statevector_simulator.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dd161cb9",
   "metadata": {},
   "source": [
    "# Statevector simulator\n",
    "\n",
    "Quick solution to the exercise of Lecture 2.\n",
    "\n",
    "## A classical simulator for quantum circuits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fdfedde6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|00> : (0.7071067811865475+0j) \n",
      "|01> : 0j \n",
      "|10> : 0j \n",
      "|11> : (0.7071067811865475+0j) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tools import Circuit, gate_dic\n",
    "from state_vector_qpu import State, StateVectorQPU\n",
    "\n",
    "# a couple of tests\n",
    "psi = State(2)\n",
    "assert(np.linalg.norm(psi.to_vec() - np.array([1, 0, 0, 0]))<1e-13)\n",
    "\n",
    "psi.apply(gate_dic[\"H\"], [0])\n",
    "assert(np.linalg.norm(psi.to_vec() - np.array([1, 0, 1, 0])/np.sqrt(2))<1e-13)\n",
    "\n",
    "psi.apply(gate_dic[\"CNOT\"], [0, 1])\n",
    "assert(np.linalg.norm(psi.to_vec() - np.array([1, 0, 0, 1])/np.sqrt(2))<1e-13)\n",
    "\n",
    "psi.apply(gate_dic[\"CNOT\"], [0, 1])\n",
    "assert(np.linalg.norm(psi.to_vec() - np.array([1, 0, 1, 0])/np.sqrt(2))<1e-13)\n",
    "\n",
    "psi.apply(gate_dic[\"CNOT\"], [1, 0])\n",
    "assert(np.linalg.norm(psi.to_vec() - np.array([1, 0, 1, 0])/np.sqrt(2))<1e-13)\n",
    "\n",
    "psi.apply(gate_dic[\"RY\"](np.pi/2), [1])\n",
    "assert(np.linalg.norm(psi.to_vec() - np.array([1, 1, 1, 1])/2)<1e-13)\n",
    "\n",
    "# test with a circuit\n",
    "circ = Circuit(2, [(\"H\", [0]), (\"CNOT\", [0, 1])])\n",
    "\n",
    "qpu = StateVectorQPU(2, gate_dic)\n",
    "res = qpu.submit(circ)\n",
    "\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51022f62",
   "metadata": {},
   "source": [
    "## Playing with random circuits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c6cc9ffc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tools import random_circuit\n",
    "\n",
    "for nqbits in [6, 8, 10]:\n",
    "\n",
    "    circ = random_circuit(nqbits, 6)\n",
    "    qpu = StateVectorQPU(nqbits, gate_dic)\n",
    "    res2 = qpu.submit(circ)\n",
    "\n",
    "    data = abs(res2.to_vec())**2 # the probabilities\n",
    "    probs = np.linspace(0, 5, 50)\n",
    "\n",
    "    # multiply by 2^n to have more probabilities close to 1\n",
    "    plt.hist(data*(2**nqbits), bins=probs, label=nqbits, density=True)\n",
    "\n",
    "plt.plot(probs, np.exp(- probs), '--k', label = \"Porter Thomas\")\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "419853b5",
   "metadata": {},
   "source": [
    "## Going further\n",
    "\n",
    "- implement controlled gates\n",
    "- implement a quantum Fourier transform (using a recursive method)\n",
    "- implement the measurement of an observable $H$ decomposed on the Pauli basis, $H = \\sum_i \\lambda_i P_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "169579b7",
   "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": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}