3s-Challenge-solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e0cacf9c-ed37-4041-8cc8-3b0a8a5e630d",
   "metadata": {},
   "source": [
    "# Optimizing a variational quantum circuit via simulated annealing\n",
    "by Mahnoor Fatima"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b476585-acca-44df-8bdf-450d62faebc6",
   "metadata": {},
   "source": [
    "**Simulated annealing** is an optimization algorithm to find the global optima for both bounded and unbounded optimization problems. The algorithm is inspired from the metallic annealing process in which a metal is first heated and then gradually cooled. In this algorithm, the optimizer first explores the solution space haphazardly which allows it to explore a greater range of values; as the temperature 'drops,' the solution space becomes less scattered and the predicted points remain close to the current state of the system.\n",
    "\n",
    "The main advantage is that it allows the determination of the stochastic global maximum of an optimization problem. However, the dowside of this algorithm is that it might return the wrong optimal point.\n",
    "\n",
    "You can read more about simulated annealing and its applications in this [open-source paper](https://projecteuclid.org/journals/statistical-science/volume-8/issue-1/Simulated-Annealing/10.1214/ss/1177011077.full)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be50b275-873e-4bd5-8f72-414256c0008d",
   "metadata": {},
   "source": [
    "## Explore the Problem Statement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "479ddf89-80a1-40db-a1c9-90e10b6d7bf6",
   "metadata": {},
   "source": [
    "A variational quantum circuit (VQC) is a quantum circuit having parametrized gates such that the behaviour of the circuit can be varied by varying the parameters. Thus, with appropriate parameters, a generic parametrized quantum circuit can be trained to perform a desired operation.\n",
    "\n",
    "This flexibility of VQCs is the inspiration for this problem: training a *n*-qubit VQC for evaluating the Quantum Fourier Transform of a number in the range $0$ to $2^n - 1$. The Quantum Fourier Transform (QFT) is itself a unitary operation which evaluates the Fourier transform of a quantum state."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e75404a-d077-4da5-a63a-8b6bb4dae3b9",
   "metadata": {},
   "source": [
    "For this challenge, you will be making a generic *n*-qubit variational quantum circuit with Hadamard gates and $R_z(\\theta)$ gates applied to each qubit. The angles $\\theta$ for each $R_z$ gate comprise the list of parameters to be optimized. An inverse-QFT block is applied to evaluate the error such that the expected output is the input number itself."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "31180bd4-c3b9-42b1-a7a4-3795ca95b3fe",
   "metadata": {},
   "source": [
    "![image.png](attachment:a4e41295-623a-4d85-b962-4e929ad4ec53.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c10c68ff-2018-40b6-9706-fa9e553a7a2f",
   "metadata": {},
   "source": [
    "## Import the libraries and define the device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "22528832-a3f1-4fad-aa38-ab8abb67b998",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane as qml\n",
    "from pennylane import numpy as np\n",
    "from math import exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6e162c33-5a78-4501-a96d-9c728dcab7ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 1\n",
    "dev = qml.device('default.qubit', wires = n)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93922576-370d-4131-9585-7111fb5dc48c",
   "metadata": {},
   "source": [
    "## Define the quantum node and circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8497a876-4b6c-4e3c-b354-784bdfa68991",
   "metadata": {},
   "source": [
    "Use the above image to form the quantum circuit. You will need the Hadamard and [RZ](https://docs.pennylane.ai/en/stable/code/api/pennylane.RZ.html) gates. You will also need [qml.adjoint](https://docs.pennylane.ai/en/stable/code/api/pennylane.adjoint.html), [qml.QFT](https://docs.pennylane.ai/en/stable/code/api/pennylane.QFT.html), and [qml.probs](https://docs.pennylane.ai/en/stable/code/api/pennylane.probs.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b61cc3da-070b-42f5-add7-edf67f00235f",
   "metadata": {},
   "outputs": [],
   "source": [
    "@qml.qnode(dev)\n",
    "def circuit(theta):\n",
    "    for i in range(n):\n",
    "        qml.Hadamard(wires = i)\n",
    "        qml.RZ(theta[i], wires = i)\n",
    "    qml.adjoint(qml.QFT)(wires=range(n))\n",
    "    return qml.probs(wires = range(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5673412-155e-4f22-992d-dd05833c7da7",
   "metadata": {},
   "source": [
    "## Define the cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2df6e91b-fae4-4f20-a90c-09b5f570ea79",
   "metadata": {},
   "source": [
    "The **Mean Square Error (MSE)** is one of the most common cost functions and is given by:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9bcc251-bb01-491c-9aec-9ad2bd5cff6f",
   "metadata": {},
   "source": [
    "<p style=\"text-align: center\">\n",
    "    $MSE = \\sum_{i=0}^{N-1} (y_i-\\hat{y}_i)^2$\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8aefc4e0-ab4e-470b-ac0c-6573e47d5606",
   "metadata": {},
   "source": [
    "where $y$ is the predicted output array and $\\hat{y}$ is the expected output array."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b05be2cd-c763-4963-827c-b8a41fe98852",
   "metadata": {},
   "source": [
    "For the given problem, the expected output $\\hat{y}$ is a $2^n$-sized array with all entries equal to zero except for the $m$-index entry, which is $1$, i.e., we want the number $m$ to be evaluated with an absolute certainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "535b1add-41a6-4ca9-a681-40163ea4e549",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(params):\n",
    "    y = np.zeros(2**n)\n",
    "    y[m] = 1\n",
    "    probs = circuit(params)\n",
    "    return np.sum(np.square((y-probs)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c89175e-4f62-4b73-bb38-020dfc7bbd2f",
   "metadata": {},
   "source": [
    "## Implement the Simulated Annealing Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd954341-5e61-4820-ae43-420fc9e08983",
   "metadata": {},
   "source": [
    "The procedure for simulated annealing is as follows:\n",
    "\n",
    "- A random point is selected as the initial state of the system.\n",
    "\n",
    "- As the temperature is initially high, the algorithm searches the solution space haphazardly and evaluates the cost value for various states. If the cost value for a certain state is less than for the current optimal state, the optimal state of the circuit is updated.\n",
    "\n",
    "The new temperature of the system is evaluated by using the following equation:\n",
    "\n",
    "<p style=\"text-align: center\">\n",
    "    $t_{i} = \\frac{t_o}{i+1}$\n",
    "</p>\n",
    "\n",
    "where $i$ is the number of the current iteration.\n",
    "\n",
    "As the temperature of the system decreases, the algorithm takes smaller strides across the solution space.\n",
    "\n",
    "Fill in the blanks in the below algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ea455024-8bab-4968-b3c7-01847f2cb819",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulated_annealing(objective, param_range, temperature, iterations, learning_rate):\n",
    "        # Define initial state\n",
    "        s0 = np.empty(np.shape(param_range)[0])\n",
    "        s_eval = 0 \n",
    "        for i in range(len(s0)):\n",
    "            s0[i] = param_range[i][0] + np.random.random()* (param_range[i][1] - param_range[i][0])\n",
    "\n",
    "        # Evaluate current state of the system \n",
    "        s = s0\n",
    "        s_eval = objective(s0)\n",
    "\n",
    "        for k in range(iterations):\n",
    "            # Find a candidate element\n",
    "            s_new = np.empty(np.shape(param_range)[0])\n",
    "            for i in range(len(s_new)):\n",
    "                rng = param_range[i][1] - param_range[i][0]     # Range of the variable\n",
    "                s_new[i] = s[i] + np.random.uniform(param_range[i][0] - rng/2, param_range[i][0] + rng/2)*learning_rate\n",
    "\n",
    "            # Evaluate the candidate element        \n",
    "            s_new_eval = objective(s_new)\n",
    "            # Update the state of the system\n",
    "            if s_new_eval < s_eval:\n",
    "                s = s_new\n",
    "                s_eval = s_new_eval\n",
    "\n",
    "            delta = s_new_eval - s_eval\n",
    "            t = temperature/float(k+1) \n",
    "\n",
    "            # Metropolis acceptance criterion\n",
    "            metropolis = exp(-delta/t)\n",
    "            if metropolis > np.random.uniform():\n",
    "                s = s_new\n",
    "                s_eval = s_new_eval\n",
    "        return s, s_eval"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e46bb04-3d29-40cf-8d08-9e649f557e04",
   "metadata": {},
   "source": [
    "## Optimization module"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59e97484-b4ff-4e00-8a1b-0ba7f24bbb1f",
   "metadata": {},
   "source": [
    "As a final step of implementing the solution of the given problem, the entire optimization problem is encapsulated in a function. This allows to quick-run the problem for different parameters without the hassle of updating the parameters. Also, the quantum circuit has been defined within the function to keep the variables (like $m$ and $n$) accessible for all functions.\n",
    "\n",
    "Fill in your code below the task descriptions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "78b38bac-0716-411b-85c9-cf91e1a5ecff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def quantum_fourier_transform(n, m, temperature, steps = 5000, learning_rate = 0.01):\n",
    "    ''' A function to generate the Quantum Fourier Transform of a number m via a quantum circuit with n-qubits. \n",
    "    \n",
    "    Args:\n",
    "    n: It is the number of qubits in the variational quantum circuit.\n",
    "    m: It is the number used to train the variational quantum circuit. Its value ranges from 0 to 2^n - 1\n",
    "    steps: It is the number of iterations of the optimzation process.\n",
    "    learning_rate: This is the step size of the optimizer.\n",
    "    \n",
    "    Return value:\n",
    "    circuit: The variational quantum circuit comprising n qubits.\n",
    "    param_arr: Shape = (steps, n). It consists of the values of the parameters after each optimization step.\n",
    "    cost_arr: Size = n. It consists of the cost value of the circuit after each optimization step.\n",
    "    cost: The cost function\n",
    "    '''\n",
    "    # Task 2: Load a Quantum Device\n",
    "    dev = qml.device('default.qubit', wires = n)\n",
    "    \n",
    "    # Task 3-6: Create the Quantum Circuit\n",
    "    @qml.qnode(dev)\n",
    "    def circuit(theta):\n",
    "        for i in range(n):\n",
    "            qml.Hadamard(wires = i)\n",
    "            qml.RZ(theta[i], wires = i)\n",
    "        qml.adjoint(qml.QFT)(wires=range(n))\n",
    "        return qml.probs(wires = range(n))\n",
    "    \n",
    "    # Task 7: Create the Cost Function\n",
    "    def cost(params):\n",
    "        y = np.zeros(2**n)\n",
    "        y[m] = 1\n",
    "        probs = circuit(params)\n",
    "        return np.sum(np.square((y-probs)))\n",
    "    \n",
    "    # Defining the bounds of the angles\n",
    "    bounds = np.empty((n, 2))\n",
    "    for bound in bounds:\n",
    "        bound[0] = 0\n",
    "        bound[1] = 2*np.pi\n",
    "        \n",
    "    angles, cost = simulated_annealing(cost, bounds, temperature, steps, learning_rate)\n",
    "    angles = angles%(np.pi*2)\n",
    "\n",
    "    # Print the results of optimization\n",
    "    print(\"Optimized rotation angles: \", angles)\n",
    "    print(\"Cost value at optimized parameters: \",cost)\n",
    "    \n",
    "    return circuit, angles, cost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e55fc30-bcc3-4617-ae1b-671ba7ded86c",
   "metadata": {},
   "source": [
    "## Optimization of the Quantum Circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e82d90c2-14e9-4280-8b7e-fc29064efeaa",
   "metadata": {},
   "source": [
    "Now, test-run the function for a random set of parameters to evaluate it's performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "166a0f6f-df0b-4df6-ac07-35c20f1f1980",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized rotation angles:  [2.80314255 4.82725244]\n",
      "Cost value at optimized parameters:  0.0014142336945561428\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 600x300 with 1 Axes>, <Axes: >)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit, angles, cost = quantum_fourier_transform(2, 3, 5, steps = 10000, learning_rate = 0.01)\n",
    "qml.draw_mpl(circuit)(angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1daa85eb-2b79-4318-974b-8999d6834cb4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}