labs/jupyter-notebooks/lab-3-diving-into-quantum-algorithms.ipynb

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   "source": [
    "# IBM's Qiskit Global Summer School 2023\n",
    "## Lab 3 - Diving Into Quantum Algorithms\n",
    "\n",
    "- In this lab, we will be applying what we've learned so far about quantum algorithms to implement our own version of Quantum Phase Estimation (QPE) as well as Shor's factoring algorithm. We will explore how increasing the number of qubits used to store the phase estimation changes the accuracy, as well as examine how this algorithm performs on real hardware. Afterwards, we will use your implementation of QPE to execute Shor's algorithm to find the prime factors of a small number. Each step will be walked through, and by the end we will have created a complete generalized function which can be run on the QasmSimulator."
   ]
  },
  {
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      "Collecting git+/~https://github.com/qiskit-community/Quantum-Challenge-Grader.git@main\n",
      "  Cloning /~https://github.com/qiskit-community/Quantum-Challenge-Grader.git (to revision main) to /tmp/pip-req-build-kxr_vi8h\n",
      "  Running command git clone --filter=blob:none --quiet /~https://github.com/qiskit-community/Quantum-Challenge-Grader.git /tmp/pip-req-build-kxr_vi8h\n",
      "  Resolved /~https://github.com/qiskit-community/Quantum-Challenge-Grader.git to commit 2eb4d129f12d37c77dfc84f1144ede8e61e611d0\n",
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     ]
    }
   ],
   "source": [
    "# upgrade/update pip library\n",
    "!pip install --upgrade pip\n",
    "\n",
    "# install the last official version of the grader from IBM's Qiskit Community\n",
    "!pip install git+/~https://github.com/qiskit-community/Quantum-Challenge-Grader.git@main"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "030d4033-274a-4f06-8299-895dc37b875b",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b82a124a",
   "metadata": {},
   "source": [
    "## Section 1: Quantum Phase Estimation (QPE)\n",
    "***\n",
    "\n",
    "<img src=\"./resources/quantum-phase-estimation-tex.png\" alt=\"Quantum Phase Estimation (QPE) Circuit\" style=\"width: 800px;\"/>\n",
    "\n",
    "\n",
    "As a reminder to you, the above figure outlines the Quantum Phase Estimation (QPE) circuit.  Below, we'll provide a few import statements and functions that you'll use throughout the lab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "01b08df9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the quantum circuit, Aer,\n",
    "# and execute instruction\n",
    "# from the IBM' Qiskit library\n",
    "from qiskit import QuantumCircuit, Aer, execute\n",
    "\n",
    "# import the numpy library\n",
    "import numpy as np\n",
    "\n",
    "# import the plot histogram function\n",
    "# from the IBM's Qiskit Visualization module\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "# import the plotting from\n",
    "# the Matplotlib's Pyplot module\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# import the GCD (Greatest Common Divisor)\n",
    "# from the built-in mathematics module\n",
    "from math import gcd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c352e6e-96ab-4312-9453-df6d8051ca7b",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 1 - Create a quantum circuit for the Quantum Phase Estimation on 4 counting qubits, with an angle $\\theta = \\frac{1}{3}$. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "206bb6b0",
   "metadata": {},
   "source": [
    "### Step 1: Set up a QPE Circuit with four counting qubits\n",
    "\n",
    "Let's pick a phase gate with $\\theta = \\frac{1}{3}$ as a simple example unitary to test creating a QPE circuit. Here we'll use IBM's Qiskit `PhaseGate` which applies $P|1\\rangle{}=e^{i\\lambda}|1\\rangle{}$.  Since we want to examine QPE under a unitary with the form $U|1\\rangle{}=e^{i2\\pi \\theta}$, we should set $\\lambda=\\frac{2\\pi}{3}$.\n",
    "\n",
    "Create a QPE circuit with four counting qubits and name the circuit `qpe4`.  It may be helpful to define two `QuantumRegister` objects, one for the \"system\" where the unitary will be applied and one for where the phase information will be stored.  Feel free to reference the IBM's Qiskit Textbook's chapter on [Quantum Phase Estimation](https://learn.qiskit.org/course/ch-algorithms/quantum-phase-estimation#getting_more_precision)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3c62e5a7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# define the function to genera the quantum circuit\n",
    "# for the Quantum Fourier Transform (QFT) on n qubits\n",
    "def qft(n):\n",
    "    \n",
    "    # creates a quantum circuit with n qubits,\n",
    "    # implementing the Quantum Fourier Transform (QFT)\n",
    "    circuit = QuantumCircuit(n)\n",
    "    \n",
    "    \n",
    "    # define the function to perform the Swap gates\n",
    "    # on the quantum registers of the quantum circuit\n",
    "    # for the Quantum Fourier Transform (QFT) on n qubits\n",
    "    def swap_registers( circuit, n ):\n",
    "        \n",
    "        # for a number of iterations equal to half of\n",
    "        # the number of qubits used on the quantum circuit\n",
    "        # for the Quantum Fourier Transform (QFT)\n",
    "        for qubit in range( n // 2 ):\n",
    "            \n",
    "            # apply the Swap gate between the kth qubit and\n",
    "            # the (n - k)th qubit on the quantum register defined before\n",
    "            circuit.swap( qubit, ( n - qubit - 1 ) )\n",
    "        \n",
    "        \n",
    "        # return the quantum circuit with the Swap gates\n",
    "        # applied on the n qubits of the quantum register,\n",
    "        # to implement the Quantum Fourier Transform (QFT)\n",
    "        return circuit\n",
    "    \n",
    "    \n",
    "    # define the function to perform the Controlled-Phase gates\n",
    "    # on the quantum registers of the quantum circuit\n",
    "    # for the Quantum Fourier Transform (QFT) on n qubits\n",
    "    # (it is applied to the first n qubits,\n",
    "    #  and without the Swap gates performed)\n",
    "    def qft_rotations( circuit, n ):\n",
    "       \n",
    "        # if it is the last opposite iteration\n",
    "        if n == 0:\n",
    "            \n",
    "            # return with the Controlled-Phase gates\n",
    "            # on the quantum registers of the quantum circuit\n",
    "            # for the Quantum Fourier Transform (QFT) on n qubits\n",
    "            # (it is applied to the first n qubits,\n",
    "            #  and without the Swap gates performed)\n",
    "            return circuit\n",
    "        \n",
    "        \n",
    "        # iterates on the opposite direction,\n",
    "        # setting a new nth iteration\n",
    "        n -= 1\n",
    "        \n",
    "        \n",
    "        # apply the Hadamard gate to the kth qubit,\n",
    "        # on the quantum register defined before,\n",
    "        # and iterating on the opposite direction\n",
    "        circuit.h(n)\n",
    "        \n",
    "        \n",
    "        # for the remaining qubits to consider\n",
    "        # i the kth opposite iteration\n",
    "        for qubit in range(n):\n",
    "            \n",
    "            # apply the Controlled-Phase gate for\n",
    "            # the theta angle equal to (pi / 2)^(n - k),\n",
    "            # with control on the nth qubit and target on the kth qubit\n",
    "            circuit.cp( ( np.pi / 2 )**( n - qubit ), qubit, n )\n",
    "        \n",
    "        \n",
    "        # call this fuction recursively for\n",
    "        # the next opposite iteration\n",
    "        qft_rotations( circuit, n )\n",
    "    \n",
    "    \n",
    "    # perform the Controlled-Phase gates\n",
    "    # on the quantum registers of the quantum circuit\n",
    "    # for the Quantum Fourier Transform (QFT) on n qubits\n",
    "    # (it is applied to the first n qubits,\n",
    "    #  and without the Swap gates performed)\n",
    "    qft_rotations( circuit, n )\n",
    "    \n",
    "    # perform the Swap gates on the quantum registers of\n",
    "    # the quantum circuit for the Quantum Fourier Transform (QFT) on n qubits\n",
    "    swap_registers( circuit, n )\n",
    "    \n",
    "    \n",
    "    # return the quantum circuit with n qubits,\n",
    "    # implementing the Quantum Fourier Transform (QFT)\n",
    "    return circuit\n",
    "\n",
    "\n",
    "# define the function to genera the quantum circuit\n",
    "# for the Inverse Quantum Fourier Transform (IQFT) on n qubits\n",
    "def qft_dagger( circuit, n ):\n",
    "\n",
    "    # note: do not forget to apply again the Swap gates\n",
    "    #       to peform its inverse operation\n",
    "    \n",
    "    # for a number of iterations equal to half of\n",
    "    # the number of qubits used on the quantum circuit\n",
    "    # for the Inverse Quantum Fourier Transform (IQFT)\n",
    "    for qubit in range( n // 2 ):\n",
    "\n",
    "        # apply the Swap gate between the kth qubit and\n",
    "        # the (n - k)th qubit on the quantum register defined before\n",
    "        circuit.swap( qubit, ( n - qubit - 1 ) )\n",
    "    \n",
    "    \n",
    "    # for each number of qubits of the quantum register defined before,\n",
    "    # to consider in the current jth iteration\n",
    "    for j in range(n):\n",
    "        \n",
    "        \n",
    "        # for each mth qubit of the quantum register defined before,\n",
    "        # to consider in the current iteration\n",
    "        for m in range(j):\n",
    "            \n",
    "            # apply the Controlled-Phase gate for\n",
    "            # the theta angle equal to -pi / ( 2^( j - m ) ),\n",
    "            # with control on the mth qubit and target on the jth qubit\n",
    "            qc.cp( -np.pi / float( 2**( j - m ) ), m, j )\n",
    "            \n",
    "        \n",
    "        # apply the Hadamard gate to the jth qubit\n",
    "        # on the quantum register defined before\n",
    "        qc.h(j)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67a189c9",
   "metadata": {},
   "source": [
    "It should look something like this (note that because IBM's Qiskit uses little endian notation, the ordering of the controlled-$U$ gates are different):\n",
    "\n",
    "<img src=\"./resources/quantum-phase-estimation-4-qubits-circuit.png\" alt=\"QPE 4 Phase Circuit\" style=\"width: 1000px;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cdf021ec",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2210.55x1705.67 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define the size n of the quantum register to\n",
    "# store the phase information\n",
    "phase_register_size = 4\n",
    "\n",
    "# create a quantum circuit with a quantum register\n",
    "# with n qubits and a classical register with n bits,\n",
    "# to implement the Quantum Phase Estimation (QPE) for n = 4 qubits\n",
    "qpe4 = QuantumCircuit( ( phase_register_size + 1 ),\n",
    "                         phase_register_size )\n",
    "\n",
    "\n",
    "####################################################\n",
    "\n",
    "#### insert your code here ####\n",
    "\n",
    "\n",
    "# define the function to perform the Quantum Hadamard Transform on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE)\n",
    "def apply_quantum_hadamard_transform( circuit, n ):    \n",
    "    \n",
    "    # for each qubit of the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE) for n qubits\n",
    "    for qubit_idx in range(n):\n",
    "        \n",
    "        # apply the Hadamard gate to the current ith qubit\n",
    "        circuit.h(qubit_idx)\n",
    "\n",
    "\n",
    "# define the function to perform the Controlled-Phase gates on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE),\n",
    "# as part of the Quantum Fourier Transform (QFT)\n",
    "def apply_controlled_phases( theta, circuit, n ):\n",
    "    \n",
    "    # for each ith step according to\n",
    "    # the number of n qubits used\n",
    "    for step in range(n):\n",
    "        \n",
    "        # compute the iteration parameter t\n",
    "        # as a power of 2, according to the current step\n",
    "        t = 2**step\n",
    "        \n",
    "        \n",
    "        # for each iteration according to\n",
    "        # the iteration parameter t\n",
    "        for _ in range(t):\n",
    "\n",
    "            # apply the Controlled-Phase gate for the theta angle,\n",
    "            # with control on the ith qubit and target on the last qubit\n",
    "            circuit.cp( theta, step, n )  \n",
    "\n",
    "\n",
    "# define the function to perform the Swap gates on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE),\n",
    "# as part of the Quantum Fourier Transform (QFT)\n",
    "def apply_swaps( circuit, n ):\n",
    "    \n",
    "    # for a number of iterations equal to half of\n",
    "    # the number of phase counting qubits used\n",
    "    # on the resepective quantum circuit\n",
    "    # for the Quantum Fourier Transform (QFT)\n",
    "    for qubit_idx in range( phase_register_size // 2 ):\n",
    "         \n",
    "        # apply the Swap gate between the kth qubit and\n",
    "        # the (n - k)th qubit on the quantum register defined before\n",
    "        circuit.swap( qubit_idx, ( n - qubit_idx - 1 ) )\n",
    "        \n",
    "\n",
    "# define the function to perform\n",
    "# the Inverse Quantum Fourier Transform (IQFT) on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE)\n",
    "def apply_quantum_fourier_transform_inverse( circuit, n ):\n",
    "    \n",
    "    # for each qubit on the quantum register\n",
    "    for j in range(n):\n",
    "        \n",
    "        # for each additional mth qubit ranging to\n",
    "        # the current jth qubit being iterated before\n",
    "        for m in range(j):\n",
    "            \n",
    "            # apply the Controlled-Phase gate for\n",
    "            # the theta angle equal to -pi / ( 2^( j - m ) ),\n",
    "            # with control on the mth qubit and target on the jth qubit\n",
    "            circuit.cp( -np.pi / float( 2**( j - m ) ), m, j )\n",
    "\n",
    "        # apply the Hadamard gate to the jth qubit (system's qubit)\n",
    "        circuit.h(j)\n",
    "\n",
    "        \n",
    "# define the function to perform a measurement of\n",
    "# all the n qubits on the quantum register of a quantum circuit,\n",
    "# and storing the classical outcomes on the n bits of\n",
    "# the classical register of that same quantum circuit\n",
    "def measure_all_qubits(circuit, n):\n",
    "    \n",
    "    # for each pair of qubits and bits\n",
    "    for j in range(n):\n",
    "        \n",
    "        # measure the current qubit on the quantum register,\n",
    "        # and stores the classical outcome obtained\n",
    "        # in the current bit on the classical register\n",
    "        circuit.measure(j, j)\n",
    "\n",
    "\n",
    "# define the function to perform the Quantum Phase Estimation (QPE)\n",
    "# according to a theta angle given, on a quantum circuit of n qubits\n",
    "def quantum_phase_estimation( theta, circuit, n ):\n",
    "    \n",
    "    # perform the Quantum Hadamard Transform on\n",
    "    # the n qubits of the quantum register of\n",
    "    # the quantum circuit implementing\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    apply_quantum_hadamard_transform( circuit, n )\n",
    "    \n",
    "    # apply the Pauli-X gate to the last qubit on\n",
    "    # the quantum register of the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE) \n",
    "    circuit.x(n)\n",
    "    \n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    circuit.barrier()\n",
    "    \n",
    "    \n",
    "    # perform the Controlled-Phase gates on\n",
    "    # the n qubits of the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE),\n",
    "    # as part of the Quantum Fourier Transform (QFT)\n",
    "    apply_controlled_phases( theta, circuit, n )\n",
    "    \n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    circuit.barrier()\n",
    "    \n",
    "    # perform the Swap gates on the n qubits of\n",
    "    # the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE),\n",
    "    # as part of the Quantum Fourier Transform (QFT)\n",
    "    apply_swaps( circuit, n )\n",
    "    \n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    circuit.barrier()\n",
    "    \n",
    "    \n",
    "    # perform the Inverse Quantum Fourier Transform (IQFT) on\n",
    "    # the n qubits of the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE)\n",
    "    apply_quantum_fourier_transform_inverse( circuit, n )\n",
    "\n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    circuit.barrier()\n",
    "    \n",
    "    \n",
    "    # perform a measurement of all the n qubits on\n",
    "    # the quantum register of the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE) and storing\n",
    "    # the classical outcomes on the n bits of\n",
    "    # the classical register of that same quantum circuit\n",
    "    measure_all_qubits( circuit, n )\n",
    "\n",
    "    \n",
    "####################################################\n",
    "\n",
    "\n",
    "# define the theta angle to be equal to (2 * pi) / 3\n",
    "theta = ( 2 * np.pi ) / 3 \n",
    "\n",
    "\n",
    "# perform the Quantum Phase Estimation (QPE)\n",
    "# according to the theta angle defined,\n",
    "# on the quantum circuit of n qubits defined before\n",
    "quantum_phase_estimation( theta, qpe4, phase_register_size )\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the Quantum Phase Estimation (QPE) defined before\n",
    "qpe4.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21259f16",
   "metadata": {},
   "source": [
    "Now use the `AerSimulator` to simulate this circuit and plot the histogram of the results.  Use 2000 shots.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f091e056",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# run this cell to simulate 'qpe4' and\n",
    "# to plot the histogram of the result\n",
    "\n",
    "# create the Aer Simulator object\n",
    "sim = Aer.get_backend(\"aer_simulator\")\n",
    "\n",
    "# define the number of shots\n",
    "shots = 20000\n",
    "\n",
    "\n",
    "# execute the simulation for the Quantum Phase Estimation (QPE),\n",
    "# with n = 4 counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation\n",
    "count_qpe4 = execute( qpe4, sim, shots=shots ).result().get_counts()\n",
    "\n",
    "\n",
    "# plot the histogram of the result counts of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n = 4 counting qubits\n",
    "plot_histogram( count_qpe4, figsize=(9,5) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fb998b47",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your answer\n",
    "\n",
    "# import the grader for the exercise 1 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex1 \n",
    "\n",
    "# grade the exercise 1 of the lab 3\n",
    "grade_lab3_ex1( count_qpe4 )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ca1785a",
   "metadata": {},
   "source": [
    "Next write a function to process the bit strings into the estimate of $\\theta$.  Recall that the phase estimate is written in the form:\n",
    "\n",
    "$$ \\theta = 0.\\theta_1\\theta_2\\theta_3...\\theta_t = \\frac{\\theta_1}{2^1} + \\frac{\\theta_2}{2^2} + \\frac{\\theta_3}{2^3} + ... + \\frac{\\theta_t}{2^t} $$\n",
    "\n",
    "where $\\theta_i = \\{0,1\\}$.  What is the estimated phase?  What is the highest power of 2 this circuit can be accurate up to given your choice of the number of counting qubits (e.g. $2^{-2}$, $2^{-3}$, $2^{-4}$, etc.)?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e15cbf0b-7552-4a2a-8495-b57e038d9919",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 2 - Estimate the phase and the accuracy of the quantum circuit for the Quantum Phase Estimation (QPE) defined before. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01742f40-0a55-42a3-bbe7-c89171a14d40",
   "metadata": {},
   "source": [
    "Let's estimate the phase and the accuracy of the quantum circuit for the Quantum Phase Estimation (QPE):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0d427100",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# process the result count data to determine accuracy of\n",
    "# the estimated phase and grab the highest probability measurement\n",
    "\n",
    "\n",
    "# define the maximum number of counts which will be obtained\n",
    "max_binary_counts = 0\n",
    "\n",
    "# define the maximum binary value which will be obtained\n",
    "max_binary_val = \"\"\n",
    "\n",
    "\n",
    "# for each count obtained from the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "for key, item in count_qpe4.items():\n",
    "    \n",
    "    # if the current number of counts is greater than\n",
    "    # the current maximum number of counts obtained\n",
    "    if item > max_binary_counts:\n",
    "        \n",
    "        # update the maximum number of counts obtained\n",
    "        max_binary_counts = item\n",
    "        \n",
    "        # update the maximum binary value obtained\n",
    "        max_binary_val = key\n",
    "\n",
    "        \n",
    "#########################################\n",
    "        \n",
    "\n",
    "#### your function to convert a binary    ####\n",
    "#### string to a decimal number goes here ####\n",
    "\n",
    "# define the function to convert\n",
    "# a binary string to a decimal number\n",
    "def bin_to_decimal( binary_string ):\n",
    "    \n",
    "    # return a binary string\n",
    "    # converted to a decimal number\n",
    "    return int( binary_string, 2 )\n",
    "\n",
    "\n",
    "# calculate the estimated phase obtained\n",
    "# from the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "estimated_phase = ( bin_to_decimal(max_binary_val) / 2**phase_register_size )\n",
    "\n",
    "# calculate the phase accuracy\n",
    "# which can be obtained from\n",
    "# the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "# with the quantum circuit defined before,\n",
    "# inverse of the highest power of 2\n",
    "# (i.e. smallest decimal) this quantum circuit can estimate\n",
    "phase_accuracy_window = 2**( -phase_register_size )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "732d9625",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your answer\n",
    "\n",
    "# import the grader for the exercise 2 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex2 \n",
    "\n",
    "# grade the exercise 2 of the lab 3\n",
    "grade_lab3_ex2( [ estimated_phase, phase_accuracy_window ] )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3820b0e3",
   "metadata": {},
   "source": [
    "## Step 2: Run on Noisy Hardware\n",
    "\n",
    "Now run this circuit using your favorite backend!  Transpile this circuit a number of times (you pick how many) and pick the one with the lowest and highest circuit depth. \n",
    "\n",
    "Transpile the circuit with the parameter optimization_level = 3 to reduce the error in the result. Qiskit by default uses a stochastic swap mapper to place the needed SWAP gates, which varies the transpiled circuit results even under the same runtime settings. Therefore, to achieve shorter depth transpiled circuit for smaller error in the outcome, transpile qpe4 multiple times and choose one with the minimum circuit depth. Select the maximum circuit depth one as well to compare against, name them `min_depth_qpe` and `max_depth_qpe`.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e44a3f5-7d1a-41a4-9081-ddec182d54c2",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 3 - Run an optimized quantum circuit for the Quantum Phase Estimation (QPE) on Quantum Noisy Hardware. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "540d14ee-6e58-496a-a78a-a334c5720545",
   "metadata": {},
   "source": [
    "Let's transpile/optimize the quantum circuit for the Quantum Phase Estimation (QPE) several times, to execute the best one on a Quantum Noisy Hardware:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8297c6da",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import the IBM's Provider from\n",
    "# the Qiskit's IBM Provider module\n",
    "from qiskit_ibm_provider import IBMProvider\n",
    "\n",
    "# import the transpile function from\n",
    "# the IBM's Qikist Compiler module\n",
    "from qiskit.compiler import transpile\n",
    "\n",
    "\n",
    "# create an IBM's Provider object\n",
    "provider = IBMProvider()\n",
    "\n",
    "\n",
    "# define the hub for the IBM's Provider\n",
    "hub = \"summer-school-6\"\n",
    "\n",
    "# define the group for the IBM's Provider\n",
    "group = \"group-3\"\n",
    "\n",
    "# define the project for the IBM's Provider\n",
    "project = \"7048813929\"\n",
    "\n",
    "\n",
    "# define the backend's name for the IBM's Provider\n",
    "backend_name = \"ibmq_manila\"\n",
    "\n",
    "\n",
    "# retrieve the backend from the IBM's Provider\n",
    "backend = provider.get_backend( backend_name, instance=f\"{hub}/{group}/{project}\" )\n",
    "\n",
    "\n",
    "\n",
    "##########################################\n",
    "\n",
    "#### your code goes here ####\n",
    "\n",
    "\n",
    "# define the initial maximum quantum circuit depth obtained\n",
    "max_depth = 1e-20\n",
    "\n",
    "# define the initial minimum quantum circuit depth obtained\n",
    "min_depth = 1e20\n",
    "\n",
    "\n",
    "# define the number of trials to transpile/optimize\n",
    "# the quantum circuit for the Quantum Phase Estimation (QPE) \n",
    "num_trials = 10\n",
    "\n",
    "\n",
    "# for each trial to transpile/optimize the quantum circuit\n",
    "# for the Quantum Phase Estimation (QPE) \n",
    "for _ in range(num_trials):\n",
    "    \n",
    "    # transpile/optimize the quantum circuit\n",
    "    # for the Quantum Phase Estimation (QPE),\n",
    "    # for the current considering trial\n",
    "    transpiled_qpe4 = transpile( qpe4, backend, optimization_level=3 )\n",
    "    \n",
    "    # retrieve the quantum circuit depth of\n",
    "    # the transpiled/optimized quantum circuit\n",
    "    # for the Quantum Phase Estimation (QPE) \n",
    "    transpiled_qpe4_depth = transpiled_qpe4.depth()\n",
    "    \n",
    "    \n",
    "    # if the quantum circuit depth of\n",
    "    # the transpiled/optimized quantum circuit\n",
    "    # for the Quantum Phase Estimation (QPE)\n",
    "    # is greater than the current maximum\n",
    "    # quantum circuit depth obtained \n",
    "    if transpiled_qpe4_depth > max_depth:\n",
    "        \n",
    "        # update the maximum quantum circuit depth\n",
    "        # obtained with the current quantum circuit depth\n",
    "        max_depth = transpiled_qpe4_depth\n",
    "        \n",
    "        # update the quantum circuit with the maximum depth\n",
    "        # with the current quantum circuit transpiled/optimized\n",
    "        max_depth_qpe = transpiled_qpe4\n",
    "    \n",
    "    \n",
    "    # if the quantum circuit depth of\n",
    "    # the transpiled/optimized quantum circuit\n",
    "    # for the Quantum Phase Estimation (QPE)\n",
    "    # is lower than the current minimum\n",
    "    # quantum circuit depth obtained \n",
    "    if transpiled_qpe4_depth < min_depth:\n",
    "\n",
    "        # update the minimum quantum circuit depth\n",
    "        # obtained with the current quantum circuit depth\n",
    "        min_depth = transpiled_qpe4_depth\n",
    "        \n",
    "        # update the quantum circuit with the minimum depth\n",
    "        # with the current quantum circuit transpiled/optimized\n",
    "        min_depth_qpe = transpiled_qpe4\n",
    "\n",
    "        \n",
    "##########################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7b389bc6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your answer\n",
    "\n",
    "# import the grader for the exercise 3 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex3\n",
    "\n",
    "# grade the exercise 3 of the lab 3\n",
    "grade_lab3_ex3( [ max_depth_qpe, min_depth_qpe ] )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d262a40-e04c-4ada-b994-26d6ff4fbf73",
   "metadata": {},
   "source": [
    "Run the best optimized/transpiled quantum circuits for the Quantum Phase Estimation (QPE) on Noisy Quantum Hardware (with the minimum quantum circuit depth):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5adcd092",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# define the number of shots\n",
    "#shots = 2000\n",
    "\n",
    "# OPTIONAL: run the minimum depth quantum circuit for\n",
    "#           the Quantum Phase Estimation (QPE)\n",
    "\n",
    "# execute and retrieve the job for the simulation\n",
    "# for the Quantum Phase Estimation (QPE),\n",
    "# with n = 4 counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation,\n",
    "# using the minimum quantum circuit depth\n",
    "#job_min_qpe4 = backend.run( min_depth_qpe, sim, shots=shots )\n",
    "\n",
    "# print the id of the job of the simulation\n",
    "# for the Quantum Phase Estimation (QPE),\n",
    "# with n = 4 counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation,\n",
    "# using the minimum quantum circuit depth\n",
    "#print( job_min_qpe4.job_id() )\n",
    "\n",
    "\n",
    "# gather the result counts data\n",
    "\n",
    "# execute the simulation for the Quantum Phase Estimation (QPE),\n",
    "# with n = 4 counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation,\n",
    "# using the minimum quantum circuit depth\n",
    "#count_min_qpe4 = job_min_qpe4.result().get_counts()\n",
    "\n",
    "# plot the histogram of the result counts of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n = 4 counting qubits,\n",
    "# and using the minimum quantum circuit depth\n",
    "#plot_histogram( count_min_qpe4, figsize=(9,5) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cec7c84f-b962-4822-a21e-a5f9c3cf508e",
   "metadata": {},
   "source": [
    "Run the best optimized/transpiled quantum circuits for the Quantum Phase Estimation (QPE) on Noisy Quantum Hardware (with the maximum quantum circuit depth):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a05d8270",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# OPTIONAL: run the maximum depth quantum circuit for\n",
    "#           the Quantum Phase Estimation (QPE)\n",
    "\n",
    "# execute and retrieve the job for the simulation\n",
    "# for the Quantum Phase Estimation (QPE),\n",
    "# with n = 4 counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation,\n",
    "# using the maximum quantum circuit depth\n",
    "#job_max_qpe4 = backend.run( max_depth_qpe, sim, shots=shots )\n",
    "\n",
    "# print the id of the job of the simulation\n",
    "# for the Quantum Phase Estimation (QPE),\n",
    "# with n = 4 counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation,\n",
    "# using the maximum quantum circuit depth\n",
    "#print( job_max_qpe4.job_id() )\n",
    "\n",
    "\n",
    "# gather the result counts data\n",
    "\n",
    "# execute the simulation for the Quantum Phase Estimation (QPE),\n",
    "# with n = 4 counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation,\n",
    "# using the maximum quantum circuit depth\n",
    "#count_max_qpe4 = job_max_qpe4.result().get_counts()\n",
    "\n",
    "# plot the histogram of the result counts of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n = 4 counting qubits,\n",
    "# and using the maximum quantum circuit depth\n",
    "#plot_histogram( count_max_qpe4, figsize=(9,5) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8138984d-c546-4785-9acc-7f407ee7c091",
   "metadata": {
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 4 - Create a quantum circuit for the Quantum Phase Estimation (QPE) of $n$ qubits, with an angle $\\theta = \\frac{1}{7}$. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b2b49a6",
   "metadata": {},
   "source": [
    "## Step 3: Try with a different $\\theta$\n",
    "\n",
    "Now try the same procedure with $\\theta = \\frac{1}{7}$.  Rewrite your code written above to create a function which generates a QPE circuit with $n$ register qubits.  How many register qubits storing the phase information are needed for the estimate to be accurate to within $2^{-6}$? \n",
    "\n",
    "*Hint: It may be easier to iterate over different phase register sizes by creating a callable function. Perhaps call it* `qpe_circuit`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5561153-f7fc-4822-b6fc-257c7cb00afb",
   "metadata": {},
   "source": [
    "Let's implement a function to generate a quantum circuit for the Quantum Phase Estimation (QPE), considering now the phase angle $\\theta = \\frac{1}{7}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b121893f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# define the function to perform the Quantum Hadamard Transform on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE)\n",
    "def apply_quantum_hadamard_transform( circuit, n ):\n",
    "    \n",
    "    # for each qubit of the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE) for n qubits\n",
    "    for qubit_idx in range(n):\n",
    "        \n",
    "        # apply the Hadamard gate to the current ith qubit\n",
    "        circuit.h(qubit_idx)\n",
    "        \n",
    "\n",
    "# define the function to perform the Controlled-Phase gates on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE),\n",
    "# as part of the Quantum Fourier Transform (QFT)\n",
    "def apply_controlled_phases( theta, circuit, n ):\n",
    "    \n",
    "    # for each ith step according to\n",
    "    # the number of n qubits used\n",
    "    for step in range(n):\n",
    "    \n",
    "        # compute the iteration parameter t\n",
    "        # as a power of 2, according to the current step\n",
    "        t = 2**step\n",
    "\n",
    "        \n",
    "        # for each iteration according to\n",
    "        # the iteration parameter t\n",
    "        for _ in range(t):\n",
    "\n",
    "            # apply the Controlled-Phase gate for the theta angle,\n",
    "            # with control on the ith qubit and target on the last qubit\n",
    "            circuit.cp( theta, step, n )  \n",
    "\n",
    "            \n",
    "# define the function to perform the Swap gates on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE),\n",
    "# as part of the Quantum Fourier Transform (QFT)\n",
    "def apply_swaps( circuit, n ):\n",
    "    \n",
    "    # for a number of iterations equal to half of\n",
    "    # the number of phase counting qubits used\n",
    "    # on the resepective quantum circuit\n",
    "    # for the Quantum Fourier Transform (QFT)\n",
    "    for qubit_idx in range( phase_register_size // 2 ):\n",
    "        \n",
    "        # apply the Swap gate between the kth qubit and\n",
    "        # the (n - k)th qubit on the quantum register defined before\n",
    "        circuit.swap( qubit_idx, ( n - qubit_idx - 1 ) )\n",
    "        \n",
    "\n",
    "# define the function to perform\n",
    "# the Inverse Quantum Fourier Transform (IQFT) on\n",
    "# the n qubits of the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE)\n",
    "def apply_quantum_fourier_transform_inverse( circuit, n ):\n",
    "    \n",
    "    # for each jth qubit on the quantum register\n",
    "    for j in range(n):\n",
    "        \n",
    "        # for each additional mth qubit ranging to\n",
    "        # the current jth qubit being iterated before\n",
    "        for m in range(j):\n",
    "            \n",
    "            # apply the Controlled-Phase gate for\n",
    "            # the theta angle equal to -pi / ( 2^( j - m ) ),\n",
    "            # with control on the mth qubit and target on the jth qubit\n",
    "            circuit.cp( -np.pi / float( 2**( j - m ) ), m, j )\n",
    "\n",
    "        \n",
    "        # apply the Hadamard gate to the jth qubit\n",
    "        circuit.h(j)\n",
    "\n",
    "\n",
    "# define the function to perform a measurement of\n",
    "# all the n qubits on the quantum register of a quantum circuit,\n",
    "# and storing the classical outcomes on the n bits of\n",
    "# the classical register of that same quantum circuit\n",
    "def measure_all_qubits( circuit, n ):\n",
    "    \n",
    "    # for each pair of qubits and bits\n",
    "    for j in range(n):    \n",
    "        \n",
    "        # measure the current qubit on the quantum register,\n",
    "        # and stores the classical outcome obtained\n",
    "        # in the current bit on the classical register\n",
    "        circuit.measure(j, j)\n",
    "\n",
    "\n",
    "# define the function to create a quantum circuit,\n",
    "# implementing the Quantum Phase Estimation (QPE) on (n + 1) qubits\n",
    "def qpe_circuit(register_size):\n",
    "    \n",
    "    #########################################\n",
    "    \n",
    "    #### your code goes here ####\n",
    "    \n",
    "    \n",
    "    # define the theta phase angle to estimate\n",
    "    theta = 1/7\n",
    "    \n",
    "    # create the quantum circuit with a quantum register with (n + 1) qubits\n",
    "    # and a classical register with n bits, intended to implement\n",
    "    # the Quantum Phase Estimation (QPE) on n qubits\n",
    "    qpe = QuantumCircuit( ( register_size + 1 ), register_size )\n",
    "    \n",
    "    \n",
    "    # perform the Quantum Hadamard Transform on\n",
    "    # the n qubits of the quantum register of\n",
    "    # the quantum circuit implementing\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    apply_quantum_hadamard_transform( qpe, register_size )\n",
    "    \n",
    "    # apply the Pauli-X gate to the last qubit on\n",
    "    # the quantum register of the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    qpe.x(register_size)\n",
    "    \n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    qpe.barrier()\n",
    "    \n",
    "    \n",
    "    # perform the Controlled-Phase gates on\n",
    "    # the n qubits of the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE),\n",
    "    # as part of the Quantum Fourier Transform (QFT)\n",
    "    apply_controlled_phases( theta, qpe, register_size )\n",
    "    \n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    qpe.barrier()\n",
    "    \n",
    "    # perform the Swap gates on the n qubits of\n",
    "    # the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE),\n",
    "    # as part of the Quantum Fourier Transform (QFT)\n",
    "    apply_swaps( qpe, register_size )\n",
    "    \n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    qpe.barrier()\n",
    "    \n",
    "    \n",
    "    # perform the Inverse Quantum Fourier Transform (IQFT) on\n",
    "    # the n qubits of the quantum register of the quantum circuit\n",
    "    # implementing the Quantum Phase Estimation (QPE)\n",
    "    apply_quantum_fourier_transform_inverse( qpe, register_size )\n",
    "    \n",
    "    # apply a barrier to the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE)\n",
    "    qpe.barrier()\n",
    "    \n",
    "    \n",
    "    # perform a measurement of all the n qubits on\n",
    "    # the quantum register of the quantum circuit of\n",
    "    # the Quantum Phase Estimation (QPE) and storing\n",
    "    # the classical outcomes on the n bits of\n",
    "    # the classical register of that same quantum circuit\n",
    "    measure_all_qubits( qpe, register_size )\n",
    "    \n",
    "    \n",
    "    # return the quantum circuit, implementing\n",
    "    # the Quantum Phase Estimation (QPE) on n qubits\n",
    "    return qpe\n",
    "    \n",
    "    #########################################"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a90df2f0-a16c-4741-a095-1cd0f3a980d9",
   "metadata": {},
   "source": [
    "Let's try the previous function with several sizes of quantum and classical register, and execute a simulation of the resulting quantum circuits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "42ec48b0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# run this cell to simulate 'qpe' and\n",
    "# to plot the histogram of the result\n",
    "\n",
    "# define several quantum register sizes\n",
    "# equal to n, allowing to vary them\n",
    "#reg_size = 4\n",
    "reg_size = 5\n",
    "#reg_size = 6\n",
    "#reg_size = 7\n",
    "#reg_size = 8\n",
    "\n",
    "# create a quantum circuit for\n",
    "# the Quantum Phase Estimation (QPE),\n",
    "# given the quantum register defined before,\n",
    "# with n counting qubits\n",
    "qpe_check = qpe_circuit( reg_size )\n",
    "\n",
    "\n",
    "# create the Aer Simulator object\n",
    "sim = Aer.get_backend(\"aer_simulator\")\n",
    "\n",
    "# define the number of shots\n",
    "shots = 10000\n",
    "\n",
    "\n",
    "# execute the simulation for the Quantum Phase Estimation (QPE),\n",
    "# with n counting qubits, and retrieve its result counts\n",
    "count_qpe = execute( qpe_check, sim, shots=shots ).result().get_counts()\n",
    "\n",
    "# plot the histogram of the result counts of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n counting qubits\n",
    "plot_histogram( count_qpe, figsize=(9,5) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a7a5290-36e1-4216-9bb7-6c655d3f13e0",
   "metadata": {},
   "source": [
    "Let's compute the estimated phase, phase accuracy of the quantum circuit, and the accuracy of the estimated phase, from the previously executed quantum simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c2691d92-19ce-4335-aaab-a7bfd6c15968",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated Phase: 0.03125\n",
      "Phase Accuracy Window: 0.03125\n",
      "Accuracy of the Estimated Phase: 0.11160714285714285\n"
     ]
    }
   ],
   "source": [
    "# process the result count data to determine accuracy of\n",
    "# the estimated phase and grab the highest probability measurement\n",
    "\n",
    "\n",
    "# define the maximum number of counts which will be obtained\n",
    "max_binary_counts = 0\n",
    "\n",
    "# define the maximum binary value which will be obtained\n",
    "max_binary_val = \"\"\n",
    "\n",
    "\n",
    "# for each count obtained from the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "for key, item in count_qpe.items():\n",
    "    \n",
    "    # if the current number of counts is greater than\n",
    "    # the current maximum number of counts obtained\n",
    "    if item > max_binary_counts:\n",
    "                \n",
    "        # update the maximum number of counts obtained\n",
    "        max_binary_counts = item\n",
    "        \n",
    "        # update the maximum binary value obtained\n",
    "        max_binary_val = key\n",
    "\n",
    "        \n",
    "#########################################\n",
    "        \n",
    "\n",
    "#### your function to convert a binary    ####\n",
    "#### string to a decimal number goes here ####\n",
    "\n",
    "# define the function to convert\n",
    "# a binary string to a decimal number\n",
    "def bin_to_decimal( binary_string ):\n",
    "    \n",
    "    # return a binary string\n",
    "    # converted to a decimal number\n",
    "    return int( binary_string, 2 )\n",
    "\n",
    "\n",
    "# calculate the estimated phase obtained\n",
    "# from the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "estimated_phase = ( bin_to_decimal(max_binary_val) / 2**reg_size )\n",
    "\n",
    "# print the estimated phase obtained\n",
    "# from the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "print(\"Estimated Phase:\", estimated_phase)\n",
    "\n",
    "\n",
    "# calculate the phase accuracy\n",
    "# which can be obtained from\n",
    "# the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "# with the quantum circuit defined before,\n",
    "# inverse of the highest power of 2\n",
    "# (i.e. smallest decimal) this quantum circuit can estimate\n",
    "phase_accuracy_window = 2**( -reg_size )\n",
    "\n",
    "# print the phase accuracy\n",
    "# which can be obtained from\n",
    "# the quantum simulation of\n",
    "# the Quantum Phase Estimation (QPE)\n",
    "# with the quantum circuit defined before,\n",
    "# inverse of the highest power of 2\n",
    "# (i.e. smallest decimal) this quantum circuit can estimate\n",
    "print(\"Phase Accuracy Window:\", phase_accuracy_window)\n",
    "\n",
    "\n",
    "# define the theta phase angle,\n",
    "# which was pretended to be estimated\n",
    "theta = 1 / 7\n",
    "\n",
    "# compute the accuracy of the estimated phase,\n",
    "# as the distance between the estimated phase \n",
    "# and the theta phase angle, which was pretended to be estimated\n",
    "accuracy_estimated_phase = abs( theta - estimated_phase )\n",
    "\n",
    "# print the accuracy of the estimated phase,\n",
    "# as the distance between the estimated phase \n",
    "# and the theta phase angle, which was pretended to be estimated\n",
    "print(\"Accuracy of the Estimated Phase:\", accuracy_estimated_phase)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "065ab0aa-c2c1-44ee-a64e-a914e64c1d03",
   "metadata": {},
   "source": [
    "Let's compute the required register size to store the phase information of the Quantum Phase Estimation (QPE) with a accuracy to be within ${2}^{-6}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "190454a7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "### put your answer here ###\n",
    "\n",
    "# to estimate accurately the phase information to be within 2^(-6)\n",
    "# we need n + 1 = 6 (=) n = 5 qubits to store the phase information\n",
    "required_register_size = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c08ac980",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "### submit your answer ###\n",
    "\n",
    "# import the grader for the exercise 4 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex4\n",
    "\n",
    "# grade the exercise 4 of the lab 3\n",
    "grade_lab3_ex4( required_register_size )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a450574",
   "metadata": {},
   "source": [
    "## Section 2: Shor's Algorithm\n",
    "***\n",
    "\n",
    "Here we will construct a set of functions to implement Shor's algorithm.  Remember that the goal of this algorithm is to find the prime factors of some large number $N$ and the key speedup this algorithm provides is by executing the period-finding part using a quantum computer.  This is where this section of the lab will focus.\n",
    "\n",
    "\n",
    "Shor's algorithm is composed of the following steps:\n",
    "1. Choose a co-prime $a$, where $a\\in [2,N-1]$ and the greatest common divisor of $a$ and $N$ is 1.\n",
    "1. Find the order (periodicity) of $a$ modulo $N$, i.e. the smallest integer $r$ such that $a^r\\text{mod} N=1$\n",
    "1. Obtain the factor of $N$ by computing the greatest common divisor of $a^{r/2} \\pm 1$ and $N$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "818edadf",
   "metadata": {},
   "source": [
    "## Step 1. Period Finding\n",
    "\n",
    "To begin, we'll use the unitary operator:\n",
    "\n",
    "$$ U|y\\rangle{} \\equiv |ay\\ \\text{mod} N\\rangle{} $$\n",
    "\n",
    "\n",
    "And explore the superposition state: \n",
    "\n",
    "$$\n",
    "|u\\rangle{} = \\frac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1} e^{-\\frac{2\\pi ik}{r}}|a^k \\text{mod}N\\rangle{}\n",
    "$$\n",
    "\n",
    "Let's pick $a=3$ and $N=35$ as an example and investigate what the action of $U$ is on $|u\\rangle{}$:\n",
    "\n",
    "\\begin{align}\n",
    "    U|u\\rangle{} &= U\\frac{1}{\\sqrt{r}}\\left( |1\\rangle{} + e^{-\\frac{2\\pi i}{r}}|3\\rangle{} + e^{\\frac{-4\\pi i}{r}}|9\\rangle{} + ... + e^{\\frac{-20\\pi i}{r}}|4\\rangle{} + e^{\\frac{-22\\pi i}{r}}|12\\rangle{} \\right) \\\\\n",
    "    & =\\frac{1}{\\sqrt{r}}\\left( U|1\\rangle{} + e^{-\\frac{2\\pi i}{r}}U|3\\rangle{} + e^{\\frac{-4\\pi i}{r}}U|9\\rangle{} + ... + e^{\\frac{-20\\pi i}{r}}U|4\\rangle{} + e^{\\frac{-22\\pi i}{r}}U|12\\rangle{} \\right) \\\\\n",
    "    &= \\frac{1}{\\sqrt{r}}\\left( |3\\rangle{} + e^{-\\frac{2\\pi i}{r}}|9\\rangle{} + e^{\\frac{-4\\pi i}{r}}|27\\rangle{} + ... + e^{\\frac{-20\\pi i}{r}}|12\\rangle{} + e^{\\frac{-22\\pi i}{r}}|1\\rangle{} \\right) \\\\\n",
    "    &= \\frac{e^{\\frac{2\\pi i}{r}}}{\\sqrt{r}}\\left( e^{-\\frac{2\\pi i}{r}}|3\\rangle{} + e^{\\frac{-4\\pi i}{r}}|9\\rangle{} + ... + e^{\\frac{-20\\pi i}{r}}|4\\rangle{} + e^{\\frac{-22\\pi i}{r}}|12\\rangle{} + |1\\rangle{} \\right) \\\\\n",
    "    &= \\frac{e^{\\frac{2\\pi i}{r}}}{\\sqrt{r}} |u\\rangle{}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "This is a particularly helpful eigenvalue as it contains $r$.  In fact, it needs to be included in order to ensure the phase differences between the basis states are equal.  This is also not the only eigenstate of $U$.  For us to generalize further, we can multiply an integer $s$ to each of these phases, which will then show up in our eigenvalue:\n",
    "\n",
    "\\begin{align}\n",
    "    |u_s\\rangle{} &= \\frac{1}{\\sqrt{r}}\\sum_{k=0}^{r-1} e^{\\frac{-2\\pi isk}{r}|a^k\\text{mod} N\\rangle{}} \\\\\n",
    "    U|u_s\\rangle{} &= e^{\\frac{2\\pi is}{r}}|u_s\\rangle{}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "Now we have an eigenstate for each integer $0 \\leq s \\leq r$.  Notably, if we add up all of these eigenstates, the phases cancel all other basis states except $|1\\rangle{}$:\n",
    "\n",
    "$$ \\frac{1}{\\sqrt{r}} \\sum_{s=0}^{r-1}|u_s\\rangle{} = |1\\rangle{} $$\n",
    "\n",
    "\n",
    "Since any state in the computational basis can be written as a linear combination of these eigenstates, if we do QPE on $U$ using the state $|1\\rangle{}$, we will measure a phase:\n",
    "\n",
    "$$ \\phi = \\frac{s}{r} $$\n",
    "\n",
    "Where $s$ is a random integer between $0$ and $r-1$.  Finally, we can use a method called the continued fraction algorithm on $\\phi$ in order to find r.  The final circuit will look something like this:\n",
    "\n",
    "\n",
    "<img src=\"./resources/shor-circuit.png\" alt=\"Shor Circuit\" style=\"width: 1000px;\"/>\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fdd37ac-0a87-4a55-9499-13ce9eabf9ef",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 5 - Create a quantum circuit to solve the Period Finding Problem (with $a=7$ and $N=15$). </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03df2e95",
   "metadata": {},
   "source": [
    "Below we'll provide the unitary $U$ needed for solving this period finding problem with $a=7$ and $N=15$:\n",
    "\n",
    "$$ \n",
    "    U|y\\rangle{} = |7y\\ \\text{mod}\\ 15\\rangle{}\n",
    "$$\n",
    "\n",
    "To create $U^x$ we will simply repeat the circuit $x$ times.  The cell below will construct this unitary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f44d5c01",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create 7 mod 15 unitary operator\n",
    "# for a quantum circuit\n",
    "N = 15\n",
    "\n",
    "# define the number of m qubits required\n",
    "# for the 7 mod 15 operator to be executed\n",
    "m = int( np.ceil( np.log2( N ) ) )\n",
    "\n",
    "# create the quantum circuit with\n",
    "# a quantum register of m qubits\n",
    "# to implement the 7 mod 15 unitary operator\n",
    "U_qc = QuantumCircuit( m )\n",
    "\n",
    "\n",
    "# apply the Pauli-X gate to all the m qubits of\n",
    "# the quantum register of the quantum circuit\n",
    "# implementing the 7 mod 15 unitary operator\n",
    "U_qc.x( range(m) )\n",
    "\n",
    "\n",
    "# apply the Swap gate between the 2nd qubit and\n",
    "# the 3rd qubit on the quantum register of\n",
    "# the quantum circuit implementing\n",
    "# the 7 mod 15 unitary operator\n",
    "U_qc.swap(1, 2)\n",
    "\n",
    "# apply the Swap gate between the 3rd qubit and\n",
    "# the 4th qubit on the quantum register of\n",
    "# the quantum circuit implementing\n",
    "# the 7 mod 15 unitary operator\n",
    "U_qc.swap(2, 3)\n",
    "\n",
    "# apply the Swap gate between the 1st qubit and\n",
    "# the 4th qubit on the quantum register of\n",
    "# the quantum circuit implementing\n",
    "# the 7 mod 15 unitary operator\n",
    "U_qc.swap(0, 3)\n",
    "\n",
    "\n",
    "# convert the quantum circuit implementing\n",
    "# the 7 mod 15 unitary operator to\n",
    "# a quantum unitary gate \n",
    "U = U_qc.to_gate()\n",
    "\n",
    "\n",
    "# define the name of the 7 mod 15\n",
    "# unitary operator created before\n",
    "U.name =\"{}Mod{}\".format(7, N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "755e83e3",
   "metadata": {},
   "source": [
    "Confirm if the operator $U$ works as intended by creating a quantum circuit with $m=4$ qubits.  Prepare the inpute state $|y\\rangle{}$ representing any integer between $0$ and $15$ (remembering that Qiskit uses little endian notation) such as $|1\\rangle{} = |0001\\rangle{}$, <br> $|5\\rangle{} = |0101\\rangle{}$, etc. and apply $U|y\\rangle{}$. Check if the circuit produces the expected outcomes for several inputs: $|1\\rangle{}$, $|2\\rangle{}$, and $|5\\rangle{}$. (For example, the outcome for input state $|2\\rangle{}$ should be $|14\\rangle{}=|1110\\rangle{}$)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61461a72-c321-4fea-afce-0f02bc7bc3c9",
   "metadata": {},
   "source": [
    "Run these quantum circuits through the `aer_simulator` backend with $20000$ shots, save the count data as `input_1`, `input_2`, and `input_5`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2413af6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Num. qubits: m = 4\n"
     ]
    }
   ],
   "source": [
    "# your code goes here\n",
    "\n",
    "# print the number of qubits\n",
    "print(\"Num. qubits: m =\", m);\n",
    "\n",
    "\n",
    "\n",
    "# define the quantum circuits for the inputs\n",
    "# |1> = |0001>, |2> = |0010>, and |5> = |0101>\n",
    "\n",
    "\n",
    "#########################################\n",
    "\n",
    "\n",
    "# create the a quantum circuit with m qubits,\n",
    "# for the input state |1> = |0001>\n",
    "qcirc_input_1 = QuantumCircuit(m)\n",
    "\n",
    "# apply the Pauli-X gate to\n",
    "# the 1st qubit of the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_1.x(0)\n",
    "\n",
    "# apply the U gate to all\n",
    "# the m qubits of the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_1.append( U, range(m) )\n",
    "\n",
    "# measure all the m qubits of\n",
    "# the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_1.measure_all()\n",
    "\n",
    "\n",
    "#########################################\n",
    "\n",
    "\n",
    "# create the a quantum circuit with m qubits,\n",
    "# for input state |2> = |0010>\n",
    "qcirc_input_2 = QuantumCircuit(m)\n",
    "\n",
    "# apply the Pauli-X gate to\n",
    "# the 2nd qubit of the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_2.x(1)\n",
    "\n",
    "# apply the U gate to all\n",
    "# the m qubits of the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_2.append( U, range(m) )\n",
    "\n",
    "# measure all the m qubits of\n",
    "# the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_2.measure_all()\n",
    "\n",
    "\n",
    "#########################################\n",
    "\n",
    "\n",
    "# create the a quantum circuit with m qubits,\n",
    "# for input state |5> = |0101>\n",
    "qcirc_input_5 = QuantumCircuit(m)\n",
    "\n",
    "# apply the Pauli-X gate to\n",
    "# the 1st qubit of the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_5.x(0)\n",
    "\n",
    "# apply the Pauli-X gate to\n",
    "# the 3rd qubit of the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_5.x(2)\n",
    "\n",
    "# apply the U gate to all\n",
    "# the m qubits of the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_5.append( U, range(m) )\n",
    "\n",
    "# measure all the m qubits of\n",
    "# the quantum register of\n",
    "# the quantum circuit defined before\n",
    "qcirc_input_5.measure_all()\n",
    "\n",
    "\n",
    "#########################################"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01aebfd7-b3e6-4289-aa14-f1fa047e989d",
   "metadata": {},
   "source": [
    "Let's execute the quantum simulation for the input quantum states defined before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "64292ddb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# run this cell to simulate 'qcirc' and to plot the histogram of the result\n",
    "\n",
    "# create the Aer Simulator object\n",
    "sim = Aer.get_backend(\"aer_simulator\")\n",
    "\n",
    "# define the number of shots\n",
    "shots = 20000\n",
    "\n",
    "# save the count data for the input state |1> = |0001>\n",
    "input_1 = execute(qcirc_input_1, sim, shots=shots).result().get_counts()\n",
    "\n",
    "# save the count data for the input state |2> = |0010>\n",
    "input_2 = execute(qcirc_input_2, sim, shots=shots).result().get_counts()\n",
    "\n",
    "# save the count data for the input state |5> = |0101>\n",
    "input_5 = execute(qcirc_input_5, sim, shots=shots).result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "fc5f5437",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your answer\n",
    "\n",
    "# import the grader for the exercise 5 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex5\n",
    "\n",
    "# grade the exercise 5 of the lab 3\n",
    "grade_lab3_ex5( [ input_1, input_2, input_5 ] )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0b545ec",
   "metadata": {},
   "source": [
    "## Step 2. Implementing $U^{2^{m-1}}$\n",
    "\n",
    "Now we'll use this controlled-$U$ to estimate the phase $\\phi=\\frac{s}{r}$.  But first, a quick point to note here.  It turns out a sequence of `7Mod15` gates produce the identity when executed by a multiple of 4 times.  To test this, create a quantum circuit implementing the `7mod15` gate $2^2$ times and run it on the `unitary_simulator` backend to obtain the matrix represenation of the gates in the circuit.  Verify $U^{2^2}=I$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcb69e74-ba1d-4992-85bc-19710cbb3bfb",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 6 - Create a quantum circuit for the Quantum Phase Estimation (QPE) of the phase angle $\\phi$. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e320b3c8-e35b-49ef-89c5-caf53887ca55",
   "metadata": {},
   "source": [
    "Let's create the unitary quantum circuit for the Quantum Phase Estimation (QPE) of the phase angle $\\phi$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "28ef3fd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create an unitary quantum circuit\n",
    "# with a quantum register of m qubits\n",
    "unitary_circ = QuantumCircuit(m)\n",
    "\n",
    "\n",
    "#### your code goes here ####\n",
    "\n",
    "# for each iteration in a range of 2^2 = 4\n",
    "for _ in range( 2**2 ):\n",
    "    \n",
    "    # apply the U gate on all\n",
    "    # the m qubits on the quantum register\n",
    "    unitary_circ.append( U, range(m) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "956fabba-7063-4966-bed1-cd39f7f218fe",
   "metadata": {},
   "source": [
    "Let's execute the unitary quantum circuit created for the Quantum Phase Estimation (QPE) of the phase angle $\\phi$ on the ``unitary_simulator``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5ba2ce23",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a Unitary Simulator object\n",
    "sim = Aer.get_backend(\"unitary_simulator\")\n",
    "\n",
    "# execute the quantum simulation of\n",
    "# an unitary quantum circuit with\n",
    "# a quantum register of m qubits,\n",
    "# defined before, retrieving its unitary operator\n",
    "unitary = execute( unitary_circ, sim ).result().get_unitary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fef158df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your answer\n",
    "\n",
    "# import the grader for the exercise 6 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex6\n",
    "\n",
    "# grade the exercise 6 of the lab 3\n",
    "grade_lab3_ex6( unitary, unitary_circ )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b80f494e",
   "metadata": {},
   "source": [
    "## Step 3. Finding $\\phi$ and Continued Fractions\n",
    "\n",
    "\n",
    "Now armed with a way to execute $U^{2^{m-1}}$, let's use it in the QPE circuit you created earlier.  Below is a function to construct a controlled-$U$ gate. Use $8$ qubits for the phase register and 4 qubits for the register which $U$ will act on, using the `aer_simulator` again, estimate the phase $\\phi$ given an input state of $|0\\rangle{}$.\n",
    "\n",
    "*Hint: at each step in the QPE circuit, you'll need to construct a new `cU_multi` circuit and append it to the QPE circuit. There will be several estimates that have approximately equal probability.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2826b389-1c0a-4908-8d5a-01f7c93e75a7",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 7 - Create a quantum circuit that implements the Quantum Phase Estimation (QPE) for the Shor's Algorithm. </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b38a0bf0-774e-4fa1-a8a5-46eb3e34ac4b",
   "metadata": {},
   "source": [
    "Let's create the ${2}^{k}$-Controlled-$U$ gate to be applied on 4 qubits for the quantum register, on which the gate $U$ will act on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "71b9775b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the function to built a 2^k-Controlled-U gate object,\n",
    "# which repeats the action of the operator U, 2^k times\n",
    "def cU_multi(k):\n",
    "    \n",
    "    # define the size n of the system's quantum register\n",
    "    sys_register_size = 4\n",
    "    \n",
    "    # create the quantum circuit with n qubits on\n",
    "    # the system's quantum register, to build\n",
    "    # a 2^k-Controlled-U gate object\n",
    "    circ = QuantumCircuit( sys_register_size )\n",
    "    \n",
    "    \n",
    "    # for each iteration ranging until 2^k\n",
    "    for _ in range(2**k):\n",
    "        \n",
    "        # apply the U gate to all the n qubits on\n",
    "        # the system's quantum register of\n",
    "        # the quantum circuit to represent\n",
    "        # the 2^k-Controlled-U gate\n",
    "        circ.append(U, range(sys_register_size))\n",
    "    \n",
    "    \n",
    "    # convert the operator resulting from the construction of\n",
    "    # the quantum circuit defined before, to a quantum gate\n",
    "    U_multi = circ.to_gate()\n",
    "    \n",
    "    \n",
    "    # define the name of the 2^k-Controlled-U gate,\n",
    "    # as being a \"7 Mod 15 gate\"\n",
    "    U_multi.name = \"7Mod15_[2^{}]\".format(k)\n",
    "    \n",
    "    # set this 2^k-Controlled-U gate as multi-qubit gate,\n",
    "    # depending on a given control qubit\n",
    "    cU_multi = U_multi.control()\n",
    "    \n",
    "    \n",
    "    # return the 2^k-Controlled-U gate object,\n",
    "    # which repeats the action of the operator U, 2^k times\n",
    "    return cU_multi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47f0a1aa-e415-40ec-bdfa-75deeda64f63",
   "metadata": {},
   "source": [
    "Let's implement the quantum circuit for the Shor's Algorithm, based on Quantum Phase Estimation (QPE), with $m = 8$ phase counting qubits and $n = 4$ qubits on which will be applied successively the ${2}^{k}$-Controlled-$U$ gate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8f0f482f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2228.58x5802.61 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define the size m of the quantum register\n",
    "# for the phase counting of the qubits\n",
    "phase_register_size = 8\n",
    "\n",
    "# define the size n of the quantum register\n",
    "# for the successive applications of\n",
    "# the 2^k-Controlled-U gate defined before\n",
    "cu_register_size = 4\n",
    "\n",
    "\n",
    "# create the Quantum Circuit needed to run\n",
    "# with m = 8 qubits for the phase counting\n",
    "# and with n = 4 qubits for the successive\n",
    "# applications of the 2^k-Controlled-U gate\n",
    "# defined before, to implement the Shor's Algorithm\n",
    "# for Factoring, based on Quantum Phase Estimation (QPE)\n",
    "shor_qpe = QuantumCircuit( ( phase_register_size + cu_register_size ),\n",
    "                             phase_register_size )\n",
    "\n",
    "\n",
    "# perform the Quantum Hadamard Transform on\n",
    "# the m qubits for the phase counting of\n",
    "# the quantum register of the quantum circuit\n",
    "# implementing the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "apply_quantum_hadamard_transform( shor_qpe, phase_register_size )\n",
    "\n",
    "# apply the Pauli-X gate to the last qubit on\n",
    "# the quantum register of the quantum circuit to\n",
    "# implement the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "shor_qpe.x( phase_register_size )\n",
    "\n",
    "# apply a barrier to the quantum circuit to\n",
    "# implement the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "shor_qpe.barrier()\n",
    "\n",
    "\n",
    "# for each kth qubit on the quantum register \n",
    "# for the phase counting of the qubits\n",
    "for k in range( phase_register_size ):\n",
    "    \n",
    "    # retrieve the 2^k-Controlled-U gate object,\n",
    "    # which repeats the action of the operator U,\n",
    "    # 2^k times, defined before\n",
    "    cU = cU_multi(k)\n",
    "    \n",
    "    # apply the 2^k-Controlled-U gate object,\n",
    "    # which repeats the action of the operator U,\n",
    "    # 2^k times, defined before, for the kth iteration,\n",
    "    # to the quantum circuit to implement\n",
    "    # the Shor's Algorithm for Factoring,\n",
    "    # based on Quantum Phase Estimation (QPE)\n",
    "    shor_qpe.append( cU, [k] + list( range( phase_register_size,\n",
    "                                            ( phase_register_size + cu_register_size ) ) ) )\n",
    "\n",
    "\n",
    "# apply a barrier to the quantum circuit to\n",
    "# implement the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)   \n",
    "shor_qpe.barrier()\n",
    "\n",
    "# perform the Swap gates on the n qubits of\n",
    "# the quantum register of the quantum circuit\n",
    "# implementing the Quantum Phase Estimation (QPE),\n",
    "# as part of the Quantum Fourier Transform (QFT),\n",
    "# required to build the quantum circuit to implement\n",
    "# the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE) \n",
    "apply_swaps(shor_qpe, phase_register_size)\n",
    "\n",
    "# apply a barrier to the quantum circuit to\n",
    "# implement the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "shor_qpe.barrier()\n",
    "\n",
    "\n",
    "# perform the Inverse Quantum Fourier Transform (IQFT) on\n",
    "# the m qubits for the phase counting of\n",
    "# the quantum register of the quantum circuit\n",
    "# implementing the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "apply_quantum_fourier_transform_inverse( shor_qpe, phase_register_size )\n",
    "\n",
    "\n",
    "# apply a barrier to the quantum circuit to\n",
    "# implement the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "shor_qpe.barrier()\n",
    "\n",
    "\n",
    "# perform a measurement of all\n",
    "# the m qubits for the phase counting of\n",
    "# the quantum register of the quantum circuit\n",
    "# implementing the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "shor_qpe.measure( range( phase_register_size ),\n",
    "                  range( phase_register_size ) )\n",
    "\n",
    "\n",
    "# draw the quantum circuit implementing\n",
    "# the quantum circuit to\n",
    "# implement the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE)\n",
    "shor_qpe.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "813b76e4-9f53-4953-be62-bd87e3e89ac5",
   "metadata": {},
   "source": [
    "Let's run the quantum simulation of the quantum circuit for the Shor's Algorithm, based on Quantum Phase Estimation (QPE), with $m = 8$ phase counting qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "f25f9d0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# run this cell to simulate 'shor_qpe' and\n",
    "# to plot the histogram of the results\n",
    "\n",
    "\n",
    "# create an Aer Simulator object\n",
    "sim = Aer.get_backend(\"aer_simulator\")\n",
    "\n",
    "# define the number of shots\n",
    "shots = 20000\n",
    "\n",
    "\n",
    "# execute the quantum simulation for\n",
    "# the quantum circuit for the Shor's Algorithm,\n",
    "# based on Quantum Phase Estimation (QPE),\n",
    "# with n phase counting qubits, and retrieve\n",
    "# the result counts of this quantum simulation\n",
    "shor_qpe_counts = execute(shor_qpe, sim, shots=shots).result().get_counts()\n",
    "\n",
    "# plot the histogram of the result counts of the quantum simulation\n",
    "# for the quantum circuit for the Shor's Algorithm, based on\n",
    "# Quantum Phase Estimation (QPE), with n phase counting qubits\n",
    "plot_histogram( shor_qpe_counts, figsize=(9,5) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "20888bbf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your answer\n",
    "\n",
    "# import the grader for the exercise 7 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex7\n",
    "\n",
    "# grade the exercise 7 of the lab 3\n",
    "grade_lab3_ex7( shor_qpe_counts )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c8b2c0",
   "metadata": {},
   "source": [
    "We can then find the integers $s$ and $r$ using the continued fractions algorithm.  Luckily python has built-in functionality for this using the `Fraction` function, where we will limit the denominator to $r<15$.  Use this to find the estimated $s$ and $r$ for each outcome you measured above."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51923e83-7afa-4938-ba11-fa0933f12756",
   "metadata": {},
   "source": [
    "Let's try the function to build ``Fraction`` objects in Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "fc619b09",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unlimited Fraction(0.666): 5998794703657501/9007199254740992 \n",
      "\n",
      "Limited Fraction(0.666), with a max. denominator of 15: 2/3\n"
     ]
    }
   ],
   "source": [
    "# import the Fraction object\n",
    "# from the built-in fractions module\n",
    "from fractions import Fraction\n",
    "\n",
    "\n",
    "# print the number '0.666',\n",
    "# as an unlimited Fraction object\n",
    "print( \"Unlimited Fraction(0.666):\",\n",
    "       Fraction(0.666), '\\n')\n",
    "\n",
    "# print the number '0.666',\n",
    "# as a limited Fraction object\n",
    "# with the denominator of 15\n",
    "print( \"Limited Fraction(0.666), with a max. denominator of 15:\",\n",
    "       Fraction(0.666).limit_denominator(15) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef44a8bd-3bc3-4411-8cad-6d5d88bac116",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 8 - Compute the estimated fractions obtained from the Shor's Algorithm for Factoring, based on Quantum Phase Estimation (QPE). </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f885c631-7793-4185-94d3-2f8def1a86c9",
   "metadata": {},
   "source": [
    "Let's compute the estimated fractions obtained from the Shor's Algorithm for Factoring, based on Quantum Phase Estimation (QPE), built before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0cd183a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated Phases: [0.5, 0.75, 0.25, 0.0]\n",
      "Estimated Fractions: [Fraction(1, 2), Fraction(3, 4), Fraction(1, 4), Fraction(0, 1)]\n"
     ]
    }
   ],
   "source": [
    "# create a list with the estimated phases of the result counts\n",
    "# obtained from the execution of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n counting qubits\n",
    "estimated_phases = [ bin_to_decimal(binary_val) / 2**phase_register_size\n",
    "                     for binary_val in shor_qpe_counts ]\n",
    "\n",
    "# print the list with the estimated phases of the result counts\n",
    "# obtained from the execution of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n counting qubits\n",
    "print( \"Estimated Phases:\", estimated_phases )\n",
    "\n",
    "\n",
    "# create a list of with the estimated phases of the result counts\n",
    "# obtained from the execution of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n counting qubits,\n",
    "# represented as Fraction objects with the format s/r\n",
    "shor_qpe_fractions = [ Fraction(estimated_phase).limit_denominator(15)\n",
    "                       for estimated_phase in estimated_phases ]\n",
    "\n",
    "# print the list of with the estimated phases of the result counts\n",
    "# obtained from the execution of the quantum simulation\n",
    "# for the Quantum Phase Estimation (QPE), with n counting qubits,\n",
    "# represented as Fraction objects with the format s/r\n",
    "print( \"Estimated Fractions:\", shor_qpe_fractions )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "64f3ab41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your answer\n",
    "\n",
    "# import the grader for the exercise 8 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex8\n",
    "\n",
    "# grade the exercise 8 of the lab 3\n",
    "grade_lab3_ex8( shor_qpe_fractions )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "151c485d-48d5-461b-82d1-dafc5d9c905f",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"> Ex. 9 - Build the Shor's Algorithm for Factoring, based on Quantum Phase Estimation (QPE). </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7be59ad2",
   "metadata": {},
   "source": [
    "## Step 4. Putting it all together\n",
    "\n",
    "Now let's put all of these steps together in order to factor the (very simple) number,  $N = 15$.  We'll continue with our example of $a=7$, remember that the phase we measure $s/r$ where $s$ is a random integer between $0$ and $r-1$ and:\n",
    "\n",
    "$$\n",
    "    a^r\\text{mod}N = 1\n",
    "$$\n",
    "\n",
    "Then, once we have $r$, we can find a factor of $N$ by:\n",
    "\n",
    "$$\n",
    "    \\left(a^r-1\\right)\\text{mod} N = 0\n",
    "$$\n",
    "which requires that $N$ must divide by $a^r-1$.  If $r$ is even, we can also write\n",
    "\n",
    "$$\n",
    "    a^r-1 = \\left(a^{r/2}+1\\right)\\left(a^{r/2}-1\\right).\n",
    "$$\n",
    "\n",
    "Put together a function called `shor_qpe` which takes an argument for $k$ (the number of counting qubits) and composes, runs, and processes Shor's algorithm to guess the factors.  Use an input state of $|y\\rangle{}=|1\\rangle{}$ for the phase estimation. (Note: The function `cU_multi()` only executes $|ay\\ \\text{mod}\\ 15\\rangle{}$ for $a=7$)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "141bf124-bb0d-46c3-9657-6cf253610fc8",
   "metadata": {},
   "source": [
    "Let's build the complete Shor's Algorithm for Factoring, based on the Quantum Phase Estimation, for the factoring problem proposed above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5be23ac1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the function to create and execute\n",
    "# the Shor's Algorithm for Factoring,\n",
    "# based on Quantum Phase Estimation (QPE),\n",
    "# with k phase counting qubits\n",
    "def shor_qpe(k):\n",
    "\n",
    "    # define the co-prime a\n",
    "    a = 7\n",
    "    \n",
    "    # define the number N to factor\n",
    "    N = 15\n",
    "    \n",
    "    # compute the number m of\n",
    "    # additional qubits required\n",
    "    m = int( np.ceil( np.log2(N) ) )\n",
    "        \n",
    "        \n",
    "    #################################################\n",
    "    \n",
    "    # step 1. Begin a while loop until a nontrivial guess is found\n",
    "    #### your code goes here ####\n",
    "    \n",
    "    # define the boolean flag to determine\n",
    "    # if a non trivial guess was found, initially as False\n",
    "    non_trivial_guess_found = False\n",
    "    \n",
    "    \n",
    "    # while no trivial factor guess was found,\n",
    "    # execute the while loop\n",
    "    while( not non_trivial_guess_found ):\n",
    "        \n",
    "        \n",
    "        #################################################\n",
    "\n",
    "        # step 2a. construct a QPE quantum circuit\n",
    "        #          with m phase counting qubits to guess\n",
    "        #          the phase phi = s/r, using the function\n",
    "        #          cU_multi() defined before\n",
    "        \n",
    "        \n",
    "        #### your code goes here ####\n",
    "        \n",
    "        # create a quantum circuit for\n",
    "        # the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE),\n",
    "        # with k phase counting qubits,\n",
    "        # and additional m qubits for\n",
    "        # the successive applications of\n",
    "        # the 2^k-Controlled-U gate defined before\n",
    "        qc = QuantumCircuit( ( k + m ), k)\n",
    "        \n",
    "        \n",
    "        # perform the Quantum Hadamard Transform on\n",
    "        # the k phase counting qubits of the respective\n",
    "        # quantum register of the quantum circuit\n",
    "        # for the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE)\n",
    "        apply_quantum_hadamard_transform( qc, k )\n",
    "        \n",
    "        # apply a Pauli-X gate to the last\n",
    "        # phase counting qubit of the respective\n",
    "        # quantum register of the quantum circuit\n",
    "        # for the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE)\n",
    "        qc.x(k)\n",
    "\n",
    "        # apply a barrier to the quantum circuit for\n",
    "        # the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE),\n",
    "        # with k phase counting qubits,\n",
    "        # and additional m qubits for\n",
    "        # the successive applications of\n",
    "        # the 2^k-Controlled-U gate defined before\n",
    "        qc.barrier()\n",
    "        \n",
    "        \n",
    "        # for each kth qubit on the quantum register \n",
    "        # for the phase counting of the qubits\n",
    "        for k_i in range(k):\n",
    "\n",
    "            # retrieve the 2^k-Controlled-U gate object,\n",
    "            # which repeats the action of the operator U,\n",
    "            # 2^k times, defined before\n",
    "            cU = cU_multi(k_i)\n",
    "            \n",
    "            # apply the 2^k-Controlled-U gate object,\n",
    "            # which repeats the action of the operator U,\n",
    "            # 2^k times, defined before, for the kth iteration,\n",
    "            # to the quantum circuit for the Shor's Algorithm\n",
    "            # for Factoring, based on Quantum Phase Estimation (QPE),\n",
    "            # with k phase counting qubits, and additional m qubits\n",
    "            # for the successive applications of\n",
    "            # the 2^k-Controlled-U gate defined before\n",
    "            qc.append( cU, [k_i] + list( range( k, ( k + m ) ) ) )\n",
    "\n",
    "        \n",
    "        # apply a barrier to the quantum circuit for\n",
    "        # the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE),\n",
    "        # with k phase counting qubits,\n",
    "        # and additional m qubits for\n",
    "        # the successive applications of\n",
    "        # the 2^k-Controlled-U gate defined before\n",
    "        qc.barrier()\n",
    "        \n",
    "        # perform the Swap gates on the k\n",
    "        # phase counting qubits of the respective\n",
    "        # quantum register of the quantum circuit\n",
    "        # for the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE),\n",
    "        # as part of the Quantum Fourier Transform (QFT)\n",
    "        apply_swaps( qc, k )\n",
    "\n",
    "        # apply a barrier to the quantum circuit for\n",
    "        # the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE),\n",
    "        # with k phase counting qubits,\n",
    "        # and additional m qubits for\n",
    "        # the successive applications of\n",
    "        # the 2^k-Controlled-U gate defined before\n",
    "        qc.barrier()\n",
    "        \n",
    "        \n",
    "        # perform the Inverse Quantum Fourier Transform (IQFT) on\n",
    "        # the k phase counting qubits of the respective\n",
    "        # quantum register of the quantum circuit\n",
    "        # for the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE)\n",
    "        apply_quantum_fourier_transform_inverse( qc, k )\n",
    "\n",
    "        # apply a barrier to the quantum circuit for\n",
    "        # the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE),\n",
    "        # with k phase counting qubits,\n",
    "        # and additional m qubits for\n",
    "        # the successive applications of\n",
    "        # the 2^k-Controlled-U gate defined before\n",
    "        qc.barrier()\n",
    "        \n",
    "        \n",
    "        # perform a measurement of all\n",
    "        # the k phase counting qubits of the respective\n",
    "        # quantum register of the quantum circuit\n",
    "        # for the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE)\n",
    "        qc.measure( range(k), range(k) )\n",
    "        \n",
    "        \n",
    "        #################################################\n",
    "        \n",
    "        \n",
    "        # step 2b. run the QPE quantum circuit with a single shot,\n",
    "        #          record the results and convert the estimated phase\n",
    "        #          bitstring to a decimal format\n",
    "        \n",
    "        \n",
    "        #### your code goes here ####\n",
    "        \n",
    "        # create an Aer Simulator object\n",
    "        sim = Aer.get_backend(\"aer_simulator\")\n",
    "        \n",
    "        \n",
    "        # define the number of shots\n",
    "        shots = 1\n",
    "        \n",
    "        \n",
    "        # execute the simulation for the Quantum Phase Estimation (QPE),\n",
    "        # with n counting qubits, and retrieve the result counts\n",
    "        # obtained from this quantum simulation\n",
    "        shor_qpe_counts = execute( qc, sim, shots=shots ).result().get_counts()\n",
    "        \n",
    "        \n",
    "        # plot the histogram of the result counts of the quantum simulation\n",
    "        # for the Quantum Phase Estimation (QPE), with n counting qubits\n",
    "        plot_histogram( shor_qpe_counts, figsize=(9,5) )\n",
    "        \n",
    "        \n",
    "        # compute the estimated phases from the result counts\n",
    "        # obtained from the quantum simulation of the quantum circuit\n",
    "        # implementing the Shor's Algorithm for Factoring,\n",
    "        # based on Quantum Phase Estimation (QPE)\n",
    "        estimated_phases = [ bin_to_decimal( binary_val ) / 2**k\n",
    "                             for binary_val in shor_qpe_counts ]\n",
    "        \n",
    "        \n",
    "        #################################################\n",
    "\n",
    "        \n",
    "        # step 3. use the Fraction object to find the guess for r\n",
    "       \n",
    "        #### your code goes here ####\n",
    "\n",
    "        # convert the estimated phase to a fraction s/r format\n",
    "        fraction_s_r = [ Fraction(estimated_phase).limit_denominator(N)\n",
    "                         for estimated_phase in estimated_phases ][0]\n",
    "        \n",
    "        # retrieve the numerator s and the denominator r\n",
    "        # from the estimated phase represented as a fraction\n",
    "        s, r = fraction_s_r.numerator, fraction_s_r.denominator\n",
    "        \n",
    "        \n",
    "        #################################################\n",
    "        \n",
    "        \n",
    "        # step 4. now that r has been found, use the built-in\n",
    "        #         greatest common divisor function to determine\n",
    "        #         the guesses for a factor of N\n",
    "        \n",
    "        # build the list of guesses for possible non-trivial factors of N\n",
    "        guesses = [ gcd( a**( r // 2 ) - 1, N ),\n",
    "                    gcd( a**( r // 2 ) + 1, N ) ]\n",
    "        \n",
    "        \n",
    "        #################################################\n",
    "        \n",
    "        \n",
    "        # step 5. for each guess in guesses, check if\n",
    "        #         at least one is a non-trivial factor,\n",
    "        #         i.e., ( ( guess != 1 ) or ( guess != N ) )\n",
    "        #               and ( N % guess == 0 )\n",
    "        \n",
    "        #### your code goes here ####\n",
    "        \n",
    "        # for each of the guesses computed before\n",
    "        for guess in guesses:\n",
    "            \n",
    "            # if the current guess is not a trivial factor\n",
    "            if ( ( ( guess != 1 ) or ( guess != N ) )\n",
    "                  and ( N % guess == 0 ) ):\n",
    "                \n",
    "                # update the boolean flag to determine\n",
    "                # if a non trivial guess was found, as True\n",
    "                non_trivial_guess_found = True\n",
    "                \n",
    "                # break the current for loop\n",
    "                break\n",
    "    \n",
    "        \n",
    "    #################################################\n",
    "    \n",
    "    # step 6. if a non-trivial factor is found return\n",
    "    #         the list 'guesses', otherwise\n",
    "    #         continue the while loop\n",
    "    \n",
    "    # return the list of the guesses,\n",
    "    # containing a non-trivial factor of N\n",
    "    return guesses\n",
    "    \n",
    "    #################################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "03a369ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "# submit your circuit\n",
    "\n",
    "# import the grader for the exercise 9 of the lab 3\n",
    "from qc_grader.challenges.qgss_2023 import grade_lab3_ex9\n",
    "\n",
    "# grade the exercise 9 of the lab 3\n",
    "grade_lab3_ex9( shor_qpe )"
   ]
  },
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       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.24.1</td></tr><tr><td><code>qiskit-aer</code></td><td>0.12.1</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.20.2</td></tr><tr><td><code>qiskit</code></td><td>0.43.2</td></tr><tr><td><code>qiskit-nature</code></td><td>0.6.2</td></tr><tr><td><code>qiskit-finance</code></td><td>0.3.4</td></tr><tr><td><code>qiskit-optimization</code></td><td>0.5.0</td></tr><tr><td><code>qiskit-machine-learning</code></td><td>0.6.1</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.10.8</td></tr><tr><td>Python compiler</td><td>GCC 10.4.0</td></tr><tr><td>Python build</td><td>main, Nov 22 2022 08:26:04</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>31.211322784423828</td></tr><tr><td colspan='2'>Wed Aug 02 17:17:13 2023 UTC</td></tr></table>"
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   "source": [
    "# import the IBM's Qiskit Jupyter Tools\n",
    "import qiskit.tools.jupyter\n",
    "\n",
    "# show the table of the IBM's Qiskit version\n",
    "%qiskit_version_table"
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "Congratulations! You've completed Lab 3 of the Global Summer School!! 🎉\n",
    "\n",
    "This lab was adapted from both the [Qiskit QPE Lab](https://learn.qiskit.org/course/ch-labs/lab-5-accuracy-of-quantum-phase-estimation#lab-3-0) as well as the [Qiskit Shor's Algorithm](https://learn.qiskit.org/course/ch-labs/lab-7-scalable-shors-algorithm) lab."
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  {
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   "id": "d7eb40e3-2737-42d0-97f7-0ae1006b0908",
   "metadata": {},
   "source": [
    "Made with ❤ by Rúben André Barreiro (and adapted from IBM Quantum)."
   ]
  }
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