controlled_modular_multiplication.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "81ead48d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#controlled modular multiplcation: https://arxiv.org/abs/quant-ph/0205095\n",
    "#medium post: https://medium.com/mit-6-s089-intro-to-quantum-computing/a-general-implementation-of-shors-algorithm-da1595694430\n",
    "#draper paper: https://arxiv.org/pdf/quant-ph/0008033.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3f79ab5d",
   "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": "262ce607",
   "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": "ff8ea9d8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/tr/w3stjb6j0pg_svqnfxtymf0w0000gn/T/ipykernel_9261/3827830370.py:2: DeprecationWarning: The package qiskit_ibm_provider is being deprecated. Please see https://docs.quantum.ibm.com/api/migration-guides/qiskit-runtime to get instructions on how to migrate to qiskit-ibm-runtime (https://github.com/Qiskit/qiskit-ibm-runtime).\n",
      "  from qiskit_ibm_provider import IBMProvider\n"
     ]
    },
    {
     "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": "f4a955ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, transpile\n",
    "from qiskit_aer import Aer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5bc8c5ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Controlled multiplication by a mod 15\"\"\"\n",
    "def c_amod15(a, power):\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": "0fb07b28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Instruction(name='c7^1 mod 15', num_qubits=5, num_clbits=0, params=[])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_amod15(7,2**0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f5c9c268",
   "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: ┤ X ├───────■───────┤M├────────────\n",
       "     ├───┤┌──────┴──────┐└╥┘┌─┐         \n",
       "q_1: ┤ X ├┤0            ├─╫─┤M├─────────\n",
       "     ├───┤│             │ ║ └╥┘┌─┐      \n",
       "q_2: ┤ X ├┤1            ├─╫──╫─┤M├──────\n",
       "     ├───┤│  7^1 mod 15 │ ║  ║ └╥┘┌─┐   \n",
       "q_3: ┤ X ├┤2            ├─╫──╫──╫─┤M├───\n",
       "     └───┘│             │ ║  ║  ║ └╥┘┌─┐\n",
       "q_4: ─────┤3            ├─╫──╫──╫──╫─┤M├\n",
       "          └─────────────┘ ║  ║  ║  ║ └╥┘\n",
       "c: 5/═════════════════════╩══╩══╩══╩══╩═\n",
       "                          0  1  2  3  4 </pre>"
      ],
      "text/plain": [
       "     ┌───┐               ┌─┐            \n",
       "q_0: ┤ X ├───────■───────┤M├────────────\n",
       "     ├───┤┌──────┴──────┐└╥┘┌─┐         \n",
       "q_1: ┤ X ├┤0            ├─╫─┤M├─────────\n",
       "     ├───┤│             │ ║ └╥┘┌─┐      \n",
       "q_2: ┤ X ├┤1            ├─╫──╫─┤M├──────\n",
       "     ├───┤│  7^1 mod 15 │ ║  ║ └╥┘┌─┐   \n",
       "q_3: ┤ X ├┤2            ├─╫──╫──╫─┤M├───\n",
       "     └───┘│             │ ║  ║  ║ └╥┘┌─┐\n",
       "q_4: ─────┤3            ├─╫──╫──╫──╫─┤M├\n",
       "          └─────────────┘ ║  ║  ║  ║ └╥┘\n",
       "c: 5/═════════════════════╩══╩══╩══╩══╩═\n",
       "                          0  1  2  3  4 "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc=QuantumCircuit(5,5)\n",
    "qc.x(0)\n",
    "qc.x(1)\n",
    "qc.x(2)\n",
    "qc.x(3)\n",
    "#qc.x(4)\n",
    "qc.append(c_amod15(7,2**0),[0]+[1+i for i in range(4)])\n",
    "qc.measure(range(5), range(5))\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8fdbd3a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    "import matplotlib\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "t_qc = transpile(qc, aer_sim)\n",
    "counts = aer_sim.run(t_qc).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "87535549",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit.circuit.library import QFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9c27a6d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#build the phi adder circuit\n",
    "a=[0,0,1,1]\n",
    "b=[0,0,1,1]\n",
    "def phi_add(num_bits):\n",
    "    qc = QuantumCircuit(2*num_bits,num_bits)\n",
    "    #initialize a register\n",
    "    for i in range(len(a)):\n",
    "        if a[i] != 0: \n",
    "            qc.x(i)\n",
    "    #initialize b register\n",
    "    for i in range(len(b)):\n",
    "        if b[i] != 0: \n",
    "            qc.x(num_bits+i)\n",
    "    #append Fourier transform to second register\n",
    "    qc.append(QFT(num_qubits=num_bits,do_swaps=False),range(num_bits,2*num_bits))\n",
    "    #append controlled phase addition gates\n",
    "    for k in range(num_bits):\n",
    "        for j in range(num_bits-k):\n",
    "            qc.cp(2*np.pi/2**(j+1),control_qubit=num_bits-k-1-j,target_qubit=2*num_bits-k-1)\n",
    "    #append inverse Fourier transform to second register\n",
    "    qc.append(QFT(num_qubits=num_bits,do_swaps=False,inverse=True),range(num_bits,2*num_bits))\n",
    "    qc.measure(range(num_bits,2*num_bits), range(num_bits))\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fff94ac5",
   "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: ──────────────────────────────────────────────■─────────────────■───────»\n",
       "                                                   │                 │       »\n",
       "q_1: ──────────────────────────────■───────────────┼────────■────────┼───────»\n",
       "     ┌───┐                         │               │        │        │       »\n",
       "q_2: ┤ X ├────────────────■────────┼────────■──────┼────────┼────────┼───────»\n",
       "     ├───┤                │        │        │      │        │        │       »\n",
       "q_3: ┤ X ├─────────■──────┼────────┼────────┼──────┼────────┼────────┼───────»\n",
       "     └───┘┌──────┐ │      │        │        │      │        │        │       »\n",
       "q_4: ─────┤0     ├─┼──────┼────────┼────────┼──────┼────────┼────────┼───────»\n",
       "          │      │ │      │        │        │      │        │        │       »\n",
       "q_5: ─────┤1     ├─┼──────┼────────┼────────┼──────┼────────┼────────┼───────»\n",
       "     ┌───┐│  QFT │ │      │        │        │P(π)  │        │P(π/2)  │P(π/4) »\n",
       "q_6: ┤ X ├┤2     ├─┼──────┼────────┼────────■──────┼────────■────────■───────»\n",
       "     ├───┤│      │ │P(π)  │P(π/2)  │P(π/4)         │P(π/8)                   »\n",
       "q_7: ┤ X ├┤3     ├─■──────■────────■───────────────■─────────────────────────»\n",
       "     └───┘└──────┘                                                           »\n",
       "c: 4/════════════════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       "«                                                 \n",
       "«q_0: ────────■────────■──────────────────────────\n",
       "«             │        │                          \n",
       "«q_1: ─■──────┼────────┼──────────────────────────\n",
       "«      │      │        │                          \n",
       "«q_2: ─┼──────┼────────┼──────────────────────────\n",
       "«      │      │        │                          \n",
       "«q_3: ─┼──────┼────────┼──────────────────────────\n",
       "«      │      │        │P(π) ┌───────┐┌─┐         \n",
       "«q_4: ─┼──────┼────────■─────┤0      ├┤M├─────────\n",
       "«      │P(π)  │P(π/2)        │       │└╥┘┌─┐      \n",
       "«q_5: ─■──────■──────────────┤1      ├─╫─┤M├──────\n",
       "«                            │  IQFT │ ║ └╥┘┌─┐   \n",
       "«q_6: ───────────────────────┤2      ├─╫──╫─┤M├───\n",
       "«                            │       │ ║  ║ └╥┘┌─┐\n",
       "«q_7: ───────────────────────┤3      ├─╫──╫──╫─┤M├\n",
       "«                            └───────┘ ║  ║  ║ └╥┘\n",
       "«c: 4/═════════════════════════════════╩══╩══╩══╩═\n",
       "«                                      0  1  2  3 </pre>"
      ],
      "text/plain": [
       "                                                                             »\n",
       "q_0: ──────────────────────────────────────────────■─────────────────■───────»\n",
       "                                                   │                 │       »\n",
       "q_1: ──────────────────────────────■───────────────┼────────■────────┼───────»\n",
       "     ┌───┐                         │               │        │        │       »\n",
       "q_2: ┤ X ├────────────────■────────┼────────■──────┼────────┼────────┼───────»\n",
       "     ├───┤                │        │        │      │        │        │       »\n",
       "q_3: ┤ X ├─────────■──────┼────────┼────────┼──────┼────────┼────────┼───────»\n",
       "     └───┘┌──────┐ │      │        │        │      │        │        │       »\n",
       "q_4: ─────┤0     ├─┼──────┼────────┼────────┼──────┼────────┼────────┼───────»\n",
       "          │      │ │      │        │        │      │        │        │       »\n",
       "q_5: ─────┤1     ├─┼──────┼────────┼────────┼──────┼────────┼────────┼───────»\n",
       "     ┌───┐│  QFT │ │      │        │        │P(π)  │        │P(π/2)  │P(π/4) »\n",
       "q_6: ┤ X ├┤2     ├─┼──────┼────────┼────────■──────┼────────■────────■───────»\n",
       "     ├───┤│      │ │P(π)  │P(π/2)  │P(π/4)         │P(π/8)                   »\n",
       "q_7: ┤ X ├┤3     ├─■──────■────────■───────────────■─────────────────────────»\n",
       "     └───┘└──────┘                                                           »\n",
       "c: 4/════════════════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       "«                                                 \n",
       "«q_0: ────────■────────■──────────────────────────\n",
       "«             │        │                          \n",
       "«q_1: ─■──────┼────────┼──────────────────────────\n",
       "«      │      │        │                          \n",
       "«q_2: ─┼──────┼────────┼──────────────────────────\n",
       "«      │      │        │                          \n",
       "«q_3: ─┼──────┼────────┼──────────────────────────\n",
       "«      │      │        │P(π) ┌───────┐┌─┐         \n",
       "«q_4: ─┼──────┼────────■─────┤0      ├┤M├─────────\n",
       "«      │P(π)  │P(π/2)        │       │└╥┘┌─┐      \n",
       "«q_5: ─■──────■──────────────┤1      ├─╫─┤M├──────\n",
       "«                            │  IQFT │ ║ └╥┘┌─┐   \n",
       "«q_6: ───────────────────────┤2      ├─╫──╫─┤M├───\n",
       "«                            │       │ ║  ║ └╥┘┌─┐\n",
       "«q_7: ───────────────────────┤3      ├─╫──╫──╫─┤M├\n",
       "«                            └───────┘ ║  ║  ║ └╥┘\n",
       "«c: 4/═════════════════════════════════╩══╩══╩══╩═\n",
       "«                                      0  1  2  3 "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phi_add(4).draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8b127f9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_qc = transpile(phi_add(4), aer_sim)\n",
    "counts = aer_sim.run(t_qc).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "19779e43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1000'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(counts, key=counts.get)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c13dc6dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "#use built in Draper QFT adder\n",
    "from qiskit.circuit.library import DraperQFTAdder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "54144733",
   "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",
       "a_0: ┤0                ├\n",
       "     │                 │\n",
       "a_1: ┤1                ├\n",
       "     │                 │\n",
       "a_2: ┤2                ├\n",
       "     │  DraperQFTAdder │\n",
       "b_0: ┤3                ├\n",
       "     │                 │\n",
       "b_1: ┤4                ├\n",
       "     │                 │\n",
       "b_2: ┤5                ├\n",
       "     └─────────────────┘</pre>"
      ],
      "text/plain": [
       "     ┌─────────────────┐\n",
       "a_0: ┤0                ├\n",
       "     │                 │\n",
       "a_1: ┤1                ├\n",
       "     │                 │\n",
       "a_2: ┤2                ├\n",
       "     │  DraperQFTAdder │\n",
       "b_0: ┤3                ├\n",
       "     │                 │\n",
       "b_1: ┤4                ├\n",
       "     │                 │\n",
       "b_2: ┤5                ├\n",
       "     └─────────────────┘"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DraperQFTAdder(3).draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "685c2563",
   "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",
       "a_0: ┤0                   ├\n",
       "     │                    │\n",
       "a_1: ┤1                   ├\n",
       "     │                    │\n",
       "a_2: ┤2                   ├\n",
       "     │  DraperQFTAdder_dg │\n",
       "b_0: ┤3                   ├\n",
       "     │                    │\n",
       "b_1: ┤4                   ├\n",
       "     │                    │\n",
       "b_2: ┤5                   ├\n",
       "     └────────────────────┘</pre>"
      ],
      "text/plain": [
       "     ┌────────────────────┐\n",
       "a_0: ┤0                   ├\n",
       "     │                    │\n",
       "a_1: ┤1                   ├\n",
       "     │                    │\n",
       "a_2: ┤2                   ├\n",
       "     │  DraperQFTAdder_dg │\n",
       "b_0: ┤3                   ├\n",
       "     │                    │\n",
       "b_1: ┤4                   ├\n",
       "     │                    │\n",
       "b_2: ┤5                   ├\n",
       "     └────────────────────┘"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DraperQFTAdder(3).inverse().draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f6f86b21",
   "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: ┤ X ├┤0                ├─────────\n",
       "     ├───┤│                 │         \n",
       "q_1: ┤ X ├┤1                ├─────────\n",
       "     ├───┤│                 │         \n",
       "q_2: ┤ X ├┤2                ├─────────\n",
       "     ├───┤│  DraperQFTAdder │┌─┐      \n",
       "q_3: ┤ X ├┤3                ├┤M├──────\n",
       "     ├───┤│                 │└╥┘┌─┐   \n",
       "q_4: ┤ X ├┤4                ├─╫─┤M├───\n",
       "     ├───┤│                 │ ║ └╥┘┌─┐\n",
       "q_5: ┤ X ├┤5                ├─╫──╫─┤M├\n",
       "     └───┘└─────────────────┘ ║  ║ └╥┘\n",
       "c: 3/═════════════════════════╩══╩══╩═\n",
       "                              0  1  2 </pre>"
      ],
      "text/plain": [
       "     ┌───┐┌─────────────────┐         \n",
       "q_0: ┤ X ├┤0                ├─────────\n",
       "     ├───┤│                 │         \n",
       "q_1: ┤ X ├┤1                ├─────────\n",
       "     ├───┤│                 │         \n",
       "q_2: ┤ X ├┤2                ├─────────\n",
       "     ├───┤│  DraperQFTAdder │┌─┐      \n",
       "q_3: ┤ X ├┤3                ├┤M├──────\n",
       "     ├───┤│                 │└╥┘┌─┐   \n",
       "q_4: ┤ X ├┤4                ├─╫─┤M├───\n",
       "     ├───┤│                 │ ║ └╥┘┌─┐\n",
       "q_5: ┤ X ├┤5                ├─╫──╫─┤M├\n",
       "     └───┘└─────────────────┘ ║  ║ └╥┘\n",
       "c: 3/═════════════════════════╩══╩══╩═\n",
       "                              0  1  2 "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc=QuantumCircuit(6,3)\n",
    "qc.x(0)\n",
    "qc.x(1)\n",
    "qc.x(2)\n",
    "qc.x(3)\n",
    "qc.x(4)\n",
    "qc.x(5)\n",
    "qc.append(DraperQFTAdder(3),range(6))\n",
    "qc.measure(range(3,6),range(3))\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0ec2ada4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_qc = transpile(qc, aer_sim)\n",
    "counts = aer_sim.run(t_qc).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4dde9cdb",
   "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",
       "     ┌───┐│                   │         \n",
       "q_1: ┤ X ├┤1                  ├─────────\n",
       "     ├───┤│                   │         \n",
       "q_2: ┤ X ├┤2                  ├─────────\n",
       "     ├───┤│                   │         \n",
       "q_3: ┤ X ├┤3 c_DraperQFTAdder ├─────────\n",
       "     ├───┤│                   │┌─┐      \n",
       "q_4: ┤ X ├┤4                  ├┤M├──────\n",
       "     ├───┤│                   │└╥┘┌─┐   \n",
       "q_5: ┤ X ├┤5                  ├─╫─┤M├───\n",
       "     ├───┤│                   │ ║ └╥┘┌─┐\n",
       "q_6: ┤ X ├┤6                  ├─╫──╫─┤M├\n",
       "     └───┘└───────────────────┘ ║  ║ └╥┘\n",
       "c: 3/═══════════════════════════╩══╩══╩═\n",
       "                                0  1  2 </pre>"
      ],
      "text/plain": [
       "          ┌───────────────────┐         \n",
       "q_0: ─────┤0                  ├─────────\n",
       "     ┌───┐│                   │         \n",
       "q_1: ┤ X ├┤1                  ├─────────\n",
       "     ├───┤│                   │         \n",
       "q_2: ┤ X ├┤2                  ├─────────\n",
       "     ├───┤│                   │         \n",
       "q_3: ┤ X ├┤3 c_DraperQFTAdder ├─────────\n",
       "     ├───┤│                   │┌─┐      \n",
       "q_4: ┤ X ├┤4                  ├┤M├──────\n",
       "     ├───┤│                   │└╥┘┌─┐   \n",
       "q_5: ┤ X ├┤5                  ├─╫─┤M├───\n",
       "     ├───┤│                   │ ║ └╥┘┌─┐\n",
       "q_6: ┤ X ├┤6                  ├─╫──╫─┤M├\n",
       "     └───┘└───────────────────┘ ║  ║ └╥┘\n",
       "c: 3/═══════════════════════════╩══╩══╩═\n",
       "                                0  1  2 "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc=QuantumCircuit(7,3)\n",
    "#qc.x(0)\n",
    "qc.x(1)\n",
    "qc.x(2)\n",
    "qc.x(3)\n",
    "qc.x(4)\n",
    "qc.x(5)\n",
    "qc.x(6)\n",
    "qc.append(DraperQFTAdder(3).control(),range(7))\n",
    "qc.measure(range(4,7),range(3))\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "62985dde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_qc = transpile(qc, aer_sim)\n",
    "counts = aer_sim.run(t_qc).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "quantum",
   "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": "3.13.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}