qsvm_classification.ipynb

{
 "cells": [
  {
   "attachments": {
    "qiskit_header.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![qiskit_header.png](attachment:qiskit_header.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Qiskit Aqua: Experiment with classification problem with quantum-enhanced support vector machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction\n",
    "Classification algorithms and methods for machine learning are essential for pattern recognition and data mining applications. Well known techniques such as support vector machines and neural networks have blossomed over the last two decades as a result of the spectacular advances in classical hardware computational capabilities and speed. This progress in computer power made it possible to apply techniques, that were theoretically developed towards the middle of the 20th century, on classification problems that were becoming increasingly challenging.\n",
    "\n",
    "A key concept in classification methods is that of a kernel. Data cannot typically be separated by a hyperplane in its original space. A common technique used to find such a hyperplane consists of applying a non-linear transformation function to the data. This function is called a feature map, as it transforms the raw features, or measurable properties, of the phenomenon or subject under study. Classifying in this new feature space -and, as a matter of fact, also in any other space, including the raw original one- is nothing more than seeing how close data points are to each other. This is the same as computing the inner product for each pair of data points in the set. So, in fact we do not need to compute the non-linear feature map for each datum, but only the inner product of each pair of data points in the new feature space. This collection of inner products is called the kernel and it is perfectly possible to have feature maps that are hard to compute but whose kernels are not.\n",
    "\n",
    "In this notebook we provide an example of a classification problem that requires a feature map for which computing the kernel is not efficient classically -this means that the required computational resources are expected to scale exponentially with the size of the problem. We show how this can be solved in a quantum processor by a direct estimation of the kernel in the feature space. The method we used falls in the category of what is called supervised learning, consisting of a training phase (where the kernel is calculated and the support vectors obtained) and a test or classification phase (where new unlabeled data is classified according to the solution found in the training phase).\n",
    "\n",
    "References and additional details:\n",
    "\n",
    "[1] Vojtech Havlicek, Antonio D. C´orcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta1, \"Supervised learning with quantum enhanced feature spaces,\" [arXiv: 1804.11326](https://arxiv.org/pdf/1804.11326.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:49:29.493476Z",
     "start_time": "2019-12-12T15:49:25.657600Z"
    }
   },
   "outputs": [],
   "source": [
    "from datasets import *\n",
    "\n",
    "from qiskit import Aer\n",
    "from qiskit.aqua.utils import split_dataset_to_data_and_labels, map_label_to_class_name\n",
    "from qiskit.aqua.input import ClassificationInput\n",
    "from qiskit.aqua import run_algorithm, QuantumInstance\n",
    "from qiskit.aqua.algorithms import QSVM\n",
    "from qiskit.aqua.components.feature_maps import SecondOrderExpansion\n",
    "\n",
    "# setup aqua logging\n",
    "import logging\n",
    "from qiskit.aqua import set_qiskit_aqua_logging\n",
    "# set_qiskit_aqua_logging(logging.DEBUG)  # choose INFO, DEBUG to see the log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Optional] Setup token to run the experiment on a real device\n",
    "If you would like to run the experiment on a real device, you need to setup your account first.\n",
    "\n",
    "Note: If you do not store your token yet, use `IBMQ.save_account('MY_API_TOKEN')` to store it first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:49:29.521460Z",
     "start_time": "2019-12-12T15:49:29.511839Z"
    }
   },
   "outputs": [],
   "source": [
    "# from qiskit import IBMQ\n",
    "# provider = IBMQ.load_account()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we prepare the dataset, which is used for training, testing and the final prediction.\n",
    "\n",
    "*Note: You can easily switch to a different dataset, such as the Breast Cancer dataset, by replacing 'ad_hoc_data' to 'Breast_cancer' below.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:49:39.455533Z",
     "start_time": "2019-12-12T15:49:29.543659Z"
    }
   },
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'A': 0, 'B': 1}\n"
     ]
    }
   ],
   "source": [
    "feature_dim=2 # we support feature_dim 2 or 3\n",
    "sample_Total, training_input, test_input, class_labels = ad_hoc_data(\n",
    "    training_size=20, \n",
    "    test_size=10, \n",
    "    n=feature_dim, \n",
    "    gap=0.3, \n",
    "    PLOT_DATA=True\n",
    ")\n",
    "extra_test_data = sample_ad_hoc_data(sample_Total, 10, n=feature_dim)\n",
    "datapoints, class_to_label = split_dataset_to_data_and_labels(extra_test_data)\n",
    "print(class_to_label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the dataset ready we initialize the necessary inputs for the algorithm:\n",
    "- the input dictionary (params) \n",
    "- the input object containing the dataset info (algo_input).\n",
    "\n",
    "With everything set up, we can now run the algorithm.\n",
    "\n",
    "For the testing, the result includes the details and the success ratio.\n",
    "\n",
    "For the prediction, the result includes the predicted labels. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:51:08.407289Z",
     "start_time": "2019-12-12T15:51:08.213734Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "testing success ratio: 0.95\n",
      "preduction of datapoints:\n",
      "ground truth: ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n",
      "prediction:   ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']\n"
     ]
    }
   ],
   "source": [
    "seed = 10598\n",
    "\n",
    "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entanglement='linear')\n",
    "qsvm = QSVM(feature_map, training_input, test_input, datapoints[0])\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "quantum_instance = QuantumInstance(backend, shots=1024, seed_simulator=seed, seed_transpiler=seed)\n",
    "\n",
    "result = qsvm.run(quantum_instance)\n",
    "\n",
    "\"\"\"declarative approach\n",
    "params = {\n",
    "    'problem': {'name': 'classification', 'random_seed': 10598},\n",
    "    'algorithm': {\n",
    "        'name': 'QSVM'\n",
    "    },\n",
    "    'backend': {'provider': 'qiskit.Aer', 'name': 'qasm_simulator', 'shots': 1024},\n",
    "    'feature_map': {'name': 'SecondOrderExpansion', 'depth': 2, 'entanglement': 'linear'}\n",
    "}\n",
    "algo_input = ClassificationInput(training_input, test_input, datapoints[0])\n",
    "result = run_algorithm(params, algo_input)\n",
    "\"\"\"\n",
    "\n",
    "print(\"testing success ratio: {}\".format(result['testing_accuracy']))\n",
    "print(\"preduction of datapoints:\")\n",
    "print(\"ground truth: {}\".format(map_label_to_class_name(datapoints[1], qsvm.label_to_class)))\n",
    "print(\"prediction:   {}\".format(result['predicted_classes']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:50:38.389886Z",
     "start_time": "2019-12-12T15:49:29.079Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kernel matrix during the training:\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": [
    "print(\"kernel matrix during the training:\")\n",
    "kernel_matrix = result['kernel_matrix_training']\n",
    "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The breast cancer dataset\n",
    "Now we run our algorithm with the real-world dataset: the breast cancer dataset, we use the first two principal components as features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:50:38.395382Z",
     "start_time": "2019-12-12T15:49:29.986Z"
    }
   },
   "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": [
    "sample_Total, training_input, test_input, class_labels = Breast_cancer(\n",
    "    training_size=20,\n",
    "    test_size=10,\n",
    "    n=2,\n",
    "    PLOT_DATA=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:50:38.400460Z",
     "start_time": "2019-12-12T15:49:30.364Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "testing success ratio:  0.85\n"
     ]
    }
   ],
   "source": [
    "seed = 10598\n",
    "\n",
    "feature_map = SecondOrderExpansion(feature_dimension=feature_dim, depth=2, entanglement='linear')\n",
    "qsvm = QSVM(feature_map, training_input, test_input)\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "quantum_instance = QuantumInstance(backend, shots=1024, seed_simulator=seed, seed_transpiler=seed)\n",
    "\n",
    "result = qsvm.run(quantum_instance)\n",
    "\n",
    "\"\"\"declarative approach, re-use the params above\n",
    "algo_input = ClassificationInput(training_input, test_input)\n",
    "result = run_algorithm(params, algo_input)\n",
    "\"\"\"\n",
    "print(\"testing success ratio: \", result['testing_accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:50:38.406132Z",
     "start_time": "2019-12-12T15:49:30.848Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kernel matrix during the training:\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": [
    "print(\"kernel matrix during the training:\")\n",
    "kernel_matrix = result['kernel_matrix_training']\n",
    "img = plt.imshow(np.asmatrix(kernel_matrix),interpolation='nearest',origin='upper',cmap='bone_r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T15:50:38.410937Z",
     "start_time": "2019-12-12T15:49:31.209Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>0.14.0</td></tr><tr><td>Terra</td><td>0.11.0</td></tr><tr><td>Aer</td><td>0.3.4</td></tr><tr><td>Ignis</td><td>0.2.0</td></tr><tr><td>Aqua</td><td>0.6.1</td></tr><tr><td>IBM Q Provider</td><td>0.4.4</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.6.9 |Anaconda, Inc.| (default, Jul 30 2019, 19:07:31) \n",
       "[GCC 7.3.0]</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>2</td></tr><tr><td>Memory (Gb)</td><td>7.682933807373047</td></tr><tr><td colspan='2'>Wed Dec 18 08:05:58 2019 CET</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>&copy; Copyright IBM 2017, 2019.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
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   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
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