20220616_quantum_kernel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Kernel Machine Learning\n",
    "\n",
    "\n",
    "Based on [qiskit-tutorials](https://github.com/Qiskit/qiskit-tutorials) with minor modification by Rudy Raymond (rudyhar@jp.ibm.com).\n",
    "Shared at the 36th JSAI on June 17, 2022 in Kyoto. \n",
    "\n",
    "\n",
    "---\n",
    "The general task of machine learning is to find and study patterns in data. For many datasets, the datapoints are better understood in a higher dimensional feature space, through the use of a kernel function:\n",
    "$k(\\vec{x}_i, \\vec{x}_j) = \\langle f(\\vec{x}_i), f(\\vec{x}_j) \\rangle$\n",
    "where $k$ is the kernel function, $\\vec{x}_i, \\vec{x}_j$ are $n$ dimensional inputs, $f$ is a map from $n$-dimension to $m$-dimension space and $\\langle a,b \\rangle$ denotes the dot product. When considering finite data, a kernel function can be represented as a matrix: \n",
    "$K_{ij} = k(\\vec{x}_i,\\vec{x}_j)$.\n",
    "\n",
    "In quantum kernel machine learning, a quantum feature map $\\phi(\\vec{x})$ is used to map a classical feature vector $\\vec{x}$ to a quantum Hilbert space, $| \\phi(\\vec{x})\\rangle \\langle \\phi(\\vec{x})|$, such that $K_{ij} = \\left| \\langle \\phi^\\dagger(\\vec{x}_j)| \\phi(\\vec{x}_i) \\rangle \\right|^{2}$. See [_Supervised learning with quantum enhanced feature spaces_](https://arxiv.org/pdf/1804.11326.pdf) for more details.\n",
    "\n",
    "In this notebook, we use `qiskit` to calculate a kernel matrix using a quantum feature map, then use this kernel matrix in `scikit-learn` classification and clustering algorithms.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.cluster import SpectralClustering\n",
    "from sklearn.metrics import normalized_mutual_info_score\n",
    "\n",
    "from qiskit import BasicAer\n",
    "from qiskit.circuit.library import ZZFeatureMap\n",
    "from qiskit.utils import QuantumInstance, algorithm_globals\n",
    "from qiskit_machine_learning.algorithms import QSVC\n",
    "from qiskit_machine_learning.kernels import QuantumKernel\n",
    "from qiskit_machine_learning.datasets import ad_hoc_data\n",
    "\n",
    "seed = 46\n",
    "algorithm_globals.random_seed = seed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification\n",
    "\n",
    "For our classification example, we will use the _ad hoc dataset_ as described in [_Supervised learning with quantum enhanced feature spaces_](https://arxiv.org/pdf/1804.11326.pdf), and the `scikit-learn` [support vector machine](https://scikit-learn.org/stable/modules/svm.html) classification (`svc`) algorithm. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "adhoc_dimension = 2\n",
    "train_features, train_labels, test_features, test_labels, adhoc_total = ad_hoc_data(\n",
    "    training_size=20,\n",
    "    test_size=5,\n",
    "    n=adhoc_dimension,\n",
    "    gap=0.3,\n",
    "    plot_data=False,\n",
    "    one_hot=False,\n",
    "    include_sample_total=True,\n",
    ")\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.ylim(0, 2 * np.pi)\n",
    "plt.xlim(0, 2 * np.pi)\n",
    "plt.imshow(\n",
    "    np.asmatrix(adhoc_total).T,\n",
    "    interpolation=\"nearest\",\n",
    "    origin=\"lower\",\n",
    "    cmap=\"RdBu\",\n",
    "    extent=[0, 2 * np.pi, 0, 2 * np.pi],\n",
    ")\n",
    "\n",
    "plt.scatter(\n",
    "    train_features[np.where(train_labels[:] == 0), 0],\n",
    "    train_features[np.where(train_labels[:] == 0), 1],\n",
    "    marker=\"s\",\n",
    "    facecolors=\"w\",\n",
    "    edgecolors=\"b\",\n",
    "    label=\"A train\",\n",
    ")\n",
    "plt.scatter(\n",
    "    train_features[np.where(train_labels[:] == 1), 0],\n",
    "    train_features[np.where(train_labels[:] == 1), 1],\n",
    "    marker=\"o\",\n",
    "    facecolors=\"w\",\n",
    "    edgecolors=\"r\",\n",
    "    label=\"B train\",\n",
    ")\n",
    "plt.scatter(\n",
    "    test_features[np.where(test_labels[:] == 0), 0],\n",
    "    test_features[np.where(test_labels[:] == 0), 1],\n",
    "    marker=\"s\",\n",
    "    facecolors=\"b\",\n",
    "    edgecolors=\"w\",\n",
    "    label=\"A test\",\n",
    ")\n",
    "plt.scatter(\n",
    "    test_features[np.where(test_labels[:] == 1), 0],\n",
    "    test_features[np.where(test_labels[:] == 1), 1],\n",
    "    marker=\"o\",\n",
    "    facecolors=\"r\",\n",
    "    edgecolors=\"w\",\n",
    "    label=\"B test\",\n",
    ")\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=\"upper left\", borderaxespad=0.0)\n",
    "plt.title(\"Ad hoc dataset for classification\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With our training and testing datasets ready, we set up the `QuantumKernel` class to calculate a kernel matrix using the [ZZFeatureMap](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html), and the `BasicAer` `qasm_simulator` using 1024 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "adhoc_feature_map = ZZFeatureMap(feature_dimension=adhoc_dimension, reps=2, entanglement=\"linear\")\n",
    "\n",
    "adhoc_backend = QuantumInstance(\n",
    "    BasicAer.get_backend(\"qasm_simulator\"), shots=1024, seed_simulator=seed, seed_transpiler=seed\n",
    ")\n",
    "\n",
    "adhoc_kernel = QuantumKernel(feature_map=adhoc_feature_map, quantum_instance=adhoc_backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `scikit-learn` `svc` algorithm allows us to define a [custom kernel](https://scikit-learn.org/stable/modules/svm.html#custom-kernels) in two ways: by providing the kernel as a callable function or by precomputing the kernel matrix. We can do either of these using the `QuantumKernel` class in `qiskit`.\n",
    "\n",
    "The following code gives the kernel as a callable function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Callable kernel classification test score: 1.0\n"
     ]
    }
   ],
   "source": [
    "adhoc_svc = SVC(kernel=adhoc_kernel.evaluate)\n",
    "adhoc_svc.fit(train_features, train_labels)\n",
    "adhoc_score = adhoc_svc.score(test_features, test_labels)\n",
    "\n",
    "print(f\"Callable kernel classification test score: {adhoc_score}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code precomputes and plots the training and testing kernel matrices before providing them to the `scikit-learn` `svc` algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precomputed kernel classification test score: 1.0\n"
     ]
    }
   ],
   "source": [
    "adhoc_matrix_train = adhoc_kernel.evaluate(x_vec=train_features)\n",
    "adhoc_matrix_test = adhoc_kernel.evaluate(x_vec=test_features, y_vec=train_features)\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(10, 5))\n",
    "axs[0].imshow(\n",
    "    np.asmatrix(adhoc_matrix_train), interpolation=\"nearest\", origin=\"upper\", cmap=\"Blues\"\n",
    ")\n",
    "axs[0].set_title(\"Ad hoc training kernel matrix\")\n",
    "axs[1].imshow(np.asmatrix(adhoc_matrix_test), interpolation=\"nearest\", origin=\"upper\", cmap=\"Reds\")\n",
    "axs[1].set_title(\"Ad hoc testing kernel matrix\")\n",
    "plt.show()\n",
    "\n",
    "adhoc_svc = SVC(kernel=\"precomputed\")\n",
    "adhoc_svc.fit(adhoc_matrix_train, train_labels)\n",
    "adhoc_score = adhoc_svc.score(adhoc_matrix_test, test_labels)\n",
    "\n",
    "print(f\"Precomputed kernel classification test score: {adhoc_score}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`qiskit` also contains the `qsvc` class that extends the `sklearn svc` class, that can be used as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QSVC classification test score: 1.0\n"
     ]
    }
   ],
   "source": [
    "qsvc = QSVC(quantum_kernel=adhoc_kernel)\n",
    "qsvc.fit(train_features, train_labels)\n",
    "qsvc_score = qsvc.score(test_features, test_labels)\n",
    "\n",
    "print(f\"QSVC classification test score: {qsvc_score}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering\n",
    "\n",
    "For our clustering example, we will again use the _ad hoc dataset_ as described in [_Supervised learning with quantum enhanced feature spaces_](https://arxiv.org/pdf/1804.11326.pdf), and the `scikit-learn` `spectral` clustering algorithm.\n",
    "\n",
    "We will regenerate the dataset with a larger gap between the two classes, and as clustering is an unsupervised machine learning task, we don't need a test sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "adhoc_dimension = 2\n",
    "train_features, train_labels, test_features, test_labels, adhoc_total = ad_hoc_data(\n",
    "    training_size=25,\n",
    "    test_size=0,\n",
    "    n=adhoc_dimension,\n",
    "    gap=0.6,\n",
    "    plot_data=False,\n",
    "    one_hot=False,\n",
    "    include_sample_total=True,\n",
    ")\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.ylim(0, 2 * np.pi)\n",
    "plt.xlim(0, 2 * np.pi)\n",
    "plt.imshow(\n",
    "    np.asmatrix(adhoc_total).T,\n",
    "    interpolation=\"nearest\",\n",
    "    origin=\"lower\",\n",
    "    cmap=\"RdBu\",\n",
    "    extent=[0, 2 * np.pi, 0, 2 * np.pi],\n",
    ")\n",
    "plt.scatter(\n",
    "    train_features[np.where(train_labels[:] == 0), 0],\n",
    "    train_features[np.where(train_labels[:] == 0), 1],\n",
    "    marker=\"s\",\n",
    "    facecolors=\"w\",\n",
    "    edgecolors=\"b\",\n",
    "    label=\"A\",\n",
    ")\n",
    "plt.scatter(\n",
    "    train_features[np.where(train_labels[:] == 1), 0],\n",
    "    train_features[np.where(train_labels[:] == 1), 1],\n",
    "    marker=\"o\",\n",
    "    facecolors=\"w\",\n",
    "    edgecolors=\"r\",\n",
    "    label=\"B\",\n",
    ")\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=\"upper left\", borderaxespad=0.0)\n",
    "plt.title(\"Ad hoc dataset for clustering\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We again set up the `QuantumKernel` class to calculate a kernel matrix using the [ZZFeatureMap](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html), and the BasicAer `qasm_simulator` using 1024 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "adhoc_feature_map = ZZFeatureMap(feature_dimension=adhoc_dimension, reps=2, entanglement=\"linear\")\n",
    "\n",
    "adhoc_backend = QuantumInstance(\n",
    "    BasicAer.get_backend(\"qasm_simulator\"), shots=1024, seed_simulator=seed, seed_transpiler=seed\n",
    ")\n",
    "\n",
    "adhoc_kernel = QuantumKernel(feature_map=adhoc_feature_map, quantum_instance=adhoc_backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scikit-learn spectral clustering algorithm allows us to define a [custom kernel] in two ways: by providing the kernel as a callable function or by precomputing the kernel matrix. Using the QuantumKernel class in qiskit, we can only use the latter.\n",
    "\n",
    "The following code precomputes and plots the kernel matrices before providing it to the scikit-learn spectral clustering algorithm, and scoring the labels using normalized mutual information, since we a priori know the class labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clustering score: 0.7287008798015754\n"
     ]
    }
   ],
   "source": [
    "adhoc_matrix = adhoc_kernel.evaluate(x_vec=train_features)\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.imshow(np.asmatrix(adhoc_matrix), interpolation=\"nearest\", origin=\"upper\", cmap=\"Greens\")\n",
    "plt.title(\"Ad hoc clustering kernel matrix\")\n",
    "plt.show()\n",
    "\n",
    "adhoc_spectral = SpectralClustering(2, affinity=\"precomputed\")\n",
    "cluster_labels = adhoc_spectral.fit_predict(adhoc_matrix)\n",
    "cluster_score = normalized_mutual_info_score(cluster_labels, train_labels)\n",
    "\n",
    "print(f\"Clustering score: {cluster_score}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scikit-learn` has other algorithms that can use a precomputed kernel matrix, here are a few:\n",
    "\n",
    "- [Agglomerative clustering](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html)\n",
    "- [Support vector regression](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVR.html)\n",
    "- [Ridge regression](https://scikit-learn.org/stable/modules/generated/sklearn.kernel_ridge.KernelRidge.html)\n",
    "- [Gaussian process regression](https://scikit-learn.org/stable/modules/gaussian_process.html)\n",
    "- [Principal component analysis](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.KernelPCA.html)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.19.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.8.2</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.2</td></tr><tr><td><code>qiskit</code></td><td>0.27.0</td></tr><tr><td><code>qiskit-machine-learning</code></td><td>0.3.0</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.7.9 (default, Aug 31 2020, 17:10:11) [MSC v.1916 64 bit (AMD64)]</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td>CPUs</td><td>4</td></tr><tr><td>Memory (Gb)</td><td>31.837730407714844</td></tr><tr><td colspan='2'>Fri Dec 03 15:08:20 2021 GMT Standard Time</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, 2021.</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>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}