VQE_ex.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b7d51b3d",
   "metadata": {},
   "source": [
    "# Variational Algorithms using Runtime"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3694291d",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a0a48442",
   "metadata": {},
   "outputs": [],
   "source": [
    "# General imports\n",
    "import time\n",
    "import numpy as np\n",
    "\n",
    "# Pre-defined ansatz circuit from Qiskit circuit library\n",
    "from qiskit.circuit.library import EfficientSU2\n",
    "# Operators from Qiskit\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "\n",
    "# The IBM Qiskit Runtime\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "from qiskit_ibm_runtime import Estimator, Session\n",
    "\n",
    "# SciPy minimizer routine\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "# Plotting stuff\n",
    "import matplotlib.pyplot as plt\n",
    "try:\n",
    "    plt.style.use('quantum-light')\n",
    "except:\n",
    "    pass\n",
    "%config InlineBackend.figure_format='retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d695869c",
   "metadata": {},
   "source": [
    "## Load Runtime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bc380c46",
   "metadata": {},
   "outputs": [],
   "source": [
    "service = QiskitRuntimeService()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a819d550",
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = service.get_backend('ibm_canberra')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b805acc5",
   "metadata": {},
   "source": [
    "## Problem specification\n",
    "\n",
    "Variational quantum algorithms can be thought of as just another type of optimization problem that minimizes a cost function.  In general, optimization problems require 3 pieces:\n",
    "\n",
    "1. A Cost function that is the function we want to minimize (or maximize using a - sign)\n",
    "\n",
    "2. An initial guess as to the possible solution\n",
    "\n",
    "3. An numerical optimization routine for finding the minimal solution (hopefully a global minimum)\n",
    "\n",
    "\n",
    "The cost function in quantum computation makes use of the use of a Hamiltonian expressed in as a linear combination of Pauli operators (`I`, `Z`, `X` `Y`).  E.g. a simple Hamiltonian over two-qubits could be"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0ad66539",
   "metadata": {},
   "outputs": [],
   "source": [
    "hamiltonian = SparsePauliOp.from_list([('XX', 1), ('YY', 2), ('ZZ', 3)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c0e9737",
   "metadata": {},
   "source": [
    "The simplest variational algorithm aims to minimize the expectation value of the Hamiltonian, i.e. find the minimal energy of the effective system, by looking for the ground state solution $|\\psi(\\vec{\\theta})\\rangle$, where $\\vec{\\theta}$ is a vector of parameters that can be varied.  That is, we want:\n",
    "\n",
    "$$\n",
    "\\min_{\\vec{\\theta}}~\\langle\\psi(\\vec{\\theta})| H |\\psi(\\vec{\\theta})\\rangle = \\min_{\\vec{\\theta}}~\\langle\\psi(\\vec{\\theta})| XX |\\psi(\\vec{\\theta})\\rangle + 2\\langle \\psi(\\vec{\\theta})| YY |\\psi(\\vec{\\theta})\\rangle + 3\\langle \\psi(\\vec{\\theta})| ZZ |\\psi(\\vec{\\theta})\\rangle\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51f2d05e",
   "metadata": {},
   "source": [
    "Now, it is well known that the dimension of the state $|\\psi(\\vec{\\theta})\\rangle$ grows exponentially with the number of qubits; there are $2^{N}$ complex numbers that we need to find, where $N$ is the number of qubits.  However, solving for exponentially increasing number of parameters is not scalable, and we want to try to find a solution using only a polynomial number of parameters.\n",
    "\n",
    "So we aim to find a solution for $2^{N}$ parameters, using polynomial number of parameters.  This reduction in parameters is essentially a lose of information, and we must supply addition information in order to solve the problem.  This comes in the form of a specific structure for the form of $|\\psi(\\vec{\\theta})\\rangle$.  This \"guess\" or \"ansatz\" circuit is designed to have a strong overlap with the ground state solution of interest.  In order for this to be the case, in general, we need a physically motivated form of this ansatz, and thus the choice of ansatz is very much problem specific."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3598779",
   "metadata": {},
   "source": [
    "For smaller problems one can choose ansatz circuits that have wide overlap, and thus work in general.  Here we use the `EfficientSU2` circuit from the Qiskit circuit library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "59bffe5e",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 872.572x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "image/png": {
       "height": 182,
       "width": 726
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ansatz = EfficientSU2(2)\n",
    "ansatz.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8d52e74",
   "metadata": {},
   "source": [
    "We see that, for our 2Q problem, this circuit has 16 parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc90d46d",
   "metadata": {},
   "source": [
    "## Setting up the optimization\n",
    "\n",
    "We are now ready to set up the problem.  First we need to build our cost function.  Nominally a cost function has the vector of parameters, here called `params`, as its first argument.  Other arguments are problem specific.  Here we also need the ansatz circuit, the Hamiltonian to evaluate, as well as our `Estimator` instance.  The value of the Runtime comes in the simplicity of this call; minimizing the energy on a quantum computer becomes one line of code in the cost function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b22a1b00",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_func(params, ansatz, hamiltonian, estimator):\n",
    "        \"\"\"Return estimate of energy from estimator\n",
    "\n",
    "        Parameters:\n",
    "            params (ndarray): Array of ansatz parameters\n",
    "            ansatz (QuantumCircuit): Parameterized ansatz circuit\n",
    "            hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n",
    "            estimator (Estimator): Estimator primitive instance\n",
    "\n",
    "        Returns:\n",
    "            float: Energy estimate\n",
    "        \"\"\"\n",
    "        energy = estimator.run(ansatz, hamiltonian,\n",
    "                               parameter_values=params).result().values[0]\n",
    "        return energy\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4e07157",
   "metadata": {},
   "source": [
    "Our optimizer, here `scipy.optimize.minimize`, requires this cost function and an initial guess for parameter values to get started.  Without any additonal information, this is nominally a random vector, or a vector of all zeros.  Here we pick the former."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8c8989f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_params = ansatz.num_parameters\n",
    "x0 = 2*np.pi*np.random.random(num_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b69134ea",
   "metadata": {},
   "source": [
    "Although we could run the problem as is, it is often nice to have some way of tracking the progress of our iterative method, and perhaps record cost function values at each step.  This is accomplished via what is usually called a `callback` function, that gets evaluated after every iteration.  Below is an example cost function.  It will record several intermediate values so that we can plot the value of the cost function at each step in the optimization process, as well as return the current iteration number, and the average time per iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3b2f5808",
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_callback(ansatz, hamiltonian, estimator, callback_dict):\n",
    "    \"\"\"Return callback function that uses Estimator instance,\n",
    "    and stores intermediate values into a dictionary.\n",
    "\n",
    "    Parameters:\n",
    "        ansatz (QuantumCircuit): Parameterized ansatz circuit\n",
    "        hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n",
    "        estimator (Estimator): Estimator primitive instance\n",
    "        callback_dict (dict): Mutable dict for storing values\n",
    "\n",
    "    Returns:\n",
    "        Callable: Callback function object\n",
    "    \"\"\"\n",
    "\n",
    "    def callback(current_vector):\n",
    "        \"\"\"Callback function storing previous solution vector,\n",
    "        computing the intermediate cost value, and displaying number\n",
    "        of completed iterations and average time per iteration.\n",
    "\n",
    "        Values are stored in pre-defined 'callback_dict' dictionary.\n",
    "\n",
    "        Parameters:\n",
    "            current_vector (ndarray): Current vector of parameters\n",
    "                                      returned by optimizer\n",
    "        \"\"\"\n",
    "        # Keep track of the number of iterations\n",
    "        callback_dict[\"iters\"] += 1\n",
    "        # Set the prev_vector to the latest one\n",
    "        callback_dict[\"prev_vector\"] = current_vector\n",
    "        # Compute the value of the cost function at the current vector\n",
    "        callback_dict[\"cost_history\"].append(\n",
    "            estimator.run(ansatz, hamiltonian, parameter_values=current_vector).result().values[0]\n",
    "        )\n",
    "        # Grab the current time\n",
    "        current_time = time.perf_counter()\n",
    "        # Find the total time of the execute (after the 1st iteration)\n",
    "        if callback_dict[\"iters\"] > 1:\n",
    "            callback_dict[\"_total_time\"] += current_time - callback_dict[\"_prev_time\"]\n",
    "        # Set the previous time to the current time\n",
    "        callback_dict[\"_prev_time\"] = current_time\n",
    "        # Compute the average time per iteration and round it\n",
    "        time_str = (\n",
    "            round(callback_dict[\"_total_time\"] / (callback_dict[\"iters\"] - 1), 2)\n",
    "            if callback_dict[\"_total_time\"]\n",
    "            else \"-\"\n",
    "        )\n",
    "        # Print to screen on single line\n",
    "        print(\n",
    "            \"Iters. done: {} [Avg. time per iter: {}]\".format(callback_dict[\"iters\"], time_str),\n",
    "            end=\"\\r\",\n",
    "            flush=True,\n",
    "        )\n",
    "\n",
    "    return callback"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dea7f3a0",
   "metadata": {},
   "source": [
    "## Executing on hardware\n",
    "\n",
    "To begin, we first create a Runtime session so that we can use the target backend for up to 8 hours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f0eb9a04",
   "metadata": {},
   "outputs": [],
   "source": [
    "session = Session(backend=backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6ec522b",
   "metadata": {},
   "source": [
    "then we create an `Estimator` instance that we make use of our session, and will take 10,000 shots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "68def39e",
   "metadata": {},
   "outputs": [],
   "source": [
    "estimator = Estimator(session=session, options={\"shots\": int(1e4)})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9583c172",
   "metadata": {},
   "source": [
    "To run the optimizer we simply create a dict to hold our intermediate data, build our callback function, and then execute the `minimize` function from SciPy using our method of choice specifying our `callback` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f00571e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iters. done: 27 [Avg. time per iter: 256.22]\r"
     ]
    }
   ],
   "source": [
    "callback_dict = {\n",
    "    \"prev_vector\": None,\n",
    "    \"iters\": 0,\n",
    "    \"cost_history\": [],\n",
    "    \"_total_time\": 0,\n",
    "    \"_prev_time\": None,\n",
    "}\n",
    "# Build our callback function to store data and evaluate at each step\n",
    "callback = build_callback(ansatz, hamiltonian, estimator, callback_dict)\n",
    "\n",
    "# Perform actual minimization\n",
    "res = minimize(\n",
    "    cost_func,\n",
    "    x0,\n",
    "    args=(ansatz, hamiltonian, estimator),\n",
    "    method=\"cobyla\",\n",
    "    callback=callback,\n",
    ")\n",
    "session.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1baad8bd",
   "metadata": {},
   "source": [
    "When the loop is done, we can see the results in the same format as any other minimization problem.  Note that, in absence of noise, and finite sampling, the true ground state energy is -6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "02c8f921",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " message: Optimization terminated successfully.\n",
       " success: True\n",
       "  status: 1\n",
       "     fun: -2.698541176470588\n",
       "       x: [ 5.182e+00  5.920e+00 ...  4.148e+00  5.760e+00]\n",
       "    nfev: 138\n",
       "   maxcv: 0.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae46fe51",
   "metadata": {},
   "source": [
    "Having used a callback function, we can also plot the value of the cost function at each step to graphically observe the convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2c6e43e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x1800 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1666,
       "width": 2356
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(range(callback_dict[\"iters\"]), callback_dict[\"cost_history\"])\n",
    "ax.set_xlabel(\"Iterations\")\n",
    "ax.set_ylabel(\"Cost\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "458120e9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}