shors_algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "17ab7037",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Shor's Algorithm Qiskit: https://learn.qiskit.org/course/ch-algorithms/shors-algorithm\n",
    "#controlled multiplcation circuits: https://arxiv.org/abs/quant-ph/0205095"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3cf3a223",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ignoring warnings\n",
    "import sys\n",
    "import warnings\n",
    "\n",
    "if not sys.warnoptions:\n",
    "    warnings.simplefilter(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fd2ab75b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note: This can be any hub/group/project that has access to the required device and the Qiskit runtime.\n",
    "hub = \"ibm-q\"\n",
    "group = \"open\"\n",
    "project = \"main\"\n",
    "backend_name = \"ibm_brisbane\"\n",
    "hgp = f\"{hub}/{group}/{project}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cc09d924",
   "metadata": {},
   "outputs": [],
   "source": [
    "#fetch api_key\n",
    "with open(\"api_key.txt\",\"r\") as f:\n",
    "    api_key = f.read()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "08dff487",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using backend ibm_brisbane\n"
     ]
    }
   ],
   "source": [
    "import qiskit\n",
    "from qiskit_ibm_provider import IBMProvider\n",
    "\n",
    "# Save token if necessary\n",
    "IBMProvider.save_account(overwrite=True,token=api_key)\n",
    "\n",
    "# Get our backend\n",
    "provider = IBMProvider()\n",
    "available_backends = provider.backends()\n",
    "backend = provider.get_backend(backend_name, instance=hgp)\n",
    "print(f\"Using backend {backend.name}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8bb4c6df-3fd9-49d3-aadf-4cf849a23703",
   "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, transpile\n",
    "from qiskit_aer import Aer\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": 6,
   "id": "666d5a5a-f3ce-4d8f-93ec-facc084778e5",
   "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": 7,
   "id": "f4b3f259-a0cb-416a-8ad5-8feccd6d216f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Specify variables\n",
    "N_COUNT = 8  # number of counting qubits\n",
    "a = 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "104654ed-284a-40ae-9159-730451c1d0a1",
   "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": 10,
   "id": "3612def7-c5d9-463e-8703-3c56b322d12e",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "N = 2^n, e.g. N=15\n",
    "choose some integer a such that gcd(a,N) == 1, e.g. a=7\n",
    "(1/\\sqrt{2})^n \\sum_{x=0}^N |x> |---->  (1/\\sqrt{2})^n \\sum_{x=0}^N |a^x mod N>\n",
    "a^x (mod N) is a function on (Z/NZ)^* \\cong \\prod_i (Z/p^{r_i}Z)^*, |(Z/p^{r_i}Z)^*| = \\phi(p^{r_i}) = p^{r_i}-p^{r_i-1}\n",
    "in fact, this is a periodic function meaning a^x (mod N) == 1 for multiples of r, the period, e.g. a^r == 1 (mod N)\n",
    "\"\"\";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1c8eb594-eec9-4105-9337-6337f949f96a",
   "metadata": {
    "tags": []
   },
   "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: ┤ H ├───────■─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤0      ├┤M├─────────────────────\n",
       "      ├───┤       │                                                                                                                     │       │└╥┘┌─┐                  \n",
       " q_1: ┤ H ├───────┼──────────────■──────────────────────────────────────────────────────────────────────────────────────────────────────┤1      ├─╫─┤M├──────────────────\n",
       "      ├───┤       │              │                                                                                                      │       │ ║ └╥┘┌─┐               \n",
       " q_2: ┤ H ├───────┼──────────────┼──────────────■───────────────────────────────────────────────────────────────────────────────────────┤2      ├─╫──╫─┤M├───────────────\n",
       "      ├───┤       │              │              │                                                                                       │       │ ║  ║ └╥┘┌─┐            \n",
       " q_3: ┤ H ├───────┼──────────────┼──────────────┼──────────────■────────────────────────────────────────────────────────────────────────┤3      ├─╫──╫──╫─┤M├────────────\n",
       "      ├───┤       │              │              │              │                                                                        │  QFT† │ ║  ║  ║ └╥┘┌─┐         \n",
       " q_4: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────■─────────────────────────────────────────────────────────┤4      ├─╫──╫──╫──╫─┤M├─────────\n",
       "      ├───┤       │              │              │              │              │                                                         │       │ ║  ║  ║  ║ └╥┘┌─┐      \n",
       " q_5: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────┼───────────────■─────────────────────────────────────────┤5      ├─╫──╫──╫──╫──╫─┤M├──────\n",
       "      ├───┤       │              │              │              │              │               │                                         │       │ ║  ║  ║  ║  ║ └╥┘┌─┐   \n",
       " q_6: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────┼───────────────┼───────────────■─────────────────────────┤6      ├─╫──╫──╫──╫──╫──╫─┤M├───\n",
       "      ├───┤       │              │              │              │              │               │               │                         │       │ ║  ║  ║  ║  ║  ║ └╥┘┌─┐\n",
       " q_7: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────┼───────────────┼───────────────┼────────────────■────────┤7      ├─╫──╫──╫──╫──╫──╫──╫─┤M├\n",
       "      ├───┤┌──────┴──────┐┌──────┴──────┐┌──────┴──────┐┌──────┴──────┐┌──────┴───────┐┌──────┴───────┐┌──────┴───────┐┌───────┴───────┐└───────┘ ║  ║  ║  ║  ║  ║  ║ └╥┘\n",
       " q_8: ┤ X ├┤0            ├┤0            ├┤0            ├┤0            ├┤0             ├┤0             ├┤0             ├┤0              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "      └───┘│             ││             ││             ││             ││              ││              ││              ││               │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       " q_9: ─────┤1            ├┤1            ├┤1            ├┤1            ├┤1             ├┤1             ├┤1             ├┤1              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "           │  7^1 mod 15 ││  7^2 mod 15 ││  7^4 mod 15 ││  7^8 mod 15 ││  7^16 mod 15 ││  7^32 mod 15 ││  7^64 mod 15 ││  7^128 mod 15 │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "q_10: ─────┤2            ├┤2            ├┤2            ├┤2            ├┤2             ├┤2             ├┤2             ├┤2              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "           │             ││             ││             ││             ││              ││              ││              ││               │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "q_11: ─────┤3            ├┤3            ├┤3            ├┤3            ├┤3             ├┤3             ├┤3             ├┤3              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "           └─────────────┘└─────────────┘└─────────────┘└─────────────┘└──────────────┘└──────────────┘└──────────────┘└───────────────┘          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       " c: 8/════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════╩══╩══╩══╩══╩══╩══╩══╩═\n",
       "                                                                                                                                                  0  1  2  3  4  5  6  7 </pre>"
      ],
      "text/plain": [
       "      ┌───┐                                                                                                                             ┌───────┐┌─┐                     \n",
       " q_0: ┤ H ├───────■─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┤0      ├┤M├─────────────────────\n",
       "      ├───┤       │                                                                                                                     │       │└╥┘┌─┐                  \n",
       " q_1: ┤ H ├───────┼──────────────■──────────────────────────────────────────────────────────────────────────────────────────────────────┤1      ├─╫─┤M├──────────────────\n",
       "      ├───┤       │              │                                                                                                      │       │ ║ └╥┘┌─┐               \n",
       " q_2: ┤ H ├───────┼──────────────┼──────────────■───────────────────────────────────────────────────────────────────────────────────────┤2      ├─╫──╫─┤M├───────────────\n",
       "      ├───┤       │              │              │                                                                                       │       │ ║  ║ └╥┘┌─┐            \n",
       " q_3: ┤ H ├───────┼──────────────┼──────────────┼──────────────■────────────────────────────────────────────────────────────────────────┤3      ├─╫──╫──╫─┤M├────────────\n",
       "      ├───┤       │              │              │              │                                                                        │  QFT† │ ║  ║  ║ └╥┘┌─┐         \n",
       " q_4: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────■─────────────────────────────────────────────────────────┤4      ├─╫──╫──╫──╫─┤M├─────────\n",
       "      ├───┤       │              │              │              │              │                                                         │       │ ║  ║  ║  ║ └╥┘┌─┐      \n",
       " q_5: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────┼───────────────■─────────────────────────────────────────┤5      ├─╫──╫──╫──╫──╫─┤M├──────\n",
       "      ├───┤       │              │              │              │              │               │                                         │       │ ║  ║  ║  ║  ║ └╥┘┌─┐   \n",
       " q_6: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────┼───────────────┼───────────────■─────────────────────────┤6      ├─╫──╫──╫──╫──╫──╫─┤M├───\n",
       "      ├───┤       │              │              │              │              │               │               │                         │       │ ║  ║  ║  ║  ║  ║ └╥┘┌─┐\n",
       " q_7: ┤ H ├───────┼──────────────┼──────────────┼──────────────┼──────────────┼───────────────┼───────────────┼────────────────■────────┤7      ├─╫──╫──╫──╫──╫──╫──╫─┤M├\n",
       "      ├───┤┌──────┴──────┐┌──────┴──────┐┌──────┴──────┐┌──────┴──────┐┌──────┴───────┐┌──────┴───────┐┌──────┴───────┐┌───────┴───────┐└───────┘ ║  ║  ║  ║  ║  ║  ║ └╥┘\n",
       " q_8: ┤ X ├┤0            ├┤0            ├┤0            ├┤0            ├┤0             ├┤0             ├┤0             ├┤0              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "      └───┘│             ││             ││             ││             ││              ││              ││              ││               │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       " q_9: ─────┤1            ├┤1            ├┤1            ├┤1            ├┤1             ├┤1             ├┤1             ├┤1              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "           │  7^1 mod 15 ││  7^2 mod 15 ││  7^4 mod 15 ││  7^8 mod 15 ││  7^16 mod 15 ││  7^32 mod 15 ││  7^64 mod 15 ││  7^128 mod 15 │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "q_10: ─────┤2            ├┤2            ├┤2            ├┤2            ├┤2             ├┤2             ├┤2             ├┤2              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "           │             ││             ││             ││             ││              ││              ││              ││               │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "q_11: ─────┤3            ├┤3            ├┤3            ├┤3            ├┤3             ├┤3             ├┤3             ├┤3              ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "           └─────────────┘└─────────────┘└─────────────┘└─────────────┘└──────────────┘└──────────────┘└──────────────┘└───────────────┘          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       " c: 8/════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════╩══╩══╩══╩══╩══╩══╩══╩═\n",
       "                                                                                                                                                  0  1  2  3  4  5  6  7 "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create QuantumCircuit with N_COUNT counting qubits\n",
    "# plus 4 qubits for U to act on\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": 21,
   "id": "0152c54b-b5b5-43f5-a6ce-1cc362f14853",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "- takes 3n qubits to factor an n bit number\n",
    "- with 127 qubits, than means we can factor numbers as large as 127/3 = 42 bits, so N ~ 4.4 * 10^{12}\n",
    "\"\"\";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5d352c1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import SamplerV2 as Sampler, QiskitRuntimeService\n",
    " \n",
    "# Define the service.  This allows you to access IBM QPUs.\n",
    "service = QiskitRuntimeService()\n",
    " \n",
    "# Get a backend, real or simulator\n",
    "backend = service.least_busy(operational=True, simulator=False)\n",
    "#backend = Aer.get_backend('aer_simulator')\n",
    " \n",
    "# Define Sampler\n",
    "sampler = Sampler(mode=backend)\n",
    "\n",
    "# transpile the circuit\n",
    "t_qc = transpile(qc, backend)\n",
    "\n",
    "# Run calculation\n",
    "job = sampler.run([t_qc])\n",
    " \n",
    "result = job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b0f150c9-e608-46b5-b020-51c3ffd34fb4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the counts\n",
    "counts = result[0].data.c.get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7719918a-28ee-407a-9159-dcf160205d46",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Register Output           Phase  Counts\n",
      "0    11110110(bin) = 246(dec)  246/256 = 0.96      17\n",
      "1    11001111(bin) = 207(dec)  207/256 = 0.81      34\n",
      "2    11000101(bin) = 197(dec)  197/256 = 0.77      23\n",
      "3    00010101(bin) =  21(dec)   21/256 = 0.08      28\n",
      "4    00110001(bin) =  49(dec)   49/256 = 0.19      18\n",
      "..                        ...             ...     ...\n",
      "251  01110101(bin) = 117(dec)  117/256 = 0.46       6\n",
      "252  01110111(bin) = 119(dec)  119/256 = 0.46      10\n",
      "253  11101011(bin) = 235(dec)  235/256 = 0.92       9\n",
      "254  10000000(bin) = 128(dec)  128/256 = 0.50       7\n",
      "255  10000101(bin) = 133(dec)  133/256 = 0.52       9\n",
      "\n",
      "[256 rows x 3 columns]\n",
      "         Phase Fraction  Guess for r\n",
      "0     0.960938    14/15           15\n",
      "1     0.960938    14/15           15\n",
      "2     0.960938    14/15           15\n",
      "3     0.960938    14/15           15\n",
      "4     0.960938    14/15           15\n",
      "...        ...      ...          ...\n",
      "4091  0.519531     8/15           15\n",
      "4092  0.519531     8/15           15\n",
      "4093  0.519531     8/15           15\n",
      "4094  0.519531     8/15           15\n",
      "4095  0.519531     8/15           15\n",
      "\n",
      "[4096 rows x 3 columns]\n"
     ]
    }
   ],
   "source": [
    "rows, measured_phases = [], []\n",
    "for output, count in counts.items():  # Now considering actual counts\n",
    "    decimal = int(output, 2)  # Convert (base 2) string to decimal\n",
    "    phase = decimal / (2**N_COUNT)  # Find corresponding eigenvalue\n",
    "    measured_phases.extend([phase] * count)  # Store phase weighted by count\n",
    "    rows.append([f\"{output}(bin) = {decimal:>3}(dec)\",\n",
    "                 f\"{decimal}/{2**N_COUNT} = {phase:.2f}\",\n",
    "                 count])  # Add count information\n",
    "\n",
    "# Print the table with count info\n",
    "headers = [\"Register Output\", \"Phase\", \"Counts\"]\n",
    "df = pd.DataFrame(rows, columns=headers)\n",
    "print(df)\n",
    "\n",
    "# Now, convert phases to fractions\n",
    "rows = []\n",
    "for phase in measured_phases:\n",
    "    frac = Fraction(phase).limit_denominator(15)\n",
    "    rows.append([phase,\n",
    "                 f\"{frac.numerator}/{frac.denominator}\",\n",
    "                 frac.denominator])\n",
    "\n",
    "# Print fraction table\n",
    "headers = [\"Phase\", \"Fraction\", \"Guess for r\"]\n",
    "df = pd.DataFrame(rows, columns=headers)\n",
    "print(df)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "13184b4b-a0a8-41f1-b78d-8a0a0c8b5d63",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#find a suitable value a such that a and N are coprime\n",
    "from math import gcd # greatest common divisor\n",
    "N = 15\n",
    "np.random.seed(1) # This is to make sure we get reproduceable results\n",
    "a = randint(2, N)\n",
    "print(a)\n",
    "gcd(a, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "743b192c-698c-4720-a996-9357e1cff2bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "for a=7, N=15\n",
    "we have a function a^x (mod N) and seek the period r\n",
    "a^r == 1 (mod N)\n",
    "a^r - 1 == 0 (mod N)\n",
    "assuming r is even: (a^{r/2}-1)*(a^{r/2}+1) == 0 (mod N)\n",
    "implies that (a^{r/2}-1)*(a^{r/2}+1) | N\n",
    "then gcd(a^{r/2}-1,N), gcd(a^{r/2}+1,N) is a likely divisor of N\n",
    "\"\"\";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "20025ca7-71ed-4215-a8a4-a6d1ab5173a3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#quantum phase estimation for N=15 with manual U gates\n",
    "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",
    "    t_qc = transpile(qc, backend)\n",
    "    job = sampler.run([t_qc])\n",
    "    result = job.result()\n",
    "    counts = result[0].data.c.get_counts()\n",
    "    max_index = max(counts)\n",
    "    max_count = counts[max_index]\n",
    "    print(\"Register Reading: \" + str(max_count))\n",
    "    phase = max_count/(2**N_COUNT)\n",
    "    print(f\"Corresponding Phase: {phase}\")\n",
    "    return phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
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     "text": [
      "Period:  15\n",
      "Guess for factors:  [3, 1]\n"
     ]
    }
   ],
   "source": [
    "#phase = qpe_amod15(a) # Phase = s/r\n",
    "Fraction(phase).limit_denominator(15)\n",
    "r = frac.denominator\n",
    "guesses = [gcd(a**(r//2)-1, N), gcd(a**(r//2)+1, N)]\n",
    "print(\"Period: \", r)\n",
    "print(\"Guess for factors: \",guesses)"
   ]
  },
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   "cell_type": "code",
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   "id": "fd95996d-c25b-4f38-9653-127b9893d87d",
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      "\n",
      "ATTEMPT 1:\n",
      "Register Reading: 257\n",
      "Corresponding Phase: 1.00390625\n",
      "Result: r = 1\n",
      "Guessed Factors: 15 and 1\n",
      "\n",
      "ATTEMPT 2:\n",
      "Register Reading: 256\n",
      "Corresponding Phase: 1.0\n",
      "Result: r = 1\n",
      "Guessed Factors: 15 and 1\n",
      "\n",
      "ATTEMPT 3:\n",
      "Register Reading: 262\n",
      "Corresponding Phase: 1.0234375\n",
      "Result: r = 1\n",
      "Guessed Factors: 15 and 1\n",
      "\n",
      "ATTEMPT 4:\n",
      "Register Reading: 252\n",
      "Corresponding Phase: 0.984375\n",
      "Result: r = 1\n",
      "Guessed Factors: 15 and 1\n",
      "\n",
      "ATTEMPT 5:\n",
      "Register Reading: 260\n",
      "Corresponding Phase: 1.015625\n",
      "Result: r = 1\n",
      "Guessed Factors: 15 and 1\n",
      "\n",
      "ATTEMPT 6:\n",
      "Register Reading: 257\n",
      "Corresponding Phase: 1.00390625\n",
      "Result: r = 1\n",
      "Guessed Factors: 15 and 1\n",
      "\n",
      "ATTEMPT 7:\n",
      "Register Reading: 260\n",
      "Corresponding Phase: 1.015625\n",
      "Result: r = 1\n",
      "Guessed Factors: 15 and 1\n",
      "\n",
      "ATTEMPT 8:\n",
      "Register Reading: 273\n",
      "Corresponding Phase: 1.06640625\n",
      "Result: r = 15\n",
      "Guessed Factors: 3 and 1\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"
   ]
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