PHY_QUANT_GATES.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ea390047-d653-45d2-9e54-c20312147300",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imports Successful\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from qiskit import QuantumCircuit, Aer, transpile\n",
    "from qiskit.visualization import plot_histogram\n",
    "from math import gcd\n",
    "from numpy.random import randint\n",
    "import pandas as pd\n",
    "from fractions import Fraction\n",
    "print(\"Imports Successful\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "91fa7236-38f1-4075-b318-5a588638a52d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 35\n",
    "a = 3\n",
    "\n",
    "# Calculate the plotting data\n",
    "xvals = np.arange(35)\n",
    "yvals = [np.mod(a**x, N) for x in xvals]\n",
    "\n",
    "# Use matplotlib to display it nicely\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xvals, yvals, linewidth=1, linestyle='dotted', marker='x')\n",
    "ax.set(xlabel='$x$', ylabel=f'${a}^x$ mod ${N}$',\n",
    "       title=\"Example of Periodic Function in Shor's Algorithm\")\n",
    "try: # plot r on the graph\n",
    "    r = yvals[1:].index(1) + 1\n",
    "    plt.annotate('', xy=(0,1), xytext=(r,1),\n",
    "                 arrowprops=dict(arrowstyle='<->'))\n",
    "    plt.annotate(f'$r={r}$', xy=(r/3,1.5))\n",
    "except ValueError:\n",
    "    print('Could not find period, check a < N and have no common factors.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "fa9baf4a-59c8-4da3-ad8e-c9f8ed10ace1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def c_amod15(a, power):\n",
    "    \"\"\"Controlled multiplication by a mod 15\"\"\"\n",
    "    if a not in [2,4,7,8,11,13]:\n",
    "        raise ValueError(\"'a' must be 2,4,7,8,11 or 13\")\n",
    "    U = QuantumCircuit(4)\n",
    "    for _iteration in range(power):\n",
    "        if a in [2,13]:\n",
    "            U.swap(2,3)\n",
    "            U.swap(1,2)\n",
    "            U.swap(0,1)\n",
    "        if a in [7,8]:\n",
    "            U.swap(0,1)\n",
    "            U.swap(1,2)\n",
    "            U.swap(2,3)\n",
    "        if a in [4, 11]:\n",
    "            U.swap(1,3)\n",
    "            U.swap(0,2)\n",
    "        if a in [7,11,13]:\n",
    "            for q in range(4):\n",
    "                U.x(q)\n",
    "    U = U.to_gate()\n",
    "    U.name = f\"{a}^{power} mod 15\"\n",
    "    c_U = U.control()\n",
    "    return c_U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "428596dc-8573-4c72-bbb2-835fdff132fe",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def qft_dagger(n):\n",
    "    \"\"\"n-qubit QFTdagger the first n qubits in circ\"\"\"\n",
    "    qc = QuantumCircuit(n)\n",
    "    # Don't forget the Swaps!\n",
    "    for qubit in range(n//2):\n",
    "        qc.swap(qubit, n-qubit-1)\n",
    "    for j in range(n):\n",
    "        for m in range(j):\n",
    "            qc.cp(-np.pi/float(2**(j-m)), m, j)\n",
    "        qc.h(j)\n",
    "    qc.name = \"QFT†\"\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "fff8ad73-8cc9-43bf-9384-b8ba1971abd4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 15\n",
    "np.random.seed(1) # This is to make sure we get reproduceable results\n",
    "a = randint(2, 15)\n",
    "print(a)\n",
    "from math import gcd # greatest common divisor\n",
    "gcd(a, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "77ec8302-dab4-4a12-a928-daa29fd45334",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def qpe_amod15(a):\n",
    "    \"\"\"Performs quantum phase estimation on the operation a*r mod 15.\n",
    "    Args:\n",
    "        a (int): This is 'a' in a*r mod 15\n",
    "    Returns:\n",
    "        float: Estimate of the phase\n",
    "    \"\"\"\n",
    "    N_COUNT = 8\n",
    "    qc = QuantumCircuit(4+N_COUNT, N_COUNT)\n",
    "    for q in range(N_COUNT):\n",
    "        qc.h(q)     # Initialize counting qubits in state |+>\n",
    "    qc.x(3+N_COUNT) # And auxiliary register in state |1>\n",
    "    for q in range(N_COUNT): # Do controlled-U operations\n",
    "        qc.append(c_amod15(a, 2**q),\n",
    "                 [q] + [i+N_COUNT for i in range(4)])\n",
    "    qc.append(qft_dagger(N_COUNT), range(N_COUNT)) # Do inverse-QFT\n",
    "    qc.measure(range(N_COUNT), range(N_COUNT))\n",
    "    # Simulate Results\n",
    "    aer_sim = Aer.get_backend('aer_simulator')\n",
    "    # `memory=True` tells the backend to save each measurement in a list\n",
    "    job = aer_sim.run(transpile(qc, aer_sim), shots=1, memory=True)\n",
    "    readings = job.result().get_memory()\n",
    "    print(\"Register Reading: \" + readings[0])\n",
    "    phase = int(readings[0],2)/(2**N_COUNT)\n",
    "    print(f\"Corresponding Phase: {phase}\")\n",
    "    return phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "93f0d747-4a76-4de7-a3f6-e3696b0ffb6a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Register Reading: 01000000\n",
      "Corresponding Phase: 0.25\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "phase = qpe_amod15(a) # Phase = s/r\n",
    "Fraction(phase).limit_denominator(15)\n",
    "frac = Fraction(phase).limit_denominator(15)\n",
    "s, r = frac.numerator, frac.denominator\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "00b252fd-2681-44cd-8b1f-025cb7fa4b14",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 5]\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "a602cb0d-5774-498e-a30e-8e0637d17c04",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ATTEMPT 1:\n",
      "Register Reading: 00000000\n",
      "Corresponding Phase: 0.0\n",
      "Result: r = 1\n",
      "\n",
      "ATTEMPT 2:\n",
      "Register Reading: 11000000\n",
      "Corresponding Phase: 0.75\n",
      "Result: r = 4\n",
      "Guessed Factors: 3 and 5\n",
      "*** Non-trivial factor found: {guess} ***\n",
      "*** Non-trivial factor found: {guess} ***\n"
     ]
    }
   ],
   "source": [
    "a = 7\n",
    "FACTOR_FOUND = False\n",
    "ATTEMPT = 0\n",
    "while not FACTOR_FOUND:\n",
    "    ATTEMPT += 1\n",
    "    print(f\"\\nATTEMPT {ATTEMPT}:\")\n",
    "    phase = qpe_amod15(a) # Phase = s/r\n",
    "    frac = Fraction(phase).limit_denominator(N)\n",
    "    r = frac.denominator\n",
    "    print(f\"Result: r = {r}\")\n",
    "    if phase != 0:\n",
    "        # Guesses for factors are gcd(x^{r/2} ±1 , 15)\n",
    "        guesses = [gcd(a**(r//2)-1, N), gcd(a**(r//2)+1, N)]\n",
    "        print(f\"Guessed Factors: {guesses[0]} and {guesses[1]}\")\n",
    "        for guess in guesses:\n",
    "            if guess not in [1,N] and (N % guess) == 0:\n",
    "                # Guess is a factor!\n",
    "                print(\"*** Non-trivial factor found: {guess} ***\")\n",
    "                FACTOR_FOUND = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "85b202f8-88ab-4452-9194-811695f98fe3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 3064.69x1120.39 with 1 Axes>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create QuantumCircuit with N_COUNT counting qubits\n",
    "# plus 4 qubits for U to act on\n",
    "N_COUNT = 8\n",
    "qc = QuantumCircuit(N_COUNT + 4, N_COUNT)\n",
    "\n",
    "# Initialize counting qubits\n",
    "# in state |+>\n",
    "for q in range(N_COUNT):\n",
    "    qc.h(q)\n",
    "\n",
    "# And auxiliary register in state |1>\n",
    "qc.x(N_COUNT)\n",
    "\n",
    "# Do controlled-U operations\n",
    "for q in range(N_COUNT):\n",
    "    qc.append(c_amod15(a, 2**q),\n",
    "             [q] + [i+N_COUNT for i in range(4)])\n",
    "\n",
    "# Do inverse-QFT\n",
    "qc.append(qft_dagger(N_COUNT), range(N_COUNT))\n",
    "\n",
    "# Measure circuit\n",
    "qc.measure(range(N_COUNT), range(N_COUNT))\n",
    "qc.draw(fold=-1)  # -1 means 'do not fold'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "623e4bb1-80d5-4045-ac10-538acdd47494",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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