{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Basic example of use of simulated annealing\n",
        "\n",
        "Let us consider the one-dimensional Ising model of an antiferromagnet described by the Hamiltonian \n",
        "\n",
        "$$ H = J \\sum_{\\langle i, j \\rangle} \\sigma_i \\sigma_j$$\n",
        "\n",
        "where $\\langle i, j \\rangle$ denotes nearest neighbour sites, magnetic coupling J > 0 for antiferromagnetism and $\\sigma_i$ is the respective Pauli spin matrix acting on site $i$.\n",
        "\n",
        "We want to use the simulated annealing implemented on the QLM to solve this problem. The following example presents how one can do so."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Encoding and solving the problem"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from qat.qpus import SimulatedAnnealing\n",
        "from qat.core import Observable, Schedule, Variable, Term\n",
        "\n",
        "# Define the the problem\n",
        "n_spins = 100\n",
        "mag_coupling = 1  # >0 is antiferromagnetic, <0 is ferromagnetic\n",
        "    \n",
        "# Create a temperature function\n",
        "t = Variable(\"t\", float)\n",
        "temp_t = 2 * (1 - t) + 0.001  # annealing requires going from a high to a very low temperature\n",
        "\n",
        "# Create a QPU\n",
        "n_steps = 500\n",
        "qpu = SimulatedAnnealing(temp_t=temp_t,\n",
        "                         n_steps=n_steps,\n",
        "                         seed=817)\n",
        "\n",
        "# Create an observable\n",
        "observable = Observable(n_spins, pauli_terms=[Term(mag_coupling, \"ZZ\", [i, i + 1])\n",
        "                                              for i in range(n_spins - 1)])\n",
        "\n",
        "# Create a schedule for the annealing, a job, and send it to the QPU\n",
        "drive = [(1, observable)]\n",
        "schedule = Schedule(drive=drive)\n",
        "job = schedule.to_job(nbshots=1)\n",
        "result = qpu.submit(job)\n",
        "\n",
        "# Show the solution\n",
        "for sample in result:\n",
        "    print(sample.state)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Solution\n",
        "\n",
        "We can see that as expected for an antiferromagnet, the resulting spin configuration is alternating spins up and spins down which translates to alternating $|0>$ and $|1>$ qubit states."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "documentation-tags": {
      "icon": [
        ":material-outlined:`swap_vert;40px`",
        ":material-outlined:`grid_4x4;40px`"
      ],
      "level": "beginner"
    },
    "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": "3.12.11"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 4
}