quantum_fourier_transf.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Fourier Transform\n",
    "In this notebook, we write the code for the Quantum Fourier Transform using Qiskit. The code is designed for an arbitrary number of qubits\n",
    "\n",
    "References:\n",
    "- Qiskit Textbook, Quantum Fourier Transform: https://qiskit.org/textbook/ch-algorithms/quantum-fourier-transform.html\n",
    "\n",
    "- Nielsen, M., & Chuang, I. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge: Cambridge University Press.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "# importing Qiskit\n",
    "from qiskit import QuantumCircuit\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can start by doing an example for 3 qubits. First, we apply a Hadamard gate in the last qubit, qubit 2, and then apply controlled rotations using qubit 2 and the PRECEDING qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 538.33x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(3)\n",
    "qc.h(2)\n",
    "qc.cp(np.pi/2, 1, 2)\n",
    "qc.cp(np.pi/4, 0, 2)\n",
    "qc.draw('mpl')\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then do the same for qubit 1, but this time we will only have one PRECEDING qubit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 789.163x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.h(1)\n",
    "qc.cp(np.pi/2, 0, 1) # CROT from qubit 0 to qubit 1\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we do the same for qubit 0, but it has no preceding qubits, so it's only a Hadamard gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 872.774x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.h(0)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to perform a swap before we complete the circuit, so we invert the order of the qubits. For 3 qubits, we only need one swap gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 956.385x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.swap(0,2)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now generalize the code for an arbitraty number of qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def qft_rotations(n):\n",
    "    ''' Apply the rotarions for Quantum Fourier Transform\n",
    "    n: Number of Qubits\n",
    "    '''\n",
    "    list_qubits = range(n)\n",
    "    qc = QuantumCircuit(n)\n",
    "    for i in range(n):\n",
    "        qc.h(n-1-i)\n",
    "        for j in range(n-1-i):\n",
    "            p = np.pi/(2**(j+1))\n",
    "            qc.cp(p, j, n-1-i)\n",
    "    return qc\n",
    "\n",
    "def qft_swaps(n):\n",
    "    ''' Apply the swaps for the Quantum Fourier Transform\n",
    "    n: Number of qubits\n",
    "    '''\n",
    "    qc = QuantumCircuit(n)\n",
    "    for j in range(n//2):\n",
    "        qc.swap(j, n-j-1)\n",
    "    return qc\n",
    "\n",
    "def qft(n_qubits):\n",
    "    ''' Apply Quantum Fourier Transform in n qubits. Performs qubits swap at the end\n",
    "    n_qubits: Number of qubits\n",
    "    '''\n",
    "    qc = QuantumCircuit(n_qubits)\n",
    "    qc.append(qft_rotations(n_qubits), range(n_qubits))\n",
    "    qc.append(qft_swaps(n_qubits), range(n_qubits))\n",
    "\n",
    "    return qc\n",
    "    \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 956.385x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = qft(3)\n",
    "qc.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2210.55x953.167 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = qft(5)\n",
    "qc.decompose().draw('mpl')"
   ]
  }
 ],
 "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": "3.10.8"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}