quantum_variational_classifier.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Quantum Variational Classifier\n",
    "\n",
    "This tutorial discusses how a quantum computer can be used to solve a classification task.<br>\n",
    "The example is based on the following paper:\n",
    "<br>\n",
    "<br>\n",
    "<b>Supervised learning with quantum enhanced feature spaces</b><br>\n",
    "Vojtech Havlicek, Antonio D. Corcoles, Kristan Temme, Aram W. Harrow, Abhinav  Kandala, Jerry M. Chow, and Jay  M. Gambetta<br>\n",
    "<a href=\"https://arxiv.org/abs/1804.11326\">arXiv:1804.11326 (2018)</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from svm.datasets import *\n",
    "from qiskit.aqua.input import ClassificationInput\n",
    "from qiskit.aqua import run_algorithm\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from qiskit import Aer, execute\n",
    "from qiskit.aqua.components.optimizers.cobyla import COBYLA\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "Before we can train the Quantum Variational Classifier, we have to load the data set that we are interested in and split it into a training and a test set.\n",
    "<br>\n",
    "Note that the ad hoc data set is constructed suitably for the purpose of illustration.\n",
    "<br>\n",
    "<br>\n",
    "<b>Exercise:</b><br>\n",
    "Feel free to train and test the classifier with the alternatively given training data set:<br>\n",
    "<a href=\"https://archive.ics.uci.edu/ml/datasets/wine\">UCI Machine Learning Repository - Wine Data Set</a><br>\n",
    "To switch between the data sets set the <b>use_adhoc_dataset</b> to True or False."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# size of training data set\n",
    "training_size = 20\n",
    "\n",
    "# size of test data set\n",
    "test_size = 10\n",
    "\n",
    "# dimension of data sets\n",
    "n = 2\n",
    "\n",
    "# construct training and test data\n",
    "# set the following flag to True for the first data set and to False for the second dataset\n",
    "use_adhoc_dataset = True\n",
    "if use_adhoc_dataset:\n",
    "    # first (artifical) data set to test the classifier\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=True)\n",
    "else:\n",
    "    # second data set to test the classifier\n",
    "    training_input, test_input, class_labels = \\\n",
    "            Wine(training_size=training_size, test_size=test_size, n=n, plot_data=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Feature Map\n",
    "\n",
    "The Quantum Feature Map $\\cal{U}_{\\Phi(\\vec{x})}$ is a quantum circuit parametrized by a classical input datapoint $\\vec{x}$.\n",
    "Thus, $\\cal{U}$ maps $\\vec{x}$ to the quantum feature space whose dimension is exponential in the number of qubits.\n",
    "In this tutorial we use the following quantum feature map:\n",
    "<img src=\"svm/feature_map.png\">\n",
    "<br>\n",
    "where\n",
    "### $$U_{\\Phi(\\vec{x})} = e^{i\\left(x_1 Z \\otimes I + x_2 I \\otimes Z + x_1x_2Z \\otimes Z \\right)}$$\n",
    "\n",
    "The classical data sample $\\vec{x}$ is loaded by applying the Quantum Feature Map onto the initial quantum state $|0{\\rangle}^{\\otimes n}$:\n",
    "### $$|\\phi(\\vec{x})\\rangle = \\cal{U}_{\\Phi(\\vec{x})}|0{\\rangle}^{\\otimes n}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def feature_map(x, q):\n",
    "    \n",
    "    # initialize quantum circuit\n",
    "    qc = QuantumCircuit(q)\n",
    "    \n",
    "    # apply hadamards and U_Phi twice\n",
    "    for _ in range(2):\n",
    "        \n",
    "        # apply the hadamard and Z-rotatiion to all qubits\n",
    "        for i in range(x.shape[0]):\n",
    "            qc.h(q[i])\n",
    "            qc.rz(2 * x[i], q[i])\n",
    "        \n",
    "        # apply the two qubit gate\n",
    "        qc.cx(q[0], q[1])\n",
    "        qc.rz(2*(np.pi-x[0])*(np.pi-x[1]), q[1])\n",
    "        qc.cx(q[0], q[1])\n",
    "\n",
    "    # return quantum circuit\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now use a classical vector, for instance $\\begin{pmatrix} 1.5 \\\\ 0.3 \\end{pmatrix}$ to apply the quantum feature map onto the quantum state $|0{\\rangle}^{\\otimes 2}$, analyze the resulting statevector and plot the corresponding quantum circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "simulation:  Result(backend_name='statevector_simulator', backend_version='0.3.0', date=datetime.datetime(2019, 8, 24, 12, 2, 46, 689335), header=Obj(backend_name='statevector_simulator', backend_version='0.3.0'), job_id='50e6e260-cb3b-4d7a-869e-285a116a64e8', metadata={'max_memory_mb': 8103, 'omp_enabled': True, 'parallel_experiments': 1, 'time_taken': 0.0002005}, qobj_id='09bfa60f-f4b7-493c-877f-39f29e53c2ed', results=[ExperimentResult(data=ExperimentResultData(statevector=[(0.049997991887651305-0.29018719299670587j), (0.023359416632460876+0.0441673605792097j), (-0.7357557507445133-0.6039081802139161j), (0.029046334407502893-0.06252896382105116j)]), header=Obj(clbit_labels=[], creg_sizes=[], memory_slots=0, n_qubits=2, name='circuit0', qreg_sizes=[['q0', 2]], qubit_labels=[['q0', 0], ['q0', 1]]), meas_level=2, metadata={'parallel_shots': 1, 'parallel_state_update': 8}, seed_simulator=3530234561, shots=1, status='DONE', success=True, time_taken=7.96e-05)], status='COMPLETED', success=True, time_taken=0.0010178089141845703)\n",
      "statevector:  [ 0.05  -0.2902j  0.0234+0.0442j -0.7358-0.6039j  0.029 -0.0625j]\n"
     ]
    }
   ],
   "source": [
    "# initialize quantum register\n",
    "num_qubits = 2\n",
    "qr = QuantumRegister(num_qubits)\n",
    "\n",
    "# initialize test data (x1, x2)\n",
    "data = np.asarray([1.5, 0.3])\n",
    "\n",
    "# get quantum circuit\n",
    "qc_feature_map = feature_map(data, qr)\n",
    "# simulate using local statevector simulator\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "\n",
    "job_sim = execute(qc_feature_map, backend)\n",
    "sim_results = job_sim.result()\n",
    "print('simulation: ', sim_results)\n",
    "print('statevector: ', np.round(sim_results.get_statevector(), decimals=4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 769.356x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# draw circuit\n",
    "qc_feature_map.draw(output='mpl', plot_barriers=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variational Form\n",
    "\n",
    "The variational form is similar to an artifical neural network:\n",
    "<br>\n",
    "The quantum circuit receives input data, processes it through multiple layers of  parametrized quantum gates and is trained by adjusting the parameters (weights).\n",
    "<br>\n",
    "It should be noted that in order to optimize the parameters, the outcome of the Quantum Variational Circuit must be measured. The measurement outcome corresponds to classical bits which can be integrated in an optimization algorithm, such as gradient descent. \n",
    "<br>\n",
    "<br>\n",
    "In this tutorial we use the following Variational Form:\n",
    "<br>\n",
    "<img src=\"svm/variational_form.png\">\n",
    "<br>\n",
    "The single qubit rotations denoted by $\\theta_{i,j}$ correspond to Z-rotations and Y-rotations and the entangler block $U_{ent}$ consists of controlled-Z gates.\n",
    "Further, the parameter $d$ denotes the depth of the Variational Circuit, i.e. the number of repitions of entangler blocks and single qubit rotation layers.\n",
    "<br>\n",
    "<br>\n",
    "<b>Exercise:</b><br>\n",
    "See how the classification performance changes when you modify the types of gates used within the quantum circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def variational_form(q, params, depth):\n",
    "    \n",
    "    # initialize quantum circuit\n",
    "    qc = QuantumCircuit(q)\n",
    "    \n",
    "    # first set of rotations\n",
    "    param_idx = 0\n",
    "    for qubit in range(2):\n",
    "        qc.ry(params[param_idx], q[qubit])\n",
    "        qc.rz(params[param_idx+1], q[qubit])\n",
    "        param_idx += 2\n",
    "\n",
    "    # entangler blocks and succeeding rotations\n",
    "    for block in range(depth):\n",
    "        qc.cz(q[0], q[1])\n",
    "        for qubit in range(2):\n",
    "            qc.ry(params[param_idx], q[qubit])\n",
    "            qc.rz(params[param_idx+1], q[qubit])\n",
    "            param_idx += 2\n",
    "    \n",
    "    # return quantum circuit\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "simulation:  Result(backend_name='statevector_simulator', backend_version='0.3.0', date=datetime.datetime(2019, 8, 24, 12, 2, 47, 238870), header=Obj(backend_name='statevector_simulator', backend_version='0.3.0'), job_id='9d817174-0488-4179-85cd-44b2ae2f7d8e', metadata={'max_memory_mb': 8103, 'omp_enabled': True, 'parallel_experiments': 1, 'time_taken': 0.0001969}, qobj_id='725cfccf-bbd5-433c-88af-6dcabb954e0b', results=[ExperimentResult(data=ExperimentResultData(statevector=[(0.716619589106532+0.04833322141870618j), (0.5354679702552034-0.37159438291186925j), (0.07245703062900394+0.22730968702723042j), (0.045470046956351914+0.018019194238159317j)]), header=Obj(clbit_labels=[], creg_sizes=[], memory_slots=0, n_qubits=2, name='circuit2', qreg_sizes=[['q1', 2]], qubit_labels=[['q1', 0], ['q1', 1]]), meas_level=2, metadata={'parallel_shots': 1, 'parallel_state_update': 8}, seed_simulator=1640106043, shots=1, status='DONE', success=True, time_taken=5.96e-05)], status='COMPLETED', success=True, time_taken=0.0030269622802734375)\n",
      "statevector:  [0.7166+0.0483j 0.5355-0.3716j 0.0725+0.2273j 0.0455+0.018j ]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648.956x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initialize quantum register\n",
    "num_qubits = 2\n",
    "qr = QuantumRegister(num_qubits)\n",
    "\n",
    "# set depth, i.e. number of entangler blocks and rotations (after the initial rotation)\n",
    "depth = 2\n",
    "params = [0.5,-0.3, 0.2, 0.6]*(depth+1)\n",
    "qc_variational_form = variational_form(qr, params, depth)\n",
    "\n",
    "# simulate using local statevector simulator\n",
    "job_sim = execute(qc_variational_form, backend)\n",
    "sim_results = job_sim.result()\n",
    "print('simulation: ', sim_results)\n",
    "print('statevector: ', np.round(sim_results.get_statevector(), decimals=4))\n",
    "\n",
    "# draw circuit\n",
    "qc_variational_form.draw(output='mpl', plot_barriers=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Quantum Variational Classifier\n",
    "\n",
    "Before we can combine the previously introduced components to the quantum variational classifier, we need to introduce some more helper functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.  Assign a label to the measurement outcome \n",
    "We use the parity function to assign a class label to the measurement outcomes which are given as bit strings. In explicit, a measurement consisting of an even number of '1's is mapped to the first class, and a measurement outcome consisting of an odd number of '1's is mapped to the second class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'B'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# assigns a label \n",
    "assign_label('01', class_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Map the counts of multiple shots to probabilities for the classes\n",
    "After running the same circuit many times, we derive the empirical probabilities of assigning the first or second class.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.5, 'B': 0.5}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "return_probabilities({'00' : 10, '01': 10}, class_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Combine everything to build the classifier\n",
    "We combine the feature map, the variational circuit, and the label assignment to construct our (untrained) classifier.\n",
    "<br>\n",
    "Note that the classifier is already constructed in such a way that it is able to process a list of data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def classifier_circuit(x, params, depth):\n",
    "    \n",
    "    q = QuantumRegister(2)\n",
    "    c = ClassicalRegister(2)\n",
    "    qc = QuantumCircuit(q, c)\n",
    "\n",
    "    qc_feature_map = feature_map(x, q)\n",
    "    qc_variational_form = variational_form(q, params, depth)\n",
    "\n",
    "    qc += qc_feature_map\n",
    "    qc += qc_variational_form\n",
    "\n",
    "    qc.measure(q, c)\n",
    "    \n",
    "    return qc\n",
    "\n",
    "def classify(x_list, params, class_labels, depth=2, shots=100):\n",
    "    \n",
    "    qc_list = []\n",
    "    for x in x_list:\n",
    "        qc = classifier_circuit(x, params, depth)\n",
    "        qc_list += [qc]\n",
    "    qasm_backend = Aer.get_backend('qasm_simulator')    \n",
    "    jobs = execute(qc_list, qasm_backend, shots=shots)\n",
    "    \n",
    "    probs = []\n",
    "    for qc in qc_list:\n",
    "        counts = jobs.result().get_counts(qc)\n",
    "        prob = return_probabilities(counts, class_labels)\n",
    "        probs += [prob]\n",
    "            \n",
    "    return probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1371.36x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# draw classifier circuit\n",
    "qc = classifier_circuit(np.asarray([0.5, 0.5]), params, depth)\n",
    "\n",
    "\n",
    "# classify test data point (using random parameters constructed earlier)\n",
    "x = np.asarray([[0.5, 0.5]])\n",
    "classify(x, params, class_labels, depth)\n",
    "\n",
    "qc.draw(output='mpl', plot_barriers=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Assign a cost value to the estimation probabilities\n",
    "Given a training data point and the corresponding training class label, we can calculate a cost value which represents the probability of correct/false classification. \n",
    "<br>\n",
    "We only need a singificant bias towards the correct classification and, thus, use the sigmoid function to evaluate the cost value (error probability).<br>\n",
    "The function is close to zero if the probability of assigning the correct class is close to one, and close to one otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_estimate_sigmoid(probs, expected_label):\n",
    "\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",
    "\n",
    "    return sig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "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()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Evaluate the overall performance for the training set\n",
    "We compute the average cost value over all training data points and use this as the objective function to train our classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def cost_function(training_input, class_labels, params, depth=2, shots=100, print_value=False):\n",
    "    \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",
    "        \n",
    "    # classify all samples\n",
    "    probs = classify(training_samples, params, class_labels, depth)\n",
    "    \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",
    "    \n",
    "    # print resulting objective function\n",
    "    if print_value:\n",
    "        print('%.4f' % cost)\n",
    "    \n",
    "    # return objective value\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5174701439112291"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_function(training_input, class_labels, params, depth)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train the classifier\n",
    "\n",
    "Training the classifier corresponds to an optimization task. Explicitly, we want to minimize the cost value (sigmoid function) such that the classifier manages to properly label the given data.\n",
    "<br>\n",
    "<br>\n",
    "<b>Exercise:</b><br>\n",
    "See how the classification performance changes when you modify the depth of the variational form, the number of shots or number of trials.<br>\n",
    "What's the best that you can achieve for the adhoc data set and the Wine data set?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4976\n",
      "0.5419\n",
      "0.5018\n",
      "0.3947\n",
      "0.3869\n",
      "0.2150\n",
      "0.3162\n",
      "0.2457\n",
      "0.3052\n",
      "0.4130\n",
      "0.2616\n",
      "0.1266\n",
      "0.1364\n",
      "0.3340\n",
      "0.1683\n",
      "0.4126\n",
      "0.1147\n",
      "0.1227\n",
      "0.1361\n",
      "0.1874\n",
      "0.1141\n",
      "0.1547\n",
      "0.2002\n",
      "0.1543\n",
      "0.1448\n",
      "0.1681\n",
      "0.1896\n",
      "0.1340\n",
      "0.1622\n",
      "0.1612\n",
      "0.1540\n",
      "0.1260\n",
      "0.1534\n",
      "0.1107\n",
      "0.1258\n",
      "0.1292\n",
      "0.1078\n",
      "0.0956\n",
      "0.0949\n",
      "0.1003\n",
      "0.1027\n",
      "0.0960\n",
      "0.1339\n",
      "0.0820\n",
      "0.0762\n",
      "0.0727\n",
      "0.0898\n",
      "0.0624\n",
      "0.0824\n",
      "0.0494\n",
      "0.0612\n",
      "0.0619\n",
      "0.0730\n",
      "0.0627\n",
      "0.0627\n",
      "0.0750\n",
      "0.0593\n",
      "0.0719\n",
      "0.0646\n",
      "0.0730\n",
      "0.0718\n",
      "0.0648\n",
      "0.0716\n",
      "0.0750\n",
      "0.0572\n",
      "0.0737\n",
      "0.0718\n",
      "0.0632\n",
      "0.0741\n",
      "0.0838\n",
      "0.0688\n",
      "0.0686\n",
      "0.0572\n",
      "0.0605\n",
      "0.0687\n",
      "0.0777\n",
      "0.0696\n",
      "0.0700\n",
      "0.0762\n",
      "0.0759\n",
      "0.0651\n",
      "0.0721\n",
      "0.0776\n",
      "0.0657\n",
      "0.0616\n",
      "0.0698\n",
      "0.0736\n",
      "0.0653\n",
      "0.0576\n",
      "0.0787\n",
      "0.0687\n",
      "0.0666\n",
      "0.0733\n",
      "0.0590\n",
      "0.0845\n",
      "0.0714\n",
      "0.0628\n",
      "0.0561\n",
      "0.0767\n",
      "0.0558\n",
      "0.0792\n",
      "0.0630\n",
      "0.0677\n",
      "0.0719\n",
      "0.0758\n",
      "0.0620\n",
      "0.0850\n",
      "0.0671\n",
      "0.0667\n",
      "0.0584\n",
      "0.0628\n",
      "0.0799\n",
      "0.0628\n",
      "0.0691\n",
      "0.0748\n",
      "0.0766\n",
      "0.0892\n",
      "0.0677\n",
      "\n",
      "opt_params: [0.46537684 3.01203121 3.34499308 6.60826593 1.88255287 3.77234427\n",
      " 4.68233135 3.95397507 0.90662879 6.19788929 3.03135655 3.72127197]\n",
      "opt_value:  0.06769543701480436\n"
     ]
    }
   ],
   "source": [
    "# set depth of variational form\n",
    "depth = 2\n",
    "\n",
    "# set number of shots to evaluate the classification circuit\n",
    "shots = 100\n",
    "\n",
    "# setup the optimizer\n",
    "optimizer = COBYLA()\n",
    "\n",
    "# define objective function for training\n",
    "objective_function = lambda params: cost_function(training_input, class_labels, params, depth, shots, print_value=True)\n",
    "\n",
    "# randomly initialize the parameters\n",
    "init_params = 2*np.pi*np.random.rand(num_qubits*(depth+1)*2)\n",
    "\n",
    "# train classifier\n",
    "opt_params, value, _ = optimizer.optimize(len(init_params), objective_function, initial_point=init_params)\n",
    "\n",
    "# print results\n",
    "print()\n",
    "print('opt_params:', opt_params)\n",
    "print('opt_value: ', value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test the trained classifier\n",
    "\n",
    "To check how well we could train the classifier, we evaluate the classification performance on the test data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------------------------\n",
      "Data point:     [6.1575216  1.88495559]\n",
      "Label:          A\n",
      "Assigned:       A\n",
      "Probabilities:  {'A': 0.57, 'B': 0.43000000000000005}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [3.70707933 3.26725636]\n",
      "Label:          A\n",
      "Assigned:       A\n",
      "Probabilities:  {'A': 0.52, 'B': 0.48000000000000004}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [0.25132741 5.71769863]\n",
      "Label:          A\n",
      "Assigned:       A\n",
      "Probabilities:  {'A': 0.96, 'B': 0.04}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [2.57610598 4.46106157]\n",
      "Label:          A\n",
      "Assigned:       A\n",
      "Probabilities:  {'A': 0.5, 'B': 0.5}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [5.59203492 0.37699112]\n",
      "Label:          A\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.45999999999999996, 'B': 0.54}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [5.46637122 0.37699112]\n",
      "Label:          A\n",
      "Assigned:       A\n",
      "Probabilities:  {'A': 0.5, 'B': 0.5}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [2.32477856 3.95840674]\n",
      "Label:          A\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.35, 'B': 0.65}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [3.76991118 2.57610598]\n",
      "Label:          A\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.24, 'B': 0.76}\n",
      "Classification: INCORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [1.50796447 5.40353936]\n",
      "Label:          A\n",
      "Assigned:       A\n",
      "Probabilities:  {'A': 0.77, 'B': 0.22999999999999998}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [2.82743339 6.22035345]\n",
      "Label:          A\n",
      "Assigned:       A\n",
      "Probabilities:  {'A': 0.89, 'B': 0.11}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [5.96902604 4.20973416]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.04, 'B': 0.96}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [4.77522083 1.94778745]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.26, 'B': 0.74}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [1.88495559 3.76991118]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.25, 'B': 0.75}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [4.64955713 0.06283185]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.18, 'B': 0.8200000000000001}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [4.71238898 5.71769863]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.05, 'B': 0.95}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [5.2150438  5.15221195]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.2, 'B': 0.8}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [4.52389342 4.33539786]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.34, 'B': 0.66}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [0.75398224 3.45575192]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.32, 'B': 0.68}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [0.37699112 3.33008821]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.14, 'B': 0.8599999999999999}\n",
      "Classification: CORRECT\n",
      "----------------------------------------------------\n",
      "Data point:     [1.38230077 3.58141563]\n",
      "Label:          B\n",
      "Assigned:       B\n",
      "Probabilities:  {'A': 0.35000000000000003, 'B': 0.65}\n",
      "Classification: CORRECT\n",
      "\n",
      "85.0 % of the test data was correctly classified!\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "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",
    "\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",
    "    \n",
    "    # classify samples \n",
    "    results = classify(samples, opt_params, class_labels, depth, shots=shots)\n",
    "    \n",
    "    # analyze results\n",
    "    for i, result in enumerate(results):\n",
    "        \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",
    "        \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",
    "        \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",
    "\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', edgecolors='r')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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