
     ]
    }
   ],
   "source": [
    "loss_function_values = []\n",
    "optimizer = ADAM(maxiter=50, snapshot_dir=r'C:\\Users\\farha\\Desktop\\Quantum\\github-farhan\\QOSFProgram')\n",
    "# define objective function for training\n",
    "objective_function = lambda params: cost_function(training_input, class_labels, params, print_value=True)\n",
    "# randomly initialize the parameters\n",
    "np.random.seed(137)\n",
    "init_params = 2*np.pi*np.random.rand(n*(1)*2)\n",
    "# train classifier\n",
    "opt_params, value, _ = optimizer.optimize(len(init_params), objective_function, initial_point=init_params)\n",
    "# print results\n",
    "print()\n",
    "print('opt_params:', opt_params)\n",
    "print('opt_value: ', value) "
   ]
  },
  {
   "source": [
    "## Measuring Entropies as the QML model trains"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "vn_entropy = []\n",
    "epochs = []\n",
    "epoch_var = 0\n",
    "\n",
    "import pandas as pd \n",
    "\n",
    "# Loading the data from adam_params.csv\n",
    "df = pd.read_csv(r'C:\\Users\\farha\\Desktop\\Quantum\\github-farhan\\QOSFProgram\\adam_params.csv', usecols = ['m'])\n",
    "\n",
    "arr = df.to_numpy()\n",
    "param_array = []\n",
    "for i in arr:\n",
    "    a_list =i[0].rstrip(']').lstrip('[').split()\n",
    "    map_object = map(float, a_list)\n",
    "    list_of_integers = list(map_object)\n",
    "    param_array.append(list_of_integers)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "48\n[-0.00730427, -0.00114775, -0.00303513, 0.00280176]\n"
     ]
    }
   ],
   "source": [
    "print(len(param_array))\n",
    "print(param_array[0])"
   ]
  },
  {
   "source": [
    "### Calculating vonNeumann entropy as the circuit trains\n",
    "\n",
    "Entropy is measured by calculating the Density Matrix of the state after every iteration and passing it to the `entropy` function from `qiskit.quantum_info` library. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0606944600000000) ├──■──┤ RY(-0.0213285100000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0103910400000000) ├┤ X ├─┤ RY(0.0217171000000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0614784200000000) ├──■──┤ RY(-0.0213310600000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0105846200000000) ├┤ X ├─┤ RY(0.0218912900000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0621613300000000) ├──■──┤ RY(-0.0212868400000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0107631700000000) ├┤ X ├─┤ RY(0.0220250800000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0627530900000000) ├──■──┤ RY(-0.0212005200000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0109280800000000) ├┤ X ├─┤ RY(0.0221234000000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0632629100000000) ├──■──┤ RY(-0.0210767600000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0110803900000000) ├┤ X ├─┤ RY(0.0221901200000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0636997600000000) ├──■──┤ RY(-0.0209183000000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0112212400000000) ├┤ X ├─┤ RY(0.0222285300000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0640706200000000) ├──■──┤ RY(-0.0207299500000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0113521100000000) ├┤ X ├─┤ RY(0.0222410000000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0643826200000000) ├──■──┤ RY(-0.0205145800000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0114743400000000) ├┤ X ├─┤ RY(0.0222303500000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0646420000000000) ├──■──┤ RY(-0.0202747800000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0115887800000000) ├┤ X ├─┤ RY(0.0221995600000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0648533500000000) ├──■──┤ RY(-0.0200127800000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0116953400000000) ├┤ X ├─┤ RY(0.0221512000000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0650226900000000) ├──■──┤ RY(-0.0197320200000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0117956800000000) ├┤ X ├─┤ RY(0.0220866900000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0651535600000000) ├──■──┤ RY(-0.0194339200000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0118897600000000) ├┤ X ├─┤ RY(0.0220085400000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0652513600000000) ├──■──┤ RY(-0.0191193400000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0119784300000000) ├┤ X ├─┤ RY(0.0219177800000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0653175100000000) ├──■──┤ RY(-0.0187910200000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0120615600000000) ├┤ X ├─┤ RY(0.0218167700000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0653575000000000) ├──■──┤ RY(-0.0184504700000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0121406000000000) ├┤ X ├─┤ RY(0.0217052200000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0653731800000000) ├──■──┤ RY(-0.0180988900000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0122159500000000) ├┤ X ├─┤ RY(0.0215860500000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0653670800000000) ├──■──┤ RY(-0.0177372900000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0122873200000000) ├┤ X ├─┤ RY(0.0214591600000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0653417200000000) ├──■──┤ RY(-0.0173665500000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0123553300000000) ├┤ X ├─┤ RY(0.0213268500000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0652989100000000) ├──■──┤ RY(-0.0169881400000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0124197600000000) ├┤ X ├─┤ RY(0.0211894600000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0652419500000000) ├──■──┤ RY(-0.0166035000000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0124821800000000) ├┤ X ├─┤ RY(0.0210466000000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0651709300000000) ├──■──┤ RY(-0.0162115800000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0125415800000000) ├┤ X ├─┤ RY(0.0209008200000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0650890200000000) ├──■──┤ RY(-0.0158147700000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0125990400000000) ├┤ X ├─┤ RY(0.0207516300000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0649971000000000) ├──■──┤ RY(-0.0154134600000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0126546400000000) ├┤ X ├─┤ RY(0.0206000400000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0648960500000000) ├──■──┤ RY(-0.0150078800000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0127084600000000) ├┤ X ├─┤ RY(0.0204466200000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0647865600000000) ├──■──┤ RY(-0.0145982200000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0127598900000000) ├┤ X ├─┤ RY(0.0202930000000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0646708100000000) ├──■──┤ RY(-0.0141853300000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0128098400000000) ├┤ X ├─┤ RY(0.0201377600000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0645491000000000) ├──■──┤ RY(-0.0137696700000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0128582300000000) ├┤ X ├─┤ RY(0.0199822700000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0644228000000000) ├──■──┤ RY(-0.0133517100000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0129057900000000) ├┤ X ├─┤ RY(0.0198267900000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0642921300000000) ├──■──┤ RY(-0.0129313600000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0129512500000000) ├┤ X ├─┤ RY(0.0196718700000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n",
      "     ┌───┐┌─────────────────────┐                                 »\n",
      "q_0: ┤ H ├┤ P(1.00000000000000) ├──■───────────────────────────■──»\n",
      "     ├───┤├─────────────────────┤┌─┴─┐┌─────────────────────┐┌─┴─┐»\n",
      "q_1: ┤ H ├┤ P(1.80000000000000) ├┤ X ├┤ P(11.8427493721273) ├┤ X ├»\n",
      "     └───┘└─────────────────────┘└───┘└─────────────────────┘└───┘»\n",
      "«     ┌─────────────────────────┐     ┌─────────────────────────┐\n",
      "«q_0: ┤ RY(-0.0641588800000000) ├──■──┤ RY(-0.0125098600000000) ├\n",
      "«     ├─────────────────────────┤┌─┴─┐└┬────────────────────────┤\n",
      "«q_1: ┤ RY(-0.0129960600000000) ├┤ X ├─┤ RY(0.0195174600000000) ├\n",
      "«     └─────────────────────────┘└───┘ └────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "vn_entropy = []\n",
    "epochs = [x for x in range(len(param_array))]\n",
    "for i in range(len(param_array)):\n",
    "    x_list = np.asarray([[0.5, 0.9]])\n",
    "    for x in x_list:\n",
    "        circ_ = circuit.assign_parameters(get_data_dict(np.array(param_array[i]), x))\n",
    "        qc = sv.evolve(circ_)\n",
    "        print(circ_)\n",
    "\n",
    "    ckt_state = execute(circ_, backend = Aer.get_backend('statevector_simulator'), shots = 500).result().get_statevector()\n",
    "    D = DensityMatrix(ckt_state)\n",
    "    vn_entropy_val = entropy(D, base=2)\n",
    "    vn_entropy.append(vn_entropy_val)\n"
   ]
  },
  {
   "source": [
    "### Calculating Meyer-Wallach entropy as the circuit trains\n",
    "\n",
    "Meyer Wallach entropy is calculated using the `qutip` library and the implementation is available at `compute_Q_ptrace(ket, N)` function of `meyer_wallach_entanglement.py`."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      ".08496443+0.09360423j]\n",
      " [-0.08496443-0.09360423j  0.25509081+0.j        ]]\n",
      "0.9355921919449846\n",
      "Statevector([ 0.50872149+0.00347446j, -0.49148266+0.15106349j,\n",
      "              0.22973352+0.44667888j,  0.45441453+0.13424947j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50872149+0.00347446j]\n",
      " [-0.49148266+0.15106349j]\n",
      " [ 0.22973352+0.44667888j]\n",
      " [ 0.45441453+0.13424947j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28931464+0.j         -0.08463433-0.09181021j]\n",
      " [-0.08463433+0.09181021j  0.24294462+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27723876+0.j         -0.08514228+0.09357889j]\n",
      " [-0.08514228-0.09357889j  0.2550205 +0.j        ]]\n",
      "0.9354814846638457\n",
      "Statevector([ 0.508867  +0.00351076j, -0.49150809+0.15097079j,\n",
      "              0.2295707 +0.44669478j,  0.45430636+0.13429987j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.508867  +0.00351076j]\n",
      " [-0.49150809+0.15097079j]\n",
      " [ 0.2295707 +0.44669478j]\n",
      " [ 0.45430636+0.13429987j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28948368+0.j        -0.0846307 -0.0919058j]\n",
      " [-0.0846307 +0.0919058j  0.242823  +0.j       ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27735022+0.j         -0.08529575+0.09355534j]\n",
      " [-0.08529575-0.09355534j  0.25495645+0.j        ]]\n",
      "0.9353866535960824\n",
      "Statevector([ 0.50900716+0.00354444j, -0.49151294+0.15089346j,\n",
      "              0.22941228+0.44670428j,  0.45422413+0.1343543j ],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50900716+0.00354444j]\n",
      " [-0.49151294+0.15089346j]\n",
      " [ 0.22941228+0.44670428j]\n",
      " [ 0.45422413+0.1343543j ]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28962815+0.j         -0.08462805-0.09198621j]\n",
      " [-0.08462805+0.09198621j  0.24271883+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27744904+0.j         -0.08542754+0.09353335j]\n",
      " [-0.08542754-0.09353335j  0.25489794+0.j        ]]\n",
      "0.9353060407093436\n",
      "Statevector([ 0.50914251+0.00357562j, -0.49149943+0.15082984j,\n",
      "              0.22925787+0.44670803j,  0.454165  +0.13441242j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50914251+0.00357562j]\n",
      " [-0.49149943+0.15082984j]\n",
      " [ 0.22925787+0.44670803j]\n",
      " [ 0.454165  +0.13441242j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28975067+0.j         -0.08462625-0.09205305j]\n",
      " [-0.08462625+0.09205305j  0.24263023+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27753657+0.j         -0.08553994+0.09351275j]\n",
      " [-0.08553994-0.09351275j  0.25484433+0.j        ]]\n",
      "0.9352381979791748\n",
      "Statevector([ 0.50927329+0.00360416j, -0.4914692 +0.15077873j,\n",
      "              0.22910755+0.44670655j,  0.45412694+0.1344739j ],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50927329+0.00360416j]\n",
      " [-0.4914692 +0.15077873j]\n",
      " [ 0.22910755+0.44670655j]\n",
      " [ 0.45412694+0.1344739j ]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28985296+0.j         -0.08462524-0.09210751j]\n",
      " [-0.08462524+0.09210751j  0.24255599+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27761376+0.j         -0.08563442+0.09349358j]\n",
      " [-0.08563442-0.09349358j  0.25479519+0.j        ]]\n",
      "0.9351821000782032\n",
      "Statevector([ 0.50940007+0.00363078j, -0.4914245 +0.15073858j,\n",
      "              0.22896058+0.44670053j,  0.45410726+0.13453817j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50940007+0.00363078j]\n",
      " [-0.4914245 +0.15073858j]\n",
      " [ 0.22896058+0.44670053j]\n",
      " [ 0.45410726+0.13453817j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2899377 +0.j         -0.08462493-0.09215114j]\n",
      " [-0.08462493+0.09215114j  0.24249417+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27768186+0.j         -0.08571344+0.09347552j]\n",
      " [-0.08571344-0.09347552j  0.25475001+0.j        ]]\n",
      "0.935136269803537\n",
      "Statevector([ 0.50952301+0.00365524j, -0.49136662+0.15070843j,\n",
      "              0.22881709+0.44669035j,  0.45410428+0.13460507j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50952301+0.00365524j]\n",
      " [-0.49136662+0.15070843j]\n",
      " [ 0.22881709+0.44669035j]\n",
      " [ 0.45410428+0.13460507j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29000628+0.j         -0.08462523-0.09218485j]\n",
      " [-0.08462523+0.09218485j  0.24244377+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27774162+0.j         -0.08577812+0.09345858j]\n",
      " [-0.08577812-0.09345858j  0.25470843+0.j        ]]\n",
      "0.935099900076235\n",
      "Statevector([ 0.50964316+0.00367792j, -0.49129682+0.15068693j,\n",
      "              0.22867599+0.44667649j,  0.45411605+0.13467451j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50964316+0.00367792j]\n",
      " [-0.49129682+0.15068693j]\n",
      " [ 0.22867599+0.44667649j]\n",
      " [ 0.45411605+0.13467451j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29006087+0.j         -0.08462609-0.09221005j]\n",
      " [-0.08462609+0.09221005j  0.24240329+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27779435+0.j         -0.08583047+0.09344262j]\n",
      " [-0.08583047-0.09344262j  0.25466981+0.j        ]]\n",
      "0.9350716816925471\n",
      "Statevector([ 0.50975986+0.00369854j, -0.49121646+0.15067362j,\n",
      "              0.22853822+0.44665923j,  0.45414136+0.13474605j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50975986+0.00369854j]\n",
      " [-0.49121646+0.15067362j]\n",
      " [ 0.22853822+0.44665923j]\n",
      " [ 0.45414136+0.13474605j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29010212+0.j         -0.08462744-0.09222709j]\n",
      " [-0.08462744+0.09222709j  0.24237223+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27784016+0.j         -0.08587094+0.09342766j]\n",
      " [-0.08587094-0.09342766j  0.25463419+0.j        ]]\n",
      "0.9350513013001049\n",
      "Statevector([ 0.50987422+0.00371798j, -0.49112678+0.15066719j,\n",
      "              0.22840232+0.44663911j,  0.45417833+0.13481939j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50987422+0.00371798j]\n",
      " [-0.49112678+0.15066719j]\n",
      " [ 0.22840232+0.44663911j]\n",
      " [ 0.45417833+0.13481939j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29013232+0.j         -0.08462923-0.09223739j]\n",
      " [-0.08462923+0.09223739j  0.24234899+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27788032+0.j         -0.08590171+0.09341343j]\n",
      " [-0.08590171-0.09341343j  0.25460099+0.j        ]]\n",
      "0.9350373808965351\n",
      "Statevector([ 0.50998609+0.00373587j, -0.49102904+0.15066699j,\n",
      "              0.22826878+0.44661635j,  0.45422555+0.13489449j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.50998609+0.00373587j]\n",
      " [-0.49102904+0.15066699j]\n",
      " [ 0.22826878+0.44661635j]\n",
      " [ 0.45422555+0.13489449j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29015246+0.j         -0.08463139-0.09224143j]\n",
      " [-0.08463139+0.09224143j  0.2423328 +0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2779152 +0.j         -0.08592351+0.09339987j]\n",
      " [-0.08592351-0.09339987j  0.25457007+0.j        ]]\n",
      "0.9350294648612696\n",
      "Statevector([ 0.51009577+0.00375241j, -0.4909237 +0.15067249j,\n",
      "              0.22813724+0.44659121j,  0.45428234+0.1349711j ],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51009577+0.00375241j]\n",
      " [-0.4909237 +0.15067249j]\n",
      " [ 0.22813724+0.44659121j]\n",
      " [ 0.45428234+0.1349711j ]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29016331+0.j         -0.0846339 -0.09223986j]\n",
      " [-0.0846339 +0.09223986j  0.24232321+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27794534+0.j         -0.08593709+0.09338702j]\n",
      " [-0.08593709-0.09338702j  0.25454117+0.j        ]]\n",
      "0.9350269702025567\n",
      "Statevector([ 0.51020344+0.00376745j, -0.49081191+0.15068292j,\n",
      "              0.22800774+0.44656395j,  0.45434723+0.13504921j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51020344+0.00376745j]\n",
      " [-0.49081191+0.15068292j]\n",
      " [ 0.22800774+0.44656395j]\n",
      " [ 0.45434723+0.13504921j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2901661 +0.j         -0.08463668-0.09223333j]\n",
      " [-0.08463668+0.09223333j  0.24231927+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27797132+0.j         -0.08594344+0.09337477j]\n",
      " [-0.08594344-0.09337477j  0.25451405+0.j        ]]\n",
      "0.9350292634457835\n",
      "Statevector([ 0.5103091 +0.0037811j , -0.49069427+0.15069787j,\n",
      "              0.2278803 +0.44653481j,  0.45441957+0.13512849j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.5103091 +0.0037811j ]\n",
      " [-0.49069427+0.15069787j]\n",
      " [ 0.2278803 +0.44653481j]\n",
      " [ 0.45441957+0.13512849j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2901614 +0.j        -0.08463972-0.0922223j]\n",
      " [-0.08463972+0.0922223j  0.24232064+0.j       ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27799346+0.j         -0.0859431 +0.09336317j]\n",
      " [-0.0859431 -0.09336317j  0.25448858+0.j        ]]\n",
      "0.9350359255361442\n",
      "Statevector([ 0.51041336+0.00379412j, -0.49057177+0.15071652j,\n",
      "              0.22775396+0.44650413j,  0.45449805+0.13520868j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51041336+0.00379412j]\n",
      " [-0.49057177+0.15071652j]\n",
      " [ 0.22775396+0.44650413j]\n",
      " [ 0.45449805+0.13520868j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29015081+0.j         -0.08464298-0.09220763j]\n",
      " [-0.08464298+0.09220763j  0.24232615+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27801248+0.j         -0.08593759+0.09335194j]\n",
      " [-0.08593759-0.09335194j  0.25446448+0.j        ]]\n",
      "0.9350460806303698\n",
      "Statevector([ 0.51051612+0.00380563j, -0.49044452+0.15073873j,\n",
      "              0.22762936+0.44647186j,  0.4545824 +0.13529013j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51051612+0.00380563j]\n",
      " [-0.49044452+0.15073873j]\n",
      " [ 0.22762936+0.44647186j]\n",
      " [ 0.4545824 +0.13529013j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29013424+0.j         -0.08464642-0.09218933j]\n",
      " [-0.08464642+0.09218933j  0.24233588+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27802849+0.j         -0.08592664+0.09334124j]\n",
      " [-0.08592664-0.09334124j  0.25444163+0.j        ]]\n",
      "0.9350597625081534\n",
      "Statevector([ 0.51061768+0.00381637j, -0.49031359+0.15076377j,\n",
      "              0.22750587+0.44643839j,  0.45467138+0.13537233j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51061768+0.00381637j]\n",
      " [-0.49031359+0.15076377j]\n",
      " [ 0.22750587+0.44643839j]\n",
      " [ 0.45467138+0.13537233j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29011307+0.j         -0.08465002-0.09216823j]\n",
      " [-0.08465002+0.09216823j  0.24234886+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2780421 +0.j         -0.0859116 +0.09333089j]\n",
      " [-0.0859116 -0.09333089j  0.25441982+0.j        ]]\n",
      "0.9350761522180022\n",
      "Statevector([ 0.51071805+0.00382623j, -0.49017942+0.15079135j,\n",
      "              0.22738361+0.44640384j,  0.45476445+0.13545527j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51071805+0.00382623j]\n",
      " [-0.49017942+0.15079135j]\n",
      " [ 0.22738361+0.44640384j]\n",
      " [ 0.45476445+0.13545527j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29008771+0.j         -0.08465374-0.09214454j]\n",
      " [-0.08465374+0.09214454j  0.24236477+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2780535 +0.j         -0.08589278+0.09332088j]\n",
      " [-0.08589278-0.09332088j  0.25439898+0.j        ]]\n",
      "0.9350950334254506\n",
      "Statevector([ 0.51081733+0.00383515j, -0.49004233+0.15082124j,\n",
      "              0.22726254+0.44636826j,  0.45486121+0.13553894j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51081733+0.00383515j]\n",
      " [-0.49004233+0.15082124j]\n",
      " [ 0.22726254+0.44636826j]\n",
      " [ 0.45486121+0.13553894j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29005854+0.j         -0.08465756-0.09211851j]\n",
      " [-0.08465756+0.09211851j  0.24238336+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2780629 +0.j         -0.0858705 +0.09331119j]\n",
      " [-0.0858705 -0.09331119j  0.25437901+0.j        ]]\n",
      "0.9351161895847402\n",
      "Statevector([ 0.51091537+0.00384271j, -0.48990267+0.15085321j,\n",
      "              0.22714311+0.44633175j,  0.45496119+0.13562337j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51091537+0.00384271j]\n",
      " [-0.48990267+0.15085321j]\n",
      " [ 0.22714311+0.44633175j]\n",
      " [ 0.45496119+0.13562337j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.29002572+0.j        -0.08466145-0.0920903j]\n",
      " [-0.08466145+0.0920903j  0.24240454+0.j       ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27807043+0.j         -0.0858448 +0.09330193j]\n",
      " [-0.0858448 -0.09330193j  0.25435983+0.j        ]]\n",
      "0.935139487610003\n",
      "Statevector([ 0.51101272+0.00384963j, -0.48976077+0.15088681j,\n",
      "              0.22702439+0.44629451j,  0.45506387+0.13570831j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51101272+0.00384963j]\n",
      " [-0.48976077+0.15088681j]\n",
      " [ 0.22702439+0.44629451j]\n",
      " [ 0.45506387+0.13570831j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28999017+0.j         -0.08466542-0.09206047j]\n",
      " [-0.08466542+0.09206047j  0.24242765+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.2780766 +0.j         -0.08581665+0.09329294j]\n",
      " [-0.08581665-0.09329294j  0.25434122+0.j        ]]\n",
      "0.9351643545227928\n",
      "Statevector([ 0.51110919+0.00385564j, -0.48961707+0.15092187j,\n",
      "              0.22690678+0.44625661j,  0.45516881+0.13579376j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51110919+0.00385564j]\n",
      " [-0.48961707+0.15092187j]\n",
      " [ 0.22690678+0.44625661j]\n",
      " [ 0.45516881+0.13579376j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28995208+0.j         -0.08466943-0.09202911j]\n",
      " [-0.08466943+0.09202911j  0.24245256+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27808144+0.j         -0.08578613+0.09328422j]\n",
      " [-0.08578613-0.09328422j  0.2543232 +0.j        ]]\n",
      "0.9351907212971695\n",
      "Statevector([ 0.51120502+0.00386097j, -0.48947208+0.15095804j,\n",
      "              0.22678993+0.44621818j,  0.45527536+0.13587968j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51120502+0.00386097j]\n",
      " [-0.48947208+0.15095804j]\n",
      " [ 0.22678993+0.44621818j]\n",
      " [ 0.45527536+0.13587968j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28991217+0.j         -0.08467346-0.09199656j]\n",
      " [-0.08467346+0.09199656j  0.24247872+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27808526+0.j         -0.08575389+0.09327566j]\n",
      " [-0.08575389-0.09327566j  0.25430563+0.j        ]]\n",
      "0.9352182189585831\n",
      "Statevector([ 0.51130008+0.00386522j, -0.48932562+0.15099529j,\n",
      "              0.22667425+0.44617923j,  0.45538364+0.13596602j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51130008+0.00386522j]\n",
      " [-0.48932562+0.15099529j]\n",
      " [ 0.22667425+0.44617923j]\n",
      " [ 0.45538364+0.13596602j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28987014+0.j         -0.08467751-0.09196289j]\n",
      " [-0.08467751+0.09196289j  0.24250643+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27808812+0.j         -0.08571964+0.09326747j]\n",
      " [-0.08571964-0.09326747j  0.25428845+0.j        ]]\n",
      "0.9352468635805207\n",
      "Statevector([ 0.51139466+0.00386893j, -0.48917853+0.15103315j,\n",
      "              0.22655919+0.44613999j,  0.45549271+0.13605262j],\n",
      "            dims=(2, 2))\n",
      "KET=   Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket\n",
      "Qobj data =\n",
      "[[ 0.51139466+0.00386893j]\n",
      " [-0.48917853+0.15103315j]\n",
      " [ 0.22655919+0.44613999j]\n",
      " [ 0.45549271+0.13605262j]]\n",
      "value of n 0 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.28982708+0.j         -0.08468156-0.09192855j]\n",
      " [-0.08468156+0.09192855j  0.24253485+0.j        ]]\n",
      "value of n 1 PTrace:  Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.27809039+0.j        -0.08568438+0.0932594j]\n",
      " [-0.08568438-0.0932594j  0.25427154+0.j       ]]\n",
      "0.9352761470187869\n"
     ]
    }
   ],
   "source": [
    "from libraries.meyer_wallach_measure import compute_Q_ptrace\n",
    "mw_entropy = []\n",
    "epochs = [x for x in range(len(param_array))]\n",
    "for i in range(len(param_array)):\n",
    "    x_list = np.asarray([[0.5, 0.9]])\n",
    "    for x in x_list:\n",
    "        circ_ = circuit.assign_parameters(get_data_dict(np.array(param_array[i]), x))\n",
    "        qc = sv.evolve(circ_)\n",
    "        print(qc)\n",
    "        k = np.array(list(qc.to_dict().values()))\n",
    "  \n",
    "    \n",
    "    \n",
    "    mw_val = compute_Q_ptrace(k, 2)\n",
    "    print(mw_val)\n",
    "    mw_entropy.append(mw_val)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "----------------------------------------------------\n",
      "Data point:  [6.03185789 1.75929189]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6371296776445223, 'B': 0.36287032235547767}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [2.76460154 4.1469023 ]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.7245564219880569, 'B': 0.2754435780119432}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.52920307 0.12566371]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.5167446580353187, 'B': 0.48325534196468134}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [2.76460154 4.33539786]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.725650478670102, 'B': 0.274349521329898}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.90619419 1.82212374]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6586879715483345, 'B': 0.34131202845166564}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [0.75398224 5.96902604]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.7143204706071118, 'B': 0.28567952939288827}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [4.20973416 2.57610598]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.8246755006393902, 'B': 0.17532449936060984}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [3.70707933 2.63893783]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.7803990092014446, 'B': 0.21960099079855547}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.96902604 1.82212374]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6756464118490568, 'B': 0.32435358815094323}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [2.0106193 6.1575216]\n",
      "Label:  A\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.4889979256119784, 'B': 0.5110020743880215}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.40353936 0.18849556]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.5672338631921885, 'B': 0.43276613680781173}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [3.0787608  2.19911486]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6827752808052313, 'B': 0.3172247191947687}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [6.09468975 5.02654825]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6883462682178134, 'B': 0.31165373178218647}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.90619419 6.1575216 ]\n",
      "Label:  A\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.2796513269363199, 'B': 0.7203486730636801}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [0.06283185 1.00530965]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.7634452262065474, 'B': 0.23655477379345258}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.71769863 0.56548668]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6529079199223995, 'B': 0.3470920800776004}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.46637122 4.33539786]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.5965434250359424, 'B': 0.4034565749640575}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [2.51327412 4.20973416]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.637125013738283, 'B': 0.362874986261717}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [1.25663706 5.2150438 ]\n",
      "Label:  A\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.658671804479251, 'B': 0.3413281955207489}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [1.25663706 4.58672527]\n",
      "Label:  A\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.24588018750420662, 'B': 0.7541198124957935}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.59203492 5.71769863]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.28031134194449003, 'B': 0.71968865805551}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [0.69115038 3.89557489]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.2892192686700662, 'B': 0.7107807313299338}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.46637122 1.13097336]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.694347593861242, 'B': 0.305652406138758}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.02654825 4.1469023 ]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6095740087414102, 'B': 0.3904259912585898}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [4.46106157 0.        ]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.7290562397627246, 'B': 0.2709437602372754}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [2.70176968 2.63893783]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.31778816898857326, 'B': 0.6822118310114268}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.46637122 2.136283  ]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.13612665448822386, 'B': 0.8638733455117761}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.0893801  0.25132741]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.7367128620820742, 'B': 0.26328713791792585}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [3.70707933 0.69115038]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.13647286689406846, 'B': 0.8635271331059317}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [1.13097336 0.31415927]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.3631368056958541, 'B': 0.636863194304146}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.34070751 1.69646003]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.33120767205054086, 'B': 0.6687923279494591}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [2.38761042 0.81681409]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6990111698870909, 'B': 0.3009888301129091}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [3.64424748 3.64424748]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.40014790495534946, 'B': 0.5998520950446506}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.59203492 4.77522083]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.48080255056141874, 'B': 0.5191974494385813}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [3.64424748 1.38230077]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.4446524722007151, 'B': 0.555347527799285}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.27787566 0.9424778 ]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.7683507996118972, 'B': 0.23164920038810274}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [5.34070751 0.31415927]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.6489835743326862, 'B': 0.35101642566731384}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [4.58672527 4.71238898]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.3469484843631712, 'B': 0.6530515156368286}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [0.81681409 3.14159265]\n",
      "Label:  B\n",
      "Assigned:  A\n",
      "Probabilities:  {'A': 0.5010373741705093, 'B': 0.49896262582949075}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:  [2.45044227 5.2150438 ]\n",
      "Label:  B\n",
      "Assigned:  B\n",
      "Probabilities:  {'A': 0.30484129760738077, 'B': 0.6951587023926193}\n",
      "Classification: CORRECT\n",
      "\n",
      "72.5 % of the test data was correctly classified!\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# collect coordinates of test data\n",
    "test_label_0_x = [x[0] for x in test_input[class_labels[0]]]\n",
    "test_label_0_y = [x[1] for x in test_input[class_labels[0]]]\n",
    "test_label_1_x = [x[0] for x in test_input[class_labels[1]]]\n",
    "test_label_1_y = [x[1] for x in test_input[class_labels[1]]]\n",
    "# initialize lists for misclassified datapoints\n",
    "test_label_misclassified_x = []\n",
    "test_label_misclassified_y = []\n",
    "\n",
    "# evaluate test data\n",
    "for label, samples in test_input.items():\n",
    "    # classify samples\n",
    "    results = classify(samples, opt_params, class_labels)\n",
    "    # analyze results\n",
    "    for i, result in enumerate(results):\n",
    "        # assign label\n",
    "        assigned_label = class_labels[np.argmax([p for p in result.values()])]\n",
    "        print('----------------------------------------------------')\n",
    "        print('Data point: ', samples[i])\n",
    "        print('Label: ', label)\n",
    "        print('Assigned: ', assigned_label)\n",
    "        print('Probabilities: ', result)\n",
    "        if label != assigned_label:\n",
    "            print('Classification:', 'INCORRECT')\n",
    "            test_label_misclassified_x += [samples[i][0]]\n",
    "            test_label_misclassified_y += [samples[i][1]]\n",
    "        else:\n",
    "            print('Classification:', 'CORRECT')\n",
    "# compute fraction of misclassified samples\n",
    "total = len(test_label_0_x) + len(test_label_1_x)\n",
    "num_misclassified = len(test_label_misclassified_x)\n",
    "print()\n",
    "print(100*(1-num_misclassified/total), \"% of the test data was correctly classified!\")\n",
    "# plot results\n",
    "plt.figure()\n",
    "plt.scatter(test_label_0_x, test_label_0_y, c='b', label=class_labels[0], linewidths=5)\n",
    "plt.scatter(test_label_1_x, test_label_1_y, c='g', label=class_labels[1], linewidths=5)\n",
    "plt.scatter(test_label_misclassified_x, test_label_misclassified_y, linewidths=20, s=1, facecolors='none',\n",
    "edgecolors='r')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## Plotting the results obtained"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "### Number of epochs vs the loss function"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Loss Function')\n",
    "plt.title('Cost Function')\n",
    "plt.plot(epochs, loss_function_values[0:48], color='tab:blue')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Number of epochs vs the von-Neumann entropy measure"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('von Neumann Entropy')\n",
    "plt.title('S(X)')\n",
    "plt.plot(epochs, vn_entropy, color='tab:blue')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Number of epochs vs the Meyer Wallach entropy measure"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Meyer Wallach Entropy')\n",
    "plt.title('S(X)')\n",
    "plt.plot(epochs, mw_entropy, color='tab:green')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Loss Function vs the von-Neumann entropy measure"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.xlabel('Loss Function')\n",
    "plt.ylabel('von Neumann Entropy')\n",
    "plt.title('vN entropy vs loss')\n",
    "plt.plot( loss_function_values[0:191:2], vn_entropy, color='tab:blue')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Loss function vs the Meyer-Wallach entropy measure"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.xlabel('Loss Function')\n",
    "plt.ylabel('Meyer Wallach Entropy')\n",
    "plt.title('meyer Wallach vs loss')\n",
    "plt.plot( loss_function_values[0:48], mw_entropy, color='tab:blue')\n",
    "plt.show()"
   ]
  }
 ]
}