Pattern Matching by Grover's Search.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import qiskit\n",
    "from qiskit import IBMQ\n",
    "from qiskit import Aer, execute\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, QiskitError\n",
    "from qiskit.quantum_info.operators import Operator\n",
    "from qiskit.tools.visualization import circuit_drawer\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit.tools.visualization import plot_state_city\n",
    "from qiskit.providers.aer import noise\n",
    "import random\n",
    "from math import *\n",
    "import math\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "%config InlineBackend.figure_format = 'png' # Makes the images look nice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_oracle(circuit, n_string, index_position, match_position, pattern_position, ancilla_position):\n",
    "    temp_position = n_string\n",
    "    n_pattern = pattern_position - match_position\n",
    "    n_index = ancilla_position - index_position\n",
    "    # apply oracle\n",
    "\n",
    "\n",
    "    delta = 1\n",
    "    \n",
    "    for i in range(n_index):\n",
    "        n_reg = n_string if i < n_index - 1 else n_pattern\n",
    "        for j in range(n_reg):\n",
    "            # not shifted\n",
    "            circuit.x(index_position + i)\n",
    "#             print(temp_position - n_string + j, index_position + i, temp_position + j)\n",
    "            circuit.ccx(temp_position - n_string + j, index_position + i, temp_position + j)\n",
    "            circuit.x(index_position + i)\n",
    "            # shifted\n",
    "            if j + delta < n_string:\n",
    "                circuit.ccx(temp_position - n_string + j + delta, index_position + i, temp_position + j)\n",
    "        delta *= 2\n",
    "        temp_position += n_string\n",
    "        circuit.barrier()\n",
    "    \n",
    "    \n",
    "    \n",
    "    for i in range(n_pattern):\n",
    "        # 111\n",
    "        circuit.ccx(match_position + i, pattern_position + i, ancilla_position + i)\n",
    "        \n",
    "        # 001\n",
    "        circuit.x(match_position + i)\n",
    "        circuit.x(pattern_position + i)\n",
    "        circuit.ccx(match_position + i, pattern_position + i, ancilla_position + i)\n",
    "        circuit.x(match_position + i)\n",
    "        circuit.x(pattern_position + i)\n",
    "        \n",
    "        circuit.barrier()\n",
    "        \n",
    "    \n",
    "#     circuit.h(ancilla_position + n_pattern)\n",
    "    circuit.mct(list(range(ancilla_position, ancilla_position + n_pattern)), ancilla_position + n_pattern)\n",
    "#     circuit.h(ancilla_position + n_pattern)\n",
    "    \n",
    "    circuit.barrier()\n",
    "    \n",
    "    # reverse oracle\n",
    "    for i in range(n_pattern - 1, -1, -1):\n",
    "        # 001\n",
    "        circuit.x(pattern_position + i)\n",
    "        circuit.x(match_position + i)\n",
    "        circuit.ccx(match_position + i, pattern_position + i, ancilla_position + i)\n",
    "        circuit.x(pattern_position + i)\n",
    "        circuit.x(match_position + i)\n",
    "        \n",
    "        # 111\n",
    "        circuit.ccx(match_position + i, pattern_position + i, ancilla_position + i)\n",
    "        circuit.barrier()\n",
    "        \n",
    "\n",
    "    delta = 1\n",
    "    temp_position = n_string\n",
    "    \n",
    "    for i in range(n_index):\n",
    "        n_reg = n_string if i < n_index - 1 else n_pattern\n",
    "        for j in range(n_reg):\n",
    "            # not shifted\n",
    "            circuit.x(index_position + i)\n",
    "#             print(temp_position - n_string + j, index_position + i, temp_position + j)\n",
    "            circuit.ccx(temp_position - n_string + j, index_position + i, temp_position + j)\n",
    "            circuit.x(index_position + i)\n",
    "            # shifted\n",
    "            if j + delta < n_string:\n",
    "                circuit.ccx(temp_position - n_string + j + delta, index_position + i, temp_position + j)\n",
    "            \n",
    "        delta *= 2\n",
    "        temp_position += n_string\n",
    "        circuit.barrier()\n",
    "\n",
    "    \n",
    "    # diffusion\n",
    "    for i in range(n_index):\n",
    "        circuit.h(index_position + i)\n",
    "        circuit.x(index_position + i)\n",
    "        \n",
    "    circuit.mct(list(range(index_position, index_position + n_index)), ancilla_position + n_pattern)\n",
    "    \n",
    "    for i in range(n_index):\n",
    "        circuit.x(index_position + i)\n",
    "        circuit.h(index_position + i)\n",
    "        \n",
    "    circuit.barrier()\n",
    "    \n",
    "    return circuit\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_pattern_matching_circuit(string, pattern):    \n",
    "    n_string = len(string)\n",
    "    n_pattern = len(pattern)\n",
    "    \n",
    "    if n_pattern > n_string:\n",
    "        raise Error('pattern should be shorter than string.')\n",
    "    \n",
    "    # T = n_string - n_pattern + 1, T = 1 => 1, T = 2 => 2, T = 4 => 3 \n",
    "    n_index = math.ceil(np.log2(n_string - n_pattern + 1))\n",
    "    \n",
    "    n_qubits = n_string * n_index + n_pattern * 3 + n_index + 1\n",
    "    \n",
    "    string_reg = QuantumRegister(n_string, 'reg_string')\n",
    "    temp_regs = [QuantumRegister(n_string, 'reg_temp_' + str(i)) for i in range(n_index - 1)]\n",
    "    match_reg = QuantumRegister(n_pattern, 'reg_match')\n",
    "    pattern_reg = QuantumRegister(n_pattern, 'reg_pattern')\n",
    "    index_reg = QuantumRegister(n_index, 'reg_index')\n",
    "    ancilla_reg = QuantumRegister(n_pattern + 1, 'reg_ancilla')\n",
    "    \n",
    "    registers = [string_reg, *temp_regs, match_reg, pattern_reg, index_reg, ancilla_reg]\n",
    "    \n",
    "    qc = QuantumCircuit(*registers)\n",
    "    \n",
    "    # set positions for later use\n",
    "    temp_position = n_string\n",
    "    match_position = n_string * n_index\n",
    "    pattern_position = match_position + n_pattern\n",
    "    index_position = pattern_position + n_pattern\n",
    "    ancilla_position = index_position + n_index\n",
    "    \n",
    "    # initialize inputs\n",
    "    for i in range(n_string):\n",
    "        qc.initialize([1, 0] if string[-1-i] == 0 else [0, 1], i)\n",
    "    for i in range(n_pattern):\n",
    "        qc.initialize([1, 0] if pattern[-1-i] == 0 else [0, 1], n_string * n_index + n_pattern + i)\n",
    "\n",
    "    # initialize index\n",
    "    for i in range(n_index):\n",
    "        qc.h(n_string * n_index + n_pattern * 2 + i)\n",
    "#         qc.initialize([1, 0], n_string * n_index + n_pattern * 2 + i)\n",
    "        \n",
    "    qc.x(ancilla_position + n_pattern)\n",
    "    qc.h(ancilla_position + n_pattern)\n",
    "    \n",
    "    qc.barrier()\n",
    "        \n",
    "    # oracle\n",
    "    for i in range(2):\n",
    "        qc = apply_oracle(qc, n_string, index_position, match_position, pattern_position, ancilla_position)\n",
    "        \n",
    "    return qc\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "STRING = [1, 0, 1, 1, 0]\n",
    "PATTERN = [1, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 10774x1167.88 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = make_pattern_matching_circuit(STRING, PATTERN)\n",
    "\n",
    "\n",
    "circuit_drawer(qc, output='mpl', fold=-1)\n",
    "# qc.draw(fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = execute(qc, backend).result()\n",
    "counts = result.get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def partial_counts(counts):\n",
    "    n_string = len(STRING)\n",
    "    n_pattern = len(PATTERN)\n",
    "    n_index = math.ceil(np.log2(n_string - n_pattern + 1))\n",
    "    match_position = n_string * n_index\n",
    "    pattern_position = match_position + n_pattern\n",
    "    index_position = pattern_position + n_pattern\n",
    "    \n",
    "    nc = {}\n",
    "    for k, v in counts.items():\n",
    "        rk = k[::-1][index_position:index_position+n_index]\n",
    "        if rk not in nc: nc[rk] = 0.0\n",
    "        nc[rk] += v\n",
    "    return nc\n",
    "        \n",
    "# plot_histogram(counts)\n",
    "plot_histogram(partial_counts(counts))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 598,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0703125\n",
      "==============\n",
      "string 100101\n",
      "match 100\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 101\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0703125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 001\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 101\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0703125\n",
      "==============\n",
      "string 100101\n",
      "match 010\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 101\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0703125\n",
      "==============\n",
      "string 100101\n",
      "match 100\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 101\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 00\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0703125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 001\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 101\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 10\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0703125\n",
      "==============\n",
      "string 100101\n",
      "match 010\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 101\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.03125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 01\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 000\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 110\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 011\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n",
      "string 100101\n",
      "match 111\n",
      "pattern 101\n",
      "index 11\n",
      "probability 0.0078125\n",
      "==============\n"
     ]
    }
   ],
   "source": [
    "def format_state(state_string, n_string, n_pattern, n_index, value):\n",
    "    temp_position = n_string\n",
    "    match_position = n_string * n_index\n",
    "    pattern_position = match_position + n_pattern\n",
    "    index_position = pattern_position + n_pattern\n",
    "    ancilla_position = index_position + n_index\n",
    "    \n",
    "    rev_state = state_string[::-1]\n",
    "    print('string', rev_state[:n_string])\n",
    "    print('match', rev_state[match_position:match_position+n_pattern])\n",
    "    print('pattern', rev_state[pattern_position:pattern_position+n_pattern])\n",
    "    print('index', rev_state[index_position:index_position+n_index])\n",
    "    print('probability', value)\n",
    "    print('==============')\n",
    "\n",
    "for k, v in counts.items():\n",
    "    format_state(k, len(STRING), len(PATTERN), 2, v)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 580,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = 1/np.sqrt(2) * np.matrix([[1,1], [1,-1]])\n",
    "X = np.matrix([[0, 1], [1, 0]])\n",
    "I = np.matrix([[1, 0], [0, 1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 477,
   "metadata": {},
   "outputs": [],
   "source": [
    "CCCX = np.matrix([\n",
    "    [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],\n",
    "    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]\n",
    "])\n",
    "CX = np.matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {},
   "outputs": [],
   "source": [
    "big = np.kron(np.kron(np.kron(H*X, H*X), H*X), I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {},
   "outputs": [],
   "source": [
    "big_dagger = np.transpose(big)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 0.875,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,\n",
       "         -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125],\n",
       "        [ 0.125,  0.875,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,\n",
       "          0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125],\n",
       "        [-0.125,  0.125,  0.875,  0.125, -0.125,  0.125, -0.125,  0.125,\n",
       "         -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125],\n",
       "        [ 0.125, -0.125,  0.125,  0.875,  0.125, -0.125,  0.125, -0.125,\n",
       "          0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125],\n",
       "        [-0.125,  0.125, -0.125,  0.125,  0.875,  0.125, -0.125,  0.125,\n",
       "         -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125],\n",
       "        [ 0.125, -0.125,  0.125, -0.125,  0.125,  0.875,  0.125, -0.125,\n",
       "          0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125],\n",
       "        [-0.125,  0.125, -0.125,  0.125, -0.125,  0.125,  0.875,  0.125,\n",
       "         -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125],\n",
       "        [ 0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,  0.875,\n",
       "          0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125],\n",
       "        [-0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,\n",
       "          0.875,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125],\n",
       "        [ 0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,\n",
       "          0.125,  0.875,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125],\n",
       "        [-0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,\n",
       "         -0.125,  0.125,  0.875,  0.125, -0.125,  0.125, -0.125,  0.125],\n",
       "        [ 0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,\n",
       "          0.125, -0.125,  0.125,  0.875,  0.125, -0.125,  0.125, -0.125],\n",
       "        [-0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,\n",
       "         -0.125,  0.125, -0.125,  0.125,  0.875,  0.125, -0.125,  0.125],\n",
       "        [ 0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,\n",
       "          0.125, -0.125,  0.125, -0.125,  0.125,  0.875,  0.125, -0.125],\n",
       "        [-0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,\n",
       "         -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,  0.875,  0.125],\n",
       "        [ 0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125, -0.125,\n",
       "          0.125, -0.125,  0.125, -0.125,  0.125, -0.125,  0.125,  0.875]])"
      ]
     },
     "execution_count": 441,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "big * CCCX * big_dagger"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {},
   "outputs": [],
   "source": [
    "small = np.kron(H*X, I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [],
   "source": [
    "small_dagger = np.transpose(small)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff = small * CX * small_dagger"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {},
   "outputs": [],
   "source": [
    "orc = [0.5, -0.5, -0.5, 0.5]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 454,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.identity(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "metadata": {},
   "outputs": [],
   "source": [
    "H_2 = np.kron(H, H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_op = H_2 * (np.matrix([[1, 0, 1, 0]]).T * np.matrix([[1, 0, 1, 0]]) * 2 - np.identity(4)) * H_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 469,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-0.5,  0.5,  0.5, -0.5]])"
      ]
     },
     "execution_count": 469,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orc * diff_op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 470,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 0, 1, 0],\n",
       "        [0, 0, 0, 0],\n",
       "        [1, 0, 1, 0],\n",
       "        [0, 0, 0, 0]])"
      ]
     },
     "execution_count": 470,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matrix([[1, 0, 1, 0]]).T * np.matrix([[1, 0, 1, 0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 0.5,  0.5,  0.5,  0.5],\n",
       "        [ 0.5, -0.5,  0.5, -0.5],\n",
       "        [ 0.5,  0.5, -0.5, -0.5],\n",
       "        [ 0.5, -0.5, -0.5,  0.5]])"
      ]
     },
     "execution_count": 467,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H_2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.7 64-bit",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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