Lab6-Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"font-size:35px;\n",
    "        color:black;\n",
    "        \">Lab 6 Grover’s search with an unknown number of solutions</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prerequisite\n",
    "- [Ch.3.10 Grover's Algorithm](https://qiskit.org/textbook/ch-algorithms/grover.html)\n",
    "- [Ch.3.11 Quantum Counting](https://qiskit.org/textbook/ch-algorithms/quantum-counting.html)\n",
    "\n",
    "Other relevant materials\n",
    "- [Section 3.3 Measuring T1 in Ch.6.1](https://qiskit.org/textbook/ch-quantum-hardware/calibrating-qubits-pulse.html#3.3-Measuring-$T_1$-using-Inversion-Recovery-)\n",
    "- [QCQI] Michael A. Nielsen and Isaac L. Chuang. 2011. Quantum Computation and Quantum Information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit.quantum_info import Operator, Statevector\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "from qiskit.ignis.mitigation.measurement import *\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## *Before we start: some Qiskit tips*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have a circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "qc_x = QuantumCircuit(1)\n",
    "qc_x.x(0)\n",
    "qc_x.name = 'x'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can turn it into a gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_gate = qc_x.to_gate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then use it in other circuits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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 ├\n",
       "     └───┘\n",
       "q_1: ─────\n",
       "          </pre>"
      ],
      "text/plain": [
       "     ┌───┐\n",
       "q_0: ┤ x ├\n",
       "     └───┘\n",
       "q_1: ─────\n",
       "          "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "\n",
    "qc.append(x_gate, [0])\n",
    "\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also create a controlled version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "cx_gate = x_gate.control()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and similarly add that to circuits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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 ├──■──\n",
       "     └───┘┌─┴─┐\n",
       "q_1: ─────┤ x ├\n",
       "          └───┘</pre>"
      ],
      "text/plain": [
       "     ┌───┐     \n",
       "q_0: ┤ x ├──■──\n",
       "     └───┘┌─┴─┐\n",
       "q_1: ─────┤ x ├\n",
       "          └───┘"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.append(cx_gate, [0,1])\n",
    "\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These ideas come in very handy for phase estimation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 style=\"font-size:24px;\">Part 1: Quantum Counting</h2>\n",
    "\n",
    "<br>\n",
    "<div style=\"background: #E8E7EB; border-radius: 5px;\n",
    "-moz-border-radius: 5px;\">\n",
    "  <p style=\"background: #800080;\n",
    "            border-radius: 5px 5px 0px 0px;\n",
    "            padding: 10px 0px 10px 10px;\n",
    "            font-size:18px;\n",
    "            color:white;\n",
    "            \"><b>Goal</b></p>\n",
    "    <p style=\" padding: 0px 0px 10px 10px;\n",
    "              font-size:16px;\">Construct a circuit for quantum counting implementing the IPE (Iterative Phase Estimation) algorithm to find the number of solutions to a search problem.</p>\n",
    "</div>\n",
    "\n",
    "\n",
    "In [Ch.3.10 Grover's Algorithm](https://qiskit.org/textbook/ch-algorithms/grover.html), we learned how to find search problem solutions through Grover's algorithm and the number of solutions utilizing the quantum counting circuit in [Ch.3.11 Quantum Counting](https://qiskit.org/textbook/ch-algorithms/quantum-counting.html).  The number of solutions toghther with the numbe of total items in the search space determine how many Grover iterations, the number of oracle calls, is required. In the part 1 of this lab, we build the quantum counting circuit implementing IPE ( Iterative Phase Estimation ) algorithm rather than the way the circuit was created in [Ch.3.11 Quantum Counting](https://qiskit.org/textbook/ch-algorithms/quantum-counting.html) with Quantum Phase Estimation (QPE)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"font-size: 20px\">1. Find the number of solutions of the given oracle for a search problem through quantum counting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"font-size: 17px\">Step A. Construct a gate for Grover iteration. </h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the search space with the total numbe of item, $N = 8$. Run the following circuit to construct an oracle of a search problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 387.597x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Create an Oracle\n",
    "\n",
    "N = 8 # the number of total items in the search space\n",
    "m = int(np.log2(N)) # the number of qubits required to construct the search space with N items\n",
    "\n",
    "myqc = QuantumCircuit(m, name='Oracle')\n",
    "\n",
    "num_solutions = 3\n",
    "\n",
    "if num_solutions==4:\n",
    "\n",
    "    # solutions are 010 and 001, 110 and 101\n",
    "    \n",
    "    myqc.x(1)\n",
    "    myqc.z(range(2)) # this alone corresponds to solutions 000 and 011, 100 and 111\n",
    "    myqc.x(1)\n",
    "    \n",
    "if num_solutions in [1,3]:\n",
    "\n",
    "    # solution is 000\n",
    "    \n",
    "    myqc.x(range(m))\n",
    "    \n",
    "    # this alone corresponds to solution 111\n",
    "    myqc.h(m-1) # hadamards used to rotate mcx to mcz\n",
    "    myqc.mcx(list(range(m-1)),m-1)\n",
    "    myqc.h(m-1)\n",
    "    \n",
    "    myqc.x(range(m))\n",
    "\n",
    "if num_solutions in [2,3]:\n",
    "\n",
    "    # solutions are 011 and 111\n",
    "    \n",
    "    myqc.cz(0,1)\n",
    "    \n",
    "Oracle = myqc.to_gate()\n",
    "\n",
    "myqc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see these marked solutions in the statevector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'000': (-0.3535533905932736+0j),\n",
       " '001': (0.3535533905932736+0j),\n",
       " '010': (0.3535533905932736+0j),\n",
       " '011': (-0.3535533905932736+0j),\n",
       " '100': (0.3535533905932736+0j),\n",
       " '101': (0.3535533905932736+0j),\n",
       " '110': (0.3535533905932736+0j),\n",
       " '111': (-0.3535533905932736+0j)}"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "\n",
    "hads = QuantumCircuit(m)\n",
    "hads.h(range(m))\n",
    "ket = Statevector(hads.compose(myqc))\n",
    "ket.to_dict()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#128211; Complete the circuit, `qc`, to create Grover iteration gate/operator, `Grover`, by adding the diffuser, explained as the step 3 in the first section `1.Introdcution` of [Ch.3.10 Grover's Algorithm](https://qiskit.org/textbook/ch-algorithms/grover.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "qc = QuantumCircuit(m)\n",
    "qc.append(Oracle, range(m))\n",
    "\n",
    "### solution here\n",
    "myqc = QuantumCircuit(m, name='Diffuser')\n",
    "\n",
    "# transform |+> to |1>\n",
    "for j in range(m):\n",
    "    myqc.z(j)\n",
    "    myqc.h(j)\n",
    "\n",
    "# apply multiply controlled-Z, which gives a phase to the all |1> state\n",
    "myqc.h(m-1)\n",
    "myqc.mcx(list(range(m-1)),m-1)\n",
    "myqc.h(m-1)\n",
    "  \n",
    "# transform |1> to |+>\n",
    "for j in range(m):\n",
    "    myqc.h(j)\n",
    "    myqc.z(j)\n",
    "    \n",
    "# get global phase of -1 (there must be a better way!)\n",
    "myqc.z(0)\n",
    "myqc.x(0)\n",
    "myqc.z(0)\n",
    "myqc.x(0)\n",
    "\n",
    "Diffuser = myqc.to_gate()\n",
    "qc.append(Diffuser, range(m))\n",
    "####\n",
    "\n",
    "Grover = qc.to_gate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"font-size: 17px\">&#128211;Step B. Build a quantum circuit, 'circ', for quantum counting employing the IPE algorithm to find the eigenvalue of the Grover iterator, `Grover` that we made in Step A. </h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read [Ch.3.11 Quantum Counting](https://qiskit.org/textbook/ch-algorithms/quantum-counting.html) before you start. Suppose the number of iteration of the IPE here is three which corresponds to three counting qubits in QPE ( Quantum Phase Estimate ) circuit. (In other words, set the number of classical register three.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 990.257x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###### solution here\n",
    "\n",
    "# and a contolled version of the Grover iterator\n",
    "def cGrover(k):\n",
    "    \n",
    "    # make gate for 2^k repetitions of grover\n",
    "    qc = QuantumCircuit(m)\n",
    "    for _ in range(2**k):\n",
    "        qc.append(Grover, range(m))\n",
    "    grover_k = qc.to_gate()\n",
    "    grover_k.name = 'Grover_[2^'+str(k)+']'\n",
    "    \n",
    "    # make and return controlled version of this gate\n",
    "    cGrover_k = grover_k.control()\n",
    "    return cGrover_k   \n",
    "\n",
    "# number of bits required for the answer\n",
    "t = 3\n",
    "\n",
    "# we'll need the inverse QFT\n",
    "from qiskit.circuit.library import QFT\n",
    "qft = QFT(t)\n",
    "inv_qft = qft.inverse()\n",
    "\n",
    "\n",
    "# the first and second quantum registers, as in the lecture\n",
    "first = QuantumRegister(t,'first')\n",
    "second = QuantumRegister(m,'second')\n",
    "\n",
    "# output for the second register\n",
    "output = ClassicalRegister(t)\n",
    "\n",
    "# now make the circuit\n",
    "circ = QuantumCircuit(first, second, output)\n",
    "\n",
    "# the first register is initialized as the all |+> state\n",
    "circ.h(first)\n",
    "\n",
    "# we'll prepare the |s> state for the qubits of the second register\n",
    "circ.h(second)\n",
    "\n",
    "# apply the controlled Grover ops\n",
    "for k in range(t):    \n",
    "    circ.append(cGrover(t-k-1), [first[t-k-1]]+[q for q in second] )\n",
    "            \n",
    "# do an inverse qft\n",
    "circ.append(inv_qft, first)\n",
    "        \n",
    "# measure\n",
    "circ.measure(first, output)\n",
    "    \n",
    "\n",
    "###################    \n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"font-size: 17px\">&#128211;Step C. Execute the circuit that you built in Step B and find the number of solutions, $M$, from the estimated phase. </h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = Aer.get_backend('qasm_simulator')\n",
    "shots = 20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results with bit strings {'10001': 19, '00000': 24, '11111': 31, '01011': 54, '10011': 31, '01110': 18, '00010': 46, '10010': 18, '01111': 19, '11100': 107, '01101': 24, '10111': 116, '01010': 66, '10101': 47, '00101': 215, '01001': 125, '11011': 207, '01100': 25, '00100': 97, '10110': 77, '11101': 47, '00110': 1241, '01000': 381, '11000': 385, '10000': 17, '11001': 7580, '11010': 1236, '00001': 39, '00011': 54, '11110': 36, '10100': 25, '00111': 7593}\n",
      "\n",
      "Results with phases {'0.53125': 19, '0.0': 24, '0.96875': 31, '0.34375': 54, '0.59375': 31, '0.4375': 18, '0.0625': 46, '0.5625': 18, '0.46875': 19, '0.875': 107, '0.40625': 24, '0.71875': 116, '0.3125': 66, '0.65625': 47, '0.15625': 215, '0.28125': 125, '0.84375': 207, '0.375': 25, '0.125': 97, '0.6875': 77, '0.90625': 47, '0.1875': 1241, '0.25': 381, '0.75': 385, '0.5': 17, '0.78125': 7580, '0.8125': 1236, '0.03125': 39, '0.09375': 54, '0.9375': 36, '0.625': 25, '0.21875': 7593}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "####### solution here\n",
    "count_circ = execute(circ, sim, shots=shots).result().get_counts()\n",
    "print('Results with bit strings',count_circ)\n",
    "\n",
    "def key_convert(count):\n",
    "    phi_est = np.array([round(int(key, 2)/2**t, t) for key in list(count.keys())])\n",
    "    key_new = list(map(str, phi_est))\n",
    "    count_new = dict(zip(key_new, count.values()))\n",
    "    return count_new\n",
    "\n",
    "count_new = key_convert(count_circ)\n",
    "print('\\nResults with phases',count_new)\n",
    "\n",
    "plot_histogram(count_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To convert from this phase to an angle, we need to multiple it by $\\pi$. Also we need to recall that the angle is defined as $\\sqrt{\\frac{M}{N}} = \\cos(\\theta)$. So the number of solution, $M$, is\n",
    "\n",
    "$$ M = N \\cos(\\pi \\phi).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Phase 0.78125 implies 3.0 solutions for the given oracle.\n",
      "Phase 0.21875 implies 3.0 solutions for the given oracle.\n",
      "\n",
      "Spurious solutions occurred for 4827 out of 20000 shots.\n"
     ]
    }
   ],
   "source": [
    "errors = 0\n",
    "\n",
    "for phi in count_new:\n",
    "    \n",
    "    theta = float(phi)*np.pi\n",
    "    \n",
    "    if count_new[phi]>shots/10: # ignore spurious solutions\n",
    "\n",
    "        M = np.rint(N * np.sin(theta)**2)\n",
    "    \n",
    "        print('Phase',phi,'implies',M,'solutions for the given oracle.')\n",
    "        \n",
    "    else:\n",
    "        errors += count_new[phi]\n",
    "        \n",
    "print('\\nSpurious solutions occurred for',errors,'out of',shots,'shots.')"
   ]
  },
  {
   "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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