qiskit-ml-aug12.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# An Introduction to Qiskit Machine Learning\n",
    "<br/>\n",
    "\n",
    "<center><div><img src=\"images/qml.png\" width=\"300\" /></div></center>\n",
    "<br>\n",
    "\n",
    "<b>Adaptations of notebooks originally authored by:</b> \n",
    "Anna Phan, IBM Quantum - Australia and Anton Dekusar, IBM Quantum - IBM Research Europe - Dublin  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Contents\n",
    "\n",
    "* Overview of Qiskit Machine Learning\n",
    "* Classification Example Data\n",
    "* Data Encoding\n",
    "* Quantum Support Vector Machine\n",
    "* Variational Quantum Classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Overview of Qiskit Machine Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<br>\n",
    "<center>\n",
    "    <img src=\"images/qml1.png\" width=\"500\" >\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Support Vector Machine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Classification Problem\n",
    "<div style=\"float: left; width: 50%;\">\n",
    "<br>\n",
    "Supervised binary classification\n",
    "\n",
    "train set: $T = \\{\\mathbf{x}_1, \\mathbf{x}_2, ..., \\mathbf{x}_M\\}, \\: \\mathbf{x}_i \\in \\mathbb{R}^s$\n",
    "    \n",
    "class map: $c_{T} \\rightarrow \\{+1, -1\\}$   \n",
    "\n",
    "test set: $S = \\{\\mathbf{x}_1', \\mathbf{x}_2', ..., \\mathbf{x}_m'\\}$\n",
    "<br>    \n",
    "    \n",
    "A classification map for all $\\mathbf{x}$ is unknown:\n",
    "    \n",
    "map: $c: \\mathbf{x} \\rightarrow \\{+1, -1\\}, \\, \\forall \\mathbf{x}$    \n",
    "<br>\n",
    "Goal: find a class map $\\widetilde{c} : T \\cup \\ S \\rightarrow \\{+1, -1\\}\\,$ that agrees well with the unknown map $c$ determining all true labels.\n",
    "\n",
    "</div>\n",
    "<div style=\"float: right; width: 50%; padding-right=20px;\">\n",
    "    <img src=\"images/svm0.png\">\n",
    "    <br>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Support Vector Machine\n",
    "<div style=\"float: left; width: 50%;\">\n",
    "<br>\n",
    "Linear decision function\n",
    "\n",
    "$$\n",
    "\\widetilde{c}_{\\text{SVM}}(\\mathbf{x}) = \\mathrm{sign}(\\mathbf{w}^T\\mathbf{x} - b)\n",
    "$$\n",
    "\n",
    "This only works for linearly separable data\n",
    "\n",
    "Objective is to maximize the margin\n",
    "\n",
    "$$\n",
    "\\min_{\\mathbf{w} \\in \\mathbb{R}^s, \\, b \\in \\mathbb{R}} ||\\mathbf{w}||^2 \\\\\n",
    "\\text{s. t. } y_i(\\mathbf{w}^T \\mathbf{x}_i - b) \\geq 1\n",
    "$$\n",
    "\n",
    "</div>\n",
    "<div style=\"float: right; width: 50%; padding-right=20px;\">\n",
    "    <img src=\"images/svm1.png\">\n",
    "    <br>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Kernelized SVM\n",
    "<div style=\"float: left; width: 50%;\">\n",
    "<br>\n",
    "Introduce a nonlinear feature transformation\n",
    "\n",
    "$$\n",
    "\\phi : \\mathbb{R}^s \\rightarrow \\ \\mathcal{V}, \\text{ where} \\mathcal{V} \\text{ a Hilbert space} \\\\\n",
    "\\widetilde{c}_{\\text{SVM}}(\\mathbf{x}) = \\mathrm{sign}(\\langle \\mathbf{w}, \\phi({\\mathbf{x})}\\rangle_{\\nu} - b)\n",
    "$$\n",
    "\n",
    "Linear in feature space, but nonlinear in the original space\n",
    "\n",
    "Kernel trick is to rewrite the SVM problem to only explicitly depend on\n",
    "\n",
    "$$\n",
    "k(\\mathbf{x}, \\mathbf{x'}) = \\langle\\phi{(\\mathbf{x})}, \\phi{(\\mathbf{x'})}\\rangle_{\\nu}\n",
    "$$\n",
    "\n",
    "not the feature vectors $\\phi(\\mathbf{x})$.\n",
    "    \n",
    "</div>\n",
    "<div style=\"float: right; width: 50%; padding-right=20px;\">\n",
    "    <img src=\"images/svm2.png\">\n",
    "    <br>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Kernelized SVM\n",
    "<div style=\"float: left; width: 50%;\">\n",
    "<br>\n",
    "Original data \n",
    "$$\\mathbf{x} \\in \\mathbb{R}^2$$\n",
    "\n",
    "Feature map $$\\phi(\\mathbf{x}) = (x_1, x_2, x_1^2 + x_2^2) \\in \\mathbb{R}^3$$\n",
    "\n",
    "Kernel $$k(\\mathbf{x}, \\mathbf{x'}) = \\phi(\\mathbf{x}) \\cdot \\phi(\\mathbf{x'}) = \\mathbf{x} \\cdot \\mathbf{x'} + ||\\mathbf{x}||^2 ||\\mathbf{x'}||^2$$\n",
    "    \n",
    "</div>\n",
    "<div style=\"float: right; width: 50%; padding-right=20px;\">\n",
    "    <center>\n",
    "    <img src=\"images/svm5.png\"/>\n",
    "    </center>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Classification Example Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Some imports and seed fix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from qiskit.utils import algorithm_globals\n",
    "\n",
    "seed = 12345\n",
    "algorithm_globals.random_seed = seed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For this classification example, we will use:\n",
    "\n",
    "* _ad hoc dataset_ as described in [***Havlicek et al.*  Nature 567, 209-212 (2019)**](https://www.nature.com/articles/s41586-019-0980-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's create our train and test datasets using an utility function provided in Qiskit Machine Learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_machine_learning.datasets import ad_hoc_data\n",
    "\n",
    "train_features, train_labels, test_features, test_labels, adhoc_total = ad_hoc_data(\n",
    "    training_size=20,\n",
    "    test_size=5,\n",
    "    n=2,\n",
    "    gap=0.3,\n",
    "    plot_data=False, one_hot=False, include_sample_total=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Here we define a helper function to plot our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def plot_adhoc_dataset(train_features, train_labels, test_features, test_labels, adhoc_total):\n",
    "    \n",
    "    plt.figure(figsize=(8, 8))\n",
    "    plt.ylim(0, 2 * np.pi)\n",
    "    plt.xlim(0, 2 * np.pi)\n",
    "    plt.imshow(np.asmatrix(adhoc_total).T, interpolation='nearest',\n",
    "               origin='lower', cmap='RdBu', extent=[0, 2 * np.pi, 0, 2 * np.pi])\n",
    "\n",
    "    plt.scatter(train_features[np.where(train_labels[:] == 0), 0], train_features[np.where(train_labels[:] == 0), 1],\n",
    "                marker='s', facecolors='w', edgecolors='b', label=\"A train\")\n",
    "    plt.scatter(train_features[np.where(train_labels[:] == 1), 0], train_features[np.where(train_labels[:] == 1), 1],\n",
    "                marker='o', facecolors='w', edgecolors='r', label=\"B train\")\n",
    "    plt.scatter(test_features[np.where(test_labels[:] == 0), 0], test_features[np.where(test_labels[:] == 0), 1],\n",
    "                marker='s', facecolors='b', edgecolors='w', label=\"A test\")\n",
    "    plt.scatter(test_features[np.where(test_labels[:] == 1), 0], test_features[np.where(test_labels[:] == 1), 1],\n",
    "                marker='o', facecolors='r', edgecolors='w', label=\"B test\")\n",
    "\n",
    "    plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0.)\n",
    "    plt.title(\"Ad hoc dataset for classification\")\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now plot the datasets. In this notebook we have a *pre-defined* utility function for plotting datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_adhoc_dataset(train_features, train_labels, test_features, test_labels, adhoc_total)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here is an example of a datapoint from each class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.07345115 5.84336234] 0\n",
      "[1.57079633 0.        ] 1\n"
     ]
    }
   ],
   "source": [
    "print(train_features[0], train_labels[0])\n",
    "print(train_features[20], train_labels[20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Data Encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Data representation is crucial for the success of machine learning models. For classical machine learning, this question usually takes the form how to represent the data numerically, so that it can be best processed by a classical machine learning algorithm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For quantum machine learning, this question is similar, but more fundamental: how to represent and efficiently input the data into a quantum system, so that it can be processed by a quantum machine learning algorithm. This is usually referred to as data encoding, but is also called data embedding or loading."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "There are various methods for data encoding, but the one generally used is arbitary encoding, which encodes 𝑁 features as rotations on 𝑁 parameterized gates on 𝑛 qubits, where 𝑛≤𝑁. It only encodes one datapoint at a time, rather than a whole dataset and uses a constant depth quantum circuit and 𝑛≤𝑁 qubits, meaning it can be run on current quantum hardware."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Data Encoding Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For example, to use the Qiskit [**`EfficientSU2`**](https://qiskit.org/documentation/stubs/qiskit.circuit.library.EfficientSU2.html) circuit to encode 12 features, would only use 3 qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 628.397x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import EfficientSU2\n",
    "\n",
    "circuit = EfficientSU2(num_qubits=3, reps=1, insert_barriers=True)\n",
    "circuit.decompose().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here we encode the datapoint $x = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2]$ with 12 features, using each of the parameterized gates to encode a different feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 628.397x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2]\n",
    "\n",
    "encode = circuit.bind_parameters(x)\n",
    "encode.decompose().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The Qiskit [**`ZZFeatureMap`**](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html) circuit with 3 qubits, only encodes a datapoint of 3 features, despite having 6 parameterized gates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1170.2x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import ZZFeatureMap\n",
    "\n",
    "circuit = ZZFeatureMap(3, reps=1, insert_barriers=True)\n",
    "circuit.decompose().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 989.597x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [0.1,0.2,0.3]\n",
    "\n",
    "encode = circuit.bind_parameters(x)\n",
    "encode.decompose().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The choice of which parameterized quantum circuit to use to encode what data is an active area of research."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "### Exercise 1: Data Encoding\n",
    "\n",
    "Encode the data point $x = (-0.1,0.2)$ using the `ZZFeatureMap` with 4 repetitions and default data mapping function. \n",
    "\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "x = [-0.1,0.2]\n",
    "# YOUR CODE HERE\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The parameters in the gates are a little difficult to read, but notice how the circuit is symmetrical, with one half encoding one of the data samples, the other half encoding the other. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We then simulate the circuit. We will use the `qasm_simulator` since the circuit contains measurements, but increase the number of shots to reduce the effect of sampling noise. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Quantum Support Vector Machine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Introduced in [***Havlicek et al.*  Nature 567, 209-212 (2019)**](https://www.nature.com/articles/s41586-019-0980-2), the quantum support vector classification algorithm consists of these steps:\n",
    "\n",
    "<center><img src=\"images/qsvm.png\" width=\"1000\"></center> \n",
    "\n",
    "\n",
    "1. Build the train and test quantum kernel matrices.\n",
    "    1. For each pair of datapoints in the training dataset $\\mathbf{x}_{i},\\mathbf{x}_j$, apply the feature map and measure the transition probability: $ K_{ij} = \\left| \\langle 0 | \\mathbf{U}^\\dagger_{\\Phi(\\mathbf{x_j})} \\mathbf{U}_{\\Phi(\\mathbf{x_i})} | 0 \\rangle \\right|^2 $.\n",
    "    2. For each training datapoint $\\mathbf{x_i}$ and testing point $\\mathbf{y_i}$, apply the feature map and measure the transition probability: $ K_{ij} = \\left| \\langle 0 | \\mathbf{U}^\\dagger_{\\Phi(\\mathbf{y_i})} \\mathbf{U}_{\\Phi(\\mathbf{x_i})} | 0 \\rangle \\right|^2 $.\n",
    "2. Use the train and test quantum kernel matrices in a classical support vector machine classification algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# QSVM Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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 Aer `qasm_simulator` using 1024 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit import Aer\n",
    "from qiskit.utils import QuantumInstance\n",
    "\n",
    "quantum_instance = QuantumInstance(Aer.get_backend('qasm_simulator'), shots=1024,\n",
    "                                   seed_simulator=seed, seed_transpiler=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.circuit.library import ZZFeatureMap\n",
    "from qiskit_machine_learning.kernels import QuantumKernel\n",
    "\n",
    "zz_feature_map = ZZFeatureMap(feature_dimension=2, reps=2)\n",
    "zz_kernel = QuantumKernel(feature_map=zz_feature_map, quantum_instance=quantum_instance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here we compute and plot the training and testing kernel matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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"
    }
   ],
   "source": [
    "train_matrix = zz_kernel.evaluate(x_vec=train_features)\n",
    "test_matrix = zz_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(np.asmatrix(train_matrix),\n",
    "              interpolation='nearest', origin='upper', cmap='Blues')\n",
    "axs[0].set_title(\"training kernel matrix\")\n",
    "axs[1].imshow(np.asmatrix(test_matrix),\n",
    "              interpolation='nearest', origin='upper', cmap='Reds')\n",
    "axs[1].set_title(\"testing kernel matrix\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The `scikit-learn` [**`svc`**](https://scikit-learn.org/stable/modules/svm.html) 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`**](https://qiskit.org/documentation/machine-learning/stubs/qiskit_machine_learning.kernels.QuantumKernel.html?highlight=quantumkernel) class in Qiskit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The following code takes the training and testing kernel matrices we calculated above and  provides them to the `scikit-learn` `svc` algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precomputed kernel classification test score: 1.0\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "zzpc_svc = SVC(kernel='precomputed')\n",
    "zzpc_svc.fit(train_matrix, train_labels)\n",
    "zzpc_score = zzpc_svc.score(test_matrix, test_labels)\n",
    "\n",
    "print(f'Precomputed kernel classification test score: {zzpc_score}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The following code gives the kernel as a callable function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Callable kernel classification test score: 1.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zzcb_svc = SVC(kernel=zz_kernel.evaluate)\n",
    "zzcb_svc.fit(train_features, train_labels)\n",
    "zzcb_score = zzcb_svc.score(test_features, test_labels)\n",
    "\n",
    "print(f'Callable kernel classification test score: {zzcb_score}')\n",
    "\n",
    "zzcb_svc.predict(test_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "### Exercise 2: Kernel Building\n",
    "\n",
    "Set up the QuantumKernel class to calculate a kernel matrix using the ZFeatureMap, and the Aer qasm_simulator using 1024 shots.\n",
    "\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.circuit.library import ZFeatureMap\n",
    "from qiskit_machine_learning.kernels import QuantumKernel\n",
    "\n",
    "# YOUR CODE HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here we compute and plot the training and testing kernel matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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"
    }
   ],
   "source": [
    "train_matrix = aug12_kernel.evaluate(x_vec=train_features)\n",
    "test_matrix = aug12_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(np.asmatrix(train_matrix),\n",
    "              interpolation='nearest', origin='upper', cmap='Blues')\n",
    "axs[0].set_title(\"training kernel matrix\")\n",
    "axs[1].imshow(np.asmatrix(test_matrix),\n",
    "              interpolation='nearest', origin='upper', cmap='Reds')\n",
    "axs[1].set_title(\"testing kernel matrix\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Callable kernel classification test score: 0.7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0, 1, 1, 0, 0, 0, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aug12_svc = SVC(kernel=aug12_kernel.evaluate)\n",
    "aug12_svc.fit(train_features, train_labels)\n",
    "aug12_score = aug12_svc.score(test_features, test_labels)\n",
    "\n",
    "print(f'Callable kernel classification test score: {aug12_score}')\n",
    "\n",
    "aug12_svc.predict(test_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "You have now built your very own kernel and tested it out! This is convenient, as we can easily compare the quantum kernel with various classical kernels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "linear kernel classification test score:  0.60\n",
      "Predictions for linear [1 0 0 0 0 0 1 0 1 0] \n",
      "\n",
      "poly kernel classification test score:  0.60\n",
      "Predictions for poly [0 0 0 0 0 0 1 0 0 0] \n",
      "\n",
      "rbf kernel classification test score:  0.70\n",
      "Predictions for rbf [0 0 0 0 0 0 1 0 1 0] \n",
      "\n",
      "sigmoid kernel classification test score:  0.40\n",
      "Predictions for sigmoid [1 1 1 1 0 1 1 0 1 0] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "classical_kernels = ['linear', 'poly', 'rbf', 'sigmoid']\n",
    "\n",
    "for kernel in classical_kernels:\n",
    "    classical_svc = SVC(kernel=kernel)\n",
    "    classical_svc.fit(train_features, train_labels)\n",
    "    classical_score = classical_svc.score(test_features, test_labels)\n",
    "    print('%s kernel classification test score:  %0.2f' % (kernel, classical_score))\n",
    "    print(\"Predictions for\",kernel, classical_svc.predict(test_features), \"\\n\")\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# QSVC Class\n",
    "Qiskit Machine Learning also contains the `QSVC` class that extends the `scikit-learn` `SVC` class, that can be used as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QSVC classification test score: 1.0\n"
     ]
    }
   ],
   "source": [
    "from qiskit_machine_learning.algorithms import QSVC\n",
    "\n",
    "qsvc = QSVC()\n",
    "qsvc.quantum_kernel.quantum_instance = quantum_instance\n",
    "\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": "code",
   "execution_count": 79,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qsvc.predict(test_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Resources\n",
    "\n",
    "- A blog post \"Introducing Qiskit Machine Learning\":<br>\n",
    "https://medium.com/qiskit/introducing-qiskit-machine-learning-5f06b6597526\n",
    "<br>\n",
    "\n",
    "- Qiskit Machine Learning tutorials:<br>\n",
    "https://qiskit.org/documentation/machine-learning/tutorials/\n",
    "<br>\n",
    "\n",
    "- Qiskit Machine Learning textbook course:<br>\n",
    "https://qiskit.org/learn/course/machine-learning-course\n",
    "<br>\n",
    "\n",
    "- Qiskit Global Summer School 2021 | Quantum Machine Learning:<br>\n",
    "https://qiskit.org/learn/summer-school/quantum-computing-and-quantum-learning-2021\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "Thank You!\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.21.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.10.4</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.19.2</td></tr><tr><td><code>qiskit</code></td><td>0.37.0</td></tr><tr><td><code>qiskit-nature</code></td><td>0.4.3</td></tr><tr><td><code>qiskit-finance</code></td><td>0.3.3</td></tr><tr><td><code>qiskit-optimization</code></td><td>0.4.0</td></tr><tr><td><code>qiskit-machine-learning</code></td><td>0.4.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.9.12</td></tr><tr><td>Python compiler</td><td>Clang 12.0.0 </td></tr><tr><td>Python build</td><td>main, Jun  1 2022 06:36:29</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>16.0</td></tr><tr><td colspan='2'>Mon Aug 08 00:17:10 2022 +08</td></tr></table>"
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     "metadata": {},
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   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "\n",
    "%qiskit_version_table"
   ]
  }
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