27 - qgans_for_loading_random_distributions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# qGANs for Loading Random Distributions\n",
    "\n",
    "Given $k$-dimensional data samples, we employ a quantum Generative Adversarial Network (qGAN) to learn the data's underlying random distribution and to load it directly into a quantum state:\n",
    "\n",
    "$$ \\big| g_{\\theta}\\rangle = \\sum_{j=0}^{2^n-1} \\sqrt{p_{\\theta}^{j}}\\big| j \\rangle $$\n",
    "\n",
    "where $p_{\\theta}^{j}$ describe the occurrence probabilities of the basis states $\\big| j\\rangle$. \n",
    "\n",
    "The aim of the qGAN training is to generate a state $\\big| g_{\\theta}\\rangle$ where $p_{\\theta}^{j}$, for $j\\in \\left\\{0, \\ldots, {2^n-1} \\right\\}$, describe a probability distribution that is close to the distribution underlying the training data $X=\\left\\{x^0, \\ldots, x^{k-1} \\right\\}$.\n",
    "\n",
    "For further details please refer to [Quantum Generative Adversarial Networks for Learning and Loading Random Distributions](https://arxiv.org/abs/1904.00043) _Zoufal, Lucchi, Woerner_ \\[2019\\].\n",
    "\n",
    "For an example of how to use a trained qGAN in an application, the pricing of financial derivatives, please see the\n",
    "[Option Pricing with qGANs](https://github.com/Qiskit/qiskit-finance/tree/main/docs/tutorials/10_qgan_option_pricing.ipynb) tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "seed = 71\n",
    "np.random.seed = seed\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "from qiskit import QuantumRegister, QuantumCircuit, BasicAer\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "\n",
    "from qiskit.utils import QuantumInstance, algorithm_globals\n",
    "from qiskit_machine_learning.algorithms import NumPyDiscriminator, QGAN\n",
    "\n",
    "algorithm_globals.random_seed = seed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the Training Data\n",
    "\n",
    "First, we need to load the $k$-dimensional training data samples (here k=1).\n",
    "\n",
    "Next, the data resolution is set, i.e. the min/max data values and the number of qubits used to represent each data dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number training data samples\n",
    "N = 1000\n",
    "\n",
    "# Load data samples from log-normal distribution with mean=1 and standard deviation=1\n",
    "mu = 1\n",
    "sigma = 1\n",
    "real_data = np.random.lognormal(mean=mu, sigma=sigma, size=N)\n",
    "\n",
    "# Set the data resolution\n",
    "# Set upper and lower data values as list of k min/max data values [[min_0,max_0],...,[min_k-1,max_k-1]]\n",
    "bounds = np.array([0.0, 3.0])\n",
    "# Set number of qubits per data dimension as list of k qubit values[#q_0,...,#q_k-1]\n",
    "num_qubits = [2]\n",
    "k = len(num_qubits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize the qGAN\n",
    "\n",
    "The qGAN consists of a quantum generator $G_{\\theta}$, i.e., an ansatz, and a classical discriminator $D_{\\phi}$, a neural network.\n",
    "\n",
    "To implement the quantum generator, we choose a depth-$1$ ansatz that implements $R_Y$ rotations and $CZ$ gates which takes a uniform distribution as an input state. Notably, for $k>1$ the generator's parameters must be chosen carefully. For example, the circuit depth should be $>1$ because higher circuit depths enable the representation of more complex structures.\n",
    "\n",
    "The classical discriminator used here is based on a neural network implementation using NumPy. There is also a discriminator based on PyTorch which is not installed by default when installing Qiskit - see [Optional Install](https://github.com/Qiskit/qiskit-machine-learning#optional-installs) for more information.\n",
    "\n",
    "Here, both networks are updated with the ADAM optimization algorithm (ADAM is qGAN optimizer default)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set number of training epochs\n",
    "# Note: The algorithm's runtime can be shortened by reducing the number of training epochs.\n",
    "num_epochs = 10\n",
    "# Batch size\n",
    "batch_size = 100\n",
    "\n",
    "# Initialize qGAN\n",
    "qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None)\n",
    "qgan.seed = 1\n",
    "# Set quantum instance to run the quantum generator\n",
    "quantum_instance = QuantumInstance(\n",
    "    backend=BasicAer.get_backend(\"statevector_simulator\"), seed_transpiler=seed, seed_simulator=seed\n",
    ")\n",
    "\n",
    "# Set entangler map\n",
    "entangler_map = [[0, 1]]\n",
    "\n",
    "\n",
    "# Set an initial state for the generator circuit as a uniform distribution\n",
    "# This corresponds to applying Hadamard gates on all qubits\n",
    "init_dist = QuantumCircuit(sum(num_qubits))\n",
    "init_dist.h(init_dist.qubits)\n",
    "\n",
    "# Set the ansatz circuit\n",
    "ansatz = TwoLocal(int(np.sum(num_qubits)), \"ry\", \"cz\", entanglement=entangler_map, reps=1)\n",
    "\n",
    "# Set generator's initial parameters - in order to reduce the training time and hence the\n",
    "# total running time for this notebook\n",
    "init_params = [3.0, 1.0, 0.6, 1.6]\n",
    "\n",
    "# You can increase the number of training epochs and use random initial parameters.\n",
    "# init_params = np.random.rand(ansatz.num_parameters_settable) * 2 * np.pi\n",
    "\n",
    "# Set generator circuit by adding the initial distribution infront of the ansatz\n",
    "g_circuit = ansatz.compose(init_dist, front=True)\n",
    "\n",
    "# Set quantum generator\n",
    "qgan.set_generator(generator_circuit=g_circuit, generator_init_params=init_params)\n",
    "# The parameters have an order issue that following is a temp. workaround\n",
    "qgan._generator._free_parameters = sorted(g_circuit.parameters, key=lambda p: p.name)\n",
    "# Set classical discriminator neural network\n",
    "discriminator = NumPyDiscriminator(len(num_qubits))\n",
    "qgan.set_discriminator(discriminator)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the qGAN Training\n",
    "\n",
    "During the training the discriminator's and the generator's parameters are updated alternately w.r.t the following loss functions:\n",
    "$$ L_G\\left(\\phi, \\theta\\right) = -\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log\\left(D_{\\phi}\\left(g^{l}\\right)\\right)\\right] $$\n",
    "and\n",
    "$$  L_D\\left(\\phi, \\theta\\right) =\n",
    "\t\\frac{1}{m}\\sum\\limits_{l=1}^{m}\\left[\\log D_{\\phi}\\left(x^{l}\\right) + \\log\\left(1-D_{\\phi}\\left(g^{l}\\right)\\right)\\right], $$\n",
    "with $m$ denoting the batch size and $g^l$ describing the data samples generated by the quantum generator.\n",
    "\n",
    "Please note that the training, for the purpose of this notebook, has been kept briefer by the selection of a known initial point (`init_params`). Without such prior knowledge be aware training may take some while."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run qGAN\n",
    "result = qgan.run(quantum_instance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training results:\n",
      "  params_d : [ 0.04021075  0.6069056  -0.47859933 ... -0.16278361 -0.20504783\n",
      " -0.08409329]\n",
      "  params_g : [3.00011594 1.00008287 0.60007459 1.59996968]\n",
      "  loss_d : 0.6921\n",
      "  loss_g : [0.6554]\n",
      "  rel_entr : 0.1148\n"
     ]
    }
   ],
   "source": [
    "print(\"Training results:\")\n",
    "for key, value in result.items():\n",
    "    print(f\"  {key} : {value}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Progress & Outcome\n",
    "\n",
    "Now, we plot the evolution of the generator's and the discriminator's loss functions during the training, as well as the progress in the relative entropy between the trained and the target distribution.\n",
    "\n",
    "Finally, we also compare the cumulative distribution function (CDF) of the trained distribution to the CDF of the target distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot progress w.r.t the generator's and the discriminator's loss function\n",
    "t_steps = np.arange(num_epochs)\n",
    "plt.figure(figsize=(6, 5))\n",
    "plt.title(\"Progress in the loss function\")\n",
    "plt.plot(\n",
    "    t_steps, qgan.g_loss, label=\"Generator loss function\", color=\"mediumvioletred\", linewidth=2\n",
    ")\n",
    "plt.plot(\n",
    "    t_steps, qgan.d_loss, label=\"Discriminator loss function\", color=\"rebeccapurple\", linewidth=2\n",
    ")\n",
    "plt.grid()\n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"time steps\")\n",
    "plt.ylabel(\"loss\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot progress w.r.t relative entropy\n",
    "plt.figure(figsize=(6, 5))\n",
    "plt.title(\"Relative Entropy\")\n",
    "plt.plot(\n",
    "    np.linspace(0, num_epochs, len(qgan.rel_entr)), qgan.rel_entr, color=\"mediumblue\", lw=4, ls=\":\"\n",
    ")\n",
    "plt.grid()\n",
    "plt.xlabel(\"time steps\")\n",
    "plt.ylabel(\"relative entropy\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the CDF of the resulting distribution against the target distribution, i.e. log-normal\n",
    "log_normal = np.random.lognormal(mean=1, sigma=1, size=100000)\n",
    "log_normal = np.round(log_normal)\n",
    "log_normal = log_normal[log_normal <= bounds[1]]\n",
    "temp = []\n",
    "for i in range(int(bounds[1] + 1)):\n",
    "    temp += [np.sum(log_normal == i)]\n",
    "log_normal = np.array(temp / sum(temp))\n",
    "\n",
    "plt.figure(figsize=(6, 5))\n",
    "plt.title(\"CDF (Cumulative Distribution Function)\")\n",
    "samples_g, prob_g = qgan.generator.get_output(qgan.quantum_instance, shots=10000)\n",
    "samples_g = np.array(samples_g)\n",
    "samples_g = samples_g.flatten()\n",
    "num_bins = len(prob_g)\n",
    "plt.bar(samples_g, np.cumsum(prob_g), color=\"royalblue\", width=0.8, label=\"simulation\")\n",
    "plt.plot(\n",
    "    np.cumsum(log_normal), \"-o\", label=\"log-normal\", color=\"deepskyblue\", linewidth=4, markersize=12\n",
    ")\n",
    "plt.xticks(np.arange(min(samples_g), max(samples_g) + 1, 1.0))\n",
    "plt.grid()\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"p(x)\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-22T01:49:13.439275Z",
     "start_time": "2019-08-22T01:49:13.430311Z"
    }
   },
   "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>0.21.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.10.4</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</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>3.7.7</td></tr><tr><td>Python compiler</td><td>MSC v.1916 64 bit (AMD64)</td></tr><tr><td>Python build</td><td>default, May  6 2020 11:45:54</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>15.872657775878906</td></tr><tr><td colspan='2'>Tue Aug 30 08:22:03 2022 Hora de verano romance</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, 2022.</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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.7"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}