Checking_limits.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bonus Task 1 (Checking the limits)\n",
    "\n",
    "### In this code I have checked the extrimities of my approch. The limits are $n=6$ and $m=7$\n",
    "### It's important to note that even with the circuit optimization (using transpiler) it takes considerable amount of time  \n",
    "### The algorithm that builds a general circuit that accepts vectors with random values of size $2^{n}$ with $m$ bits in length for each element and finds the states which don't have similar adjacent bits in their binary representation.\n",
    "\n",
    "\n",
    "#### Instructions\n",
    "\n",
    "- Since QASM allows to simulate at max 32 qubits, the max limit for $n = 6$ (number of addresses) and $m = 7$ (max number of bits)\n",
    "- If you are simulating for the $n = 2$ case please take $n = 3$ (Since it is impossible to converge grover's)\n",
    "- $m > n$ (Which corresponds to low range in comparison to the sampling size and thus random sampling won't work)\n",
    "- After changing the value of $m$ ar the top in cell 3, Please ensure you make a corresponding change at the bottom of cell 3. To keep the format same. For example if $m = 5$ then the bottom formatting should look like <font color=blue>\"'{0:05b}'.format(num)\"</font>\n",
    "- While reading the histogram the bottom refers to unit place i.e. $2^{0}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<AccountProvider for IBMQ(hub='ibm-q', group='open', project='main')>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importing standard Qiskit libraries\n",
    "from qiskit import IBMQ\n",
    "from qiskit.tools.jupyter import *\n",
    "\n",
    "# Loading your IBM Quantum account\n",
    "IBMQ.load_account()\n",
    "IBMQ.providers() # see a list of providers you have access to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit,  transpile\n",
    "from qiskit import IBMQ, Aer, execute\n",
    "from qiskit.visualization import plot_bloch_multivector\n",
    "# import basic plot tools\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "import matplotlib.pyplot as plt\n",
    "import itertools \n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is the input \n",
      " [104, 92, 94, 57, 39, 28, 77, 23, 114, 5, 74, 17, 86, 52, 32, 22, 78, 82, 14, 31, 0, 89, 102, 108, 40, 10, 123, 93, 63, 25, 121, 54, 18, 71, 29, 96, 107, 119, 95, 81, 103, 67, 62, 110, 91, 80, 106, 99, 7, 20, 61, 45, 38, 26, 11, 85, 3, 98, 37, 53, 36, 33, 24, 42]\n"
     ]
    }
   ],
   "source": [
    "#sample preparation\n",
    "# m > n (else random sampling won't work)\n",
    "\n",
    "n= 6 #number of address bits required\n",
    "m = 7 #length of the data in bits     #Also change the value of m (in front of b) at the end of the cell \n",
    "input_st = random.sample(range(0,(2**m)-1), 2**n)\n",
    "\n",
    "\n",
    "mark_1 = 0\n",
    "mark_2 = 0\n",
    "for i in range(0,m,2):\n",
    "    mark_1 = mark_1 + 2**i\n",
    "for i in range(1,m,2):\n",
    "    mark_2 = mark_2 + 2**i\n",
    "\n",
    "#Ensuring we have two solutions in the input array\n",
    "if mark_1 not in input_st:\n",
    "    loc =random.randint(0,2**n-1)\n",
    "    input_st[loc] = mark_1\n",
    "    \n",
    "if mark_2 not in input_st:\n",
    "    loc =random.randint(0,2**n-1)\n",
    "    input_st[loc] = mark_2 \n",
    "print('This is the input \\n', input_st)\n",
    "bin_pass = []\n",
    "for num in input_st:\n",
    "    bin_pass.append('{0:07b}'.format(num))      #Please change the value infront of b to m "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining Oracle which checks for the marked state\n",
    "def oracle(qc,data,comput,m):\n",
    "    for i in range(m-1):\n",
    "        qc.cx(data[i], comput[i])\n",
    "        qc.cx(data[i+1], comput[i])      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def diffuser(nqubits):\n",
    "    qc = QuantumCircuit(nqubits)\n",
    "    # Apply transformation |s> -> |00..0> (H-gates)\n",
    "    for qubit in range(nqubits):\n",
    "        qc.h(qubit)\n",
    "    # Apply transformation |00..0> -> |11..1> (X-gates)\n",
    "    for qubit in range(nqubits):\n",
    "        qc.x(qubit)\n",
    "    # Do multi-controlled-Z gate\n",
    "    qc.h(nqubits-1)\n",
    "    qc.mct(list(range(nqubits-1)), nqubits-1)  # multi-controlled-toffoli\n",
    "    qc.h(nqubits-1)\n",
    "    # Apply transformation |11..1> -> |00..0>\n",
    "    for qubit in range(nqubits):\n",
    "        qc.x(qubit)\n",
    "    # Apply transformation |00..0> -> |s>\n",
    "    for qubit in range(nqubits):\n",
    "        qc.h(qubit)\n",
    "    # We will return the diffuser as a gate\n",
    "    U_s = qc.to_gate()\n",
    "    U_s.name = \"$U_s$\"\n",
    "    return U_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "address = QuantumRegister(n)\n",
    "data = QuantumRegister(m)\n",
    "comput = QuantumRegister(m-1)\n",
    "flag = QuantumRegister(1)\n",
    "c = ClassicalRegister(n) #measuring address\n",
    "# c = ClassicalRegister(m) #Checking performance of qRAM\n",
    "# c = ClassicalRegister(3) #Only measuring the comput and qRAM address\n",
    "anicilla_qubit = QuantumRegister(m-3)\n",
    "if n>2:\n",
    "    qRAM_ancilla = QuantumRegister(n-2)\n",
    "qc = QuantumCircuit(address,data,qRAM_ancilla,comput,flag,anicilla_qubit,c)\n",
    "# qc = QuantumCircuit(address,data,qRAM_ancilla,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculates required Grover iterations\n",
    "grov_iter = math.floor((np.pi*np.sqrt(2**n/2))/4)\n",
    "grov_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x19a7fdccb20>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "text_list = []\n",
    "alpha = 'a'\n",
    "var = []\n",
    "diff = []\n",
    "for i in range(n):\n",
    "    diff.append(i)\n",
    "for i in range(n):\n",
    "    text_list.append(alpha)\n",
    "    alpha = chr(ord(alpha) + 1) \n",
    "for x_0 in text_list:\n",
    "    var.append([0,1])\n",
    "qc.x(flag[0]) #Flag for qram check\n",
    "qc.h(flag[0])\n",
    "for i in range(n):\n",
    "    qc.h(address[i])\n",
    "qc.barrier()    \n",
    "for grov in range(grov_iter):\n",
    "    \n",
    "    for text_list in itertools.product(*var):\n",
    "        summ = 0\n",
    "        for i in range(n):\n",
    "            summ = summ + text_list[i]*2**(abs(i-n+1))\n",
    "            if text_list[i]==0:\n",
    "                qc.x([address[i]])\n",
    "        for o in range(m):          \n",
    "            if bin_pass[summ][o]=='1':\n",
    "                qc.mct(address,data[o],qRAM_ancilla,mode='basic')\n",
    "        for j in range(n):\n",
    "            if text_list[j]==0:\n",
    "                qc.x([address[j]])\n",
    "        qc.barrier()\n",
    "    oracle(qc,data,comput,m)\n",
    "    qc.barrier()\n",
    "    qc.mct(comput,flag[0],anicilla_qubit,mode='basic')\n",
    "    qc.barrier()\n",
    "    oracle(qc,data,comput,m)\n",
    "    qc.barrier()        \n",
    " \n",
    "    for text_list in itertools.product(*var):\n",
    "        summ = 0     \n",
    "        for i in range(n):\n",
    "            summ = summ + text_list[i]*2**(abs(i-n+1))\n",
    "            if text_list[i]==0:\n",
    "                qc.x([address[i]])\n",
    "        for o in range(m):          \n",
    "            if bin_pass[summ][o]=='1':\n",
    "                qc.mct(address,data[o],qRAM_ancilla,mode='basic')\n",
    "        for j in range(n):\n",
    "            if text_list[j]==0:\n",
    "                qc.x([address[j]])                      \n",
    "        qc.barrier()\n",
    "    qc.append(diffuser(n),diff)    \n",
    "    qc.barrier() \n",
    "qc.reverse_bits()\n",
    "qc.measure(address[:], c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Image size of 1604x250997 pixels is too large. It must be less than 2^16 in each direction.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\IPython\\core\\formatters.py\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, obj)\u001b[0m\n\u001b[0;32m    339\u001b[0m                 \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    340\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 341\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mprinter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    342\u001b[0m             \u001b[1;31m# Finally look for special method names\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    343\u001b[0m             \u001b[0mmethod\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_real_method\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprint_method\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\IPython\\core\\pylabtools.py\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(fig)\u001b[0m\n\u001b[0;32m    246\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    247\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;34m'png'\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mformats\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 248\u001b[1;33m         \u001b[0mpng_formatter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfor_type\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mFigure\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mprint_figure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'png'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    249\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;34m'retina'\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mformats\u001b[0m \u001b[1;32mor\u001b[0m \u001b[1;34m'png2x'\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mformats\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    250\u001b[0m         \u001b[0mpng_formatter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfor_type\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mFigure\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mretina_figure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\IPython\\core\\pylabtools.py\u001b[0m in \u001b[0;36mprint_figure\u001b[1;34m(fig, fmt, bbox_inches, **kwargs)\u001b[0m\n\u001b[0;32m    130\u001b[0m         \u001b[0mFigureCanvasBase\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    131\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 132\u001b[1;33m     \u001b[0mfig\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprint_figure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbytes_io\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    133\u001b[0m     \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbytes_io\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgetvalue\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    134\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mfmt\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'svg'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\matplotlib\\backend_bases.py\u001b[0m in \u001b[0;36mprint_figure\u001b[1;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[0;32m   2182\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mbbox_inches\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2183\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mbbox_inches\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m\"tight\"\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2184\u001b[1;33m                     renderer = _get_renderer(\n\u001b[0m\u001b[0;32m   2185\u001b[0m                         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2186\u001b[0m                         functools.partial(\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\matplotlib\\backend_bases.py\u001b[0m in \u001b[0;36m_get_renderer\u001b[1;34m(figure, print_method)\u001b[0m\n\u001b[0;32m   1553\u001b[0m                 figure.canvas._get_output_canvas(None, fmt), f\"print_{fmt}\")\n\u001b[0;32m   1554\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1555\u001b[1;33m             \u001b[0mprint_method\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mio\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mBytesIO\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdpi\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdpi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1556\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mDone\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mexc\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1557\u001b[0m             \u001b[0mrenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfigure\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_cachedRenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\matplotlib\\backend_bases.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m   1637\u001b[0m             \u001b[0mkwargs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1638\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1639\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1640\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1641\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py\u001b[0m in \u001b[0;36mprint_png\u001b[1;34m(self, filename_or_obj, metadata, pil_kwargs, *args)\u001b[0m\n\u001b[0;32m    507\u001b[0m             \u001b[1;33m*\u001b[0m\u001b[0mmetadata\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mincluding\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mdefault\u001b[0m \u001b[1;34m'Software'\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    508\u001b[0m         \"\"\"\n\u001b[1;32m--> 509\u001b[1;33m         \u001b[0mFigureCanvasAgg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    510\u001b[0m         mpl.image.imsave(\n\u001b[0;32m    511\u001b[0m             \u001b[0mfilename_or_obj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbuffer_rgba\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mformat\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"png\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morigin\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"upper\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py\u001b[0m in \u001b[0;36mdraw\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    400\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    401\u001b[0m         \u001b[1;31m# docstring inherited\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 402\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrenderer\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_renderer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcleared\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    403\u001b[0m         \u001b[1;31m# Acquire a lock on the shared font cache.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    404\u001b[0m         \u001b[1;32mwith\u001b[0m \u001b[0mRendererAgg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlock\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py\u001b[0m in \u001b[0;36mget_renderer\u001b[1;34m(self, cleared)\u001b[0m\n\u001b[0;32m    416\u001b[0m                           and getattr(self, \"_lastKey\", None) == key)\n\u001b[0;32m    417\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mreuse_renderer\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 418\u001b[1;33m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrenderer\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mRendererAgg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mw\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mh\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdpi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    419\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_lastKey\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    420\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0mcleared\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Miniconda3\\envs\\penny\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, width, height, dpi)\u001b[0m\n\u001b[0;32m     94\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mwidth\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwidth\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     95\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mheight\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mheight\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 96\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_renderer\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_RendererAgg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwidth\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mheight\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdpi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     97\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_filter_renderers\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     98\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: Image size of 1604x250997 pixels is too large. It must be less than 2^16 in each direction."
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1604.87x250998 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit Depth before Optimization: 2923\n",
      "Gate counts before Optimization: OrderedDict([('x', 3073), ('mcx_vchain', 1812), ('barrier', 529), ('cx', 96), ('h', 7), ('measure', 6), ('$U_s$', 4)])\n",
      "\n",
      "Optimization Level 0\n",
      "Circuit Depth: 110675\n",
      "Gate counts: OrderedDict([('cx', 43584), ('h', 29055), ('t', 28992), ('tdg', 28992), ('x', 3121), ('ccx', 1812), ('barrier', 529), ('measure', 6), ('mcx_gray', 4)])\n",
      "\n",
      "Optimization Level 1\n",
      "Circuit Depth: 27322\n",
      "Gate counts: OrderedDict([('cx', 12288), ('u2', 8169), ('tdg', 4064), ('t', 4064), ('x', 3008), ('ccx', 1812), ('barrier', 529), ('u1', 8), ('h', 6), ('measure', 6), ('mcx_gray', 4)])\n",
      "\n",
      "Optimization Level 2\n",
      "Circuit Depth: 27322\n",
      "Gate counts: OrderedDict([('cx', 12288), ('u2', 8169), ('tdg', 4064), ('t', 4064), ('x', 3008), ('ccx', 1812), ('barrier', 529), ('u1', 8), ('h', 6), ('measure', 6), ('mcx_gray', 4)])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "print('Circuit Depth before Optimization:', qc.depth())\n",
    "print('Gate counts before Optimization: {}\\n'.format(qc.count_ops()))\n",
    "for kk in range(3):\n",
    "    new_cirq = transpile(qc, backend, optimization_level=kk)\n",
    "    print('Optimization Level {}'.format(kk))\n",
    "    print('Circuit Depth:', new_cirq.depth())\n",
    "    print('Gate counts:', new_cirq.count_ops())\n",
    "    print()\n",
    "# new_cirq.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\sumit\\Miniconda3\\envs\\penny\\lib\\site-packages\\qiskit\\execute_function.py:343: DeprecationWarning: Using `backend_options` kwarg has been deprecated as of qiskit-aer 0.7.0 and will be removed no earlier than 3 months from that release date. Runtime backend options should now be added directly using kwargs for each option.\n",
      "  job = backend.run(experiments, **run_kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job = execute(new_cirq, backend=backend, shots=2048, seed_simulator=4096, backend_options={\"fusion_enable\":True})\n",
    "\n",
    "result = job.result()\n",
    "count =result.get_counts()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is the input state:\n",
      "\n",
      " [104, 92, 94, 57, 39, 28, 77, 23, 114, 5, 74, 17, 86, 52, 32, 22, 78, 82, 14, 31, 0, 89, 102, 108, 40, 10, 123, 93, 63, 25, 121, 54, 18, 71, 29, 96, 107, 119, 95, 81, 103, 67, 62, 110, 91, 80, 106, 99, 7, 20, 61, 45, 38, 26, 11, 85, 3, 98, 37, 53, 36, 33, 24, 42]\n",
      "\n",
      "This is binary conversion of the solutions\t:10101010 \t 01010101\n",
      "\n",
      "Location of solution 42\t: 63 \t Location of solution 85\t: 55\n"
     ]
    }
   ],
   "source": [
    "print('This is the input state:\\n\\n',input_st)\n",
    "print('\\nThis is binary conversion of the solutions\\t:''{0:08b}'.format(170),'\\t','{0:08b}'.format(85))\n",
    "print('\\nLocation of solution 42\\t:',input_st.index(42),'\\t','Location of solution 85\\t:',input_st.index(85))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'111011': 1018, '111111': 1028, '111000': 1, '100010': 1}\n"
     ]
    }
   ],
   "source": [
    "print(count)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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