8.-Ising y MaxCut con D-Wave.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Resolviendo el modelo de Ising y el problema del corte máximo con un ordenador de D-Wave\n",
    "\n",
    "En este notebook, vamos a utilizar un ordenador cuántico de D-Wave para resolver casos del modelo de Ising que se corresponden con instancias del problema del corte máximo en grafos. \n",
    "\n",
    "El hamiltoniano del modelo de Ising es $$H = \\sum_{i,j=1}^n J_{i,j}Z_iZ_j + \\sum_{i=1}^n h_iZ_i$$ \n",
    "\n",
    "En el caso particular del problema del corte máximo, se tiene $J_{i,j}=1$ y $h_i=0$ para todos los valores $i,j$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definir el modelo con el que vamos a trabajar es muy sencillo: se reduce a especificar los valores de las conexiones entre pares de qubits y los coeficientes $h_i$. Por ejemplo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import dimod\n",
    "\n",
    "J = {(0,1):1}\n",
    "\n",
    "h = {}\n",
    "model = dimod.BinaryQuadraticModel(h, J, 0.0, dimod.SPIN)\n",
    "\n",
    "print(model)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos resolver el modelo de forma exacta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from dimod.reference.samplers import ExactSolver\n",
    "sampler = ExactSolver()\n",
    "solution = sampler.sample(model)\n",
    "print(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O con *simulated annealing* (un método heurístico de optimización para ordenadores clásicos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sampler = dimod.SimulatedAnnealingSampler()\n",
    "response = sampler.sample(model, num_reads=10)\n",
    "print(response)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y, por supuesto, con el ordenador cuántico de D-Wave (requiere registro online en https://cloud.dwavesys.com/leap/ y sustituir el token en el código de abajo con el token personal)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "!mkdir /home/jovyan/.config/dwave\n",
    "!echo \"\" > /home/jovyan/.config/dwave/dwave.conf\n",
    "!echo \"[defaults]\" >> /home/jovyan/.config/dwave/dwave.conf\n",
    "!echo \"client = qpu\" >> /home/jovyan/.config/dwave/dwave.conf\n",
    "!echo \"\" >> /home/jovyan/.config/dwave/dwave.conf\n",
    "!echo \"[prod]\" >> /home/jovyan/.config/dwave/dwave.conf\n",
    "!echo \"token = XYZ-0101010100112341234123412341234\" >> /home/jovyan/.config/dwave/dwave.conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from dwave.system.samplers import DWaveSampler\n",
    "from dwave.system.composites import EmbeddingComposite\n",
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "response = sampler.sample(model, num_reads=5000)\n",
    "print(response)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Veamos ahora un caso un poco más complicado, que se corresponde con encontrar un corte máximo en el grafo de la figura\n",
    "\n",
    "<img src=\"Images/max-cut.png\" width=\"60%\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "J = {(0,1):1,(0,2):1,(1,2):1,(1,3):1,(2,4):1,(3,4):1}\n",
    "h = {}\n",
    "model = dimod.BinaryQuadraticModel(h, J, 0.0, dimod.SPIN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primero lo resolvemos de forma exacta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sampler = ExactSolver()\n",
    "solution = sampler.sample(model)\n",
    "print(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora, con *simulated annealing*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sampler = dimod.SimulatedAnnealingSampler()\n",
    "response = sampler.sample(model, num_reads=10)\n",
    "print(response)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalmente, lo resolvemos nuevamente con el *quantum annealer*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "response = sampler.sample(model, num_reads=5000)\n",
    "print(response)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}