fourier-checking-circuit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fourier Checking Circuit\n",
    "Referenced from Coding with Qiskit S2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit.quantum_info as qi\n",
    "from qiskit.circuit.library import FourierChecking\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions as lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = [1, -1, -1, -1]\n",
    "g = [1, 1, -1, -1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fourier Checking\n",
    "The fourier checking circuit will test how correlated the fourier transform of function `g` is to our function `f`. If the output of the state `00` is greater than `0.05`, it means that the function `g` is correlated with `f`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌──────────────────────────────────────┐\n",
       "q_0: ┤0                                     ├\n",
       "     │  fc: [1, -1, -1, -1], [1, 1, -1, -1] │\n",
       "q_1: ┤1                                     ├\n",
       "     └──────────────────────────────────────┘</pre>"
      ],
      "text/plain": [
       "     ┌──────────────────────────────────────┐\n",
       "q_0: ┤0                                     ├\n",
       "     │  fc: [1, -1, -1, -1], [1, 1, -1, -1] │\n",
       "q_1: ┤1                                     ├\n",
       "     └──────────────────────────────────────┘"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = FourierChecking(f=f, g=g)\n",
    "circuit.draw()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running the Circuit\n",
    "Initializing the `00` state vector and evolving it through the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zero = qi.Statevector.from_label(\"00\")\n",
    "sv = zero.evolve(circuit)\n",
    "probs = sv.probabilities_dict()\n",
    "plot_histogram(probs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "Since the `00` state outputs the probability of `0.250` (which is greater than `0.05`), its clear that the function `g` is correlated to function `f`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Function 'g' is correlated to function 'g'\n"
     ]
    }
   ],
   "source": [
    "if probs['00'] > 0.05:\n",
    "    print(\"Function 'g' is correlated to function 'g'\")\n",
    "else:\n",
    "    print(\"Not correlated!\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "qiskit",
   "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": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}