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 "cells": [
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   "source": [
    "# Solving QUBO Problem using QAOA\n",
    "\n",
    "## Overview\n",
    "\n",
    "In this tutorial, we will demonstrate how to solve quadratic unconstrained binary optimization (QUBO) problems using QAOA. There is a specific application for portfolio optimization and we will introduce it in another [tutorial](https://tensorcircuit.readthedocs.io/en/latest/tutorials/portfolio_optimization.html).\n",
    "\n",
    "## QUBO problem\n",
    "\n",
    "### What is QUBO?\n",
    "\n",
    "Quadratic unconstrained binary optimization (QUBO) is a type of problem that aims to optimize a quadratic objective function using binary variables. The primary goal of a QUBO problem is to determine the assignments of binary variables that minimize or maximize the quadratic objective function. These variables represent choices or decision variables that can be either selected (1) or not selected (0). The objective function captures the associated costs, benefits, or constraints related to these decisions.\n",
    "\n",
    "From a computational perspective, solving a QUBO problem is NP-hard. This classification implies that solving the optimal solution to a QUBO instance is believed to be computationally challenging, and no known polynomial-time algorithm that can efficiently solve all QUBO problems.\n",
    "\n",
    "However, a promising approach called Quantum Approximate Optimization Algorithm (QAOA), introduced in [this tutorial](https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa.html), has the potential to offer significant advantages when applied to QUBO problem-solving. QAOA leverages inherent quantum parallelism and interference effects to explore the solution space more efficiently compared to classical methods. This efficiency can lead to faster and more optimal solutions. In QAOA, each qubit represents a binary variable, and the objective function is calculated as the expected value of a quantum state generated by the ansatz (a quantum circuit with parameters to be decided). The parameters in the ansatz are iteratively optimized by a classical algorithm to improve the solution quality.\n",
    "\n",
    "### General Case\n",
    "\n",
    "For the general QUBO case, we wish to minimize a cost function of the form\n",
    "\n",
    "$$ \n",
    "x^T Q x\n",
    "$$\n",
    "\n",
    "where $x\\in\\{0,1\\}^n$ and $Q\\in\\mathbb{R}^{n\\times n}$ is a real symmetric matrix.\n",
    "\n",
    "This function maps to an Ising Hamiltonian \n",
    "\n",
    "$$\n",
    "\\frac{1}{2}\\left(\\sum_{i=1}^n C_{ii} + \\sum_{i<j}C_{ij}\\right) I - \\frac{1}{2}\\sum_{i=1}^n \\left(\\sum_{j=1}^n C_{ij} \\right)Z_i +\\frac{1}{2}\\sum_{i<j}C_{ij}Z_iZ_j\n",
    "$$\n",
    "\n",
    "This Hamiltonian is then represented with quantum gates and put in the cost terms of the ansatz. At the same time, the cost function is defined as the expected value of this Ising Hamiltonian.\n",
    "\n",
    "### An example\n",
    "\n",
    "Consider minimizing the following 2x2 QUBO objective function:\n",
    "\n",
    "$$\n",
    "\\begin{pmatrix}x_1 & x_2\\end{pmatrix}\\begin{pmatrix}-5& -2 \\\\-2 & 6\\end{pmatrix}\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix} = -5x_1^2 -4x_1x_2 +6x_2^2\n",
    "$$\n",
    "\n",
    "Clearly, this cost function is minimized when $(x_1,x_2) = (1,0)$, with corresponding cost value of $-5$. Then we are going to apply QAOA to this minimization. We first convert this to an Ising Hamiltonian by mapping $x_i\\rightarrow \\frac{I-Z_i}{2}$\n",
    "\n",
    "This gives\n",
    "\n",
    "$$\n",
    "-\\frac{5}{4}(I-Z_1)^2 -\\frac{4}{4}(I-Z_1)(I-Z_2) + \\frac{6}{4}(I-Z_2)^2 \n",
    "$$\n",
    "\n",
    "which simplifies to\n",
    "\n",
    "$$\n",
    "-\\frac{1}{2}I +\\frac{7}{2}Z_1   -2Z_2 -Z_1Z_2\n",
    "$$ \n",
    "\n",
    "The $-I/2$ term is simply a constant offset, so we can solve the problem by finding the minimum of \n",
    "\n",
    "$$\n",
    "\\langle \\psi | \\frac{7}{2}Z_1 -2Z_2 -Z_1Z_2 |\\psi\\rangle\n",
    "$$ \n",
    "\n",
    "Note that the minimum should correspond to the computational basis state $|10\\rangle$, and the corresponding true objective function value should be $-4.5$ (ignoring the offset value of $-1/2$). Below, the code used to solve this QUBO problem is shown.\n",
    "\n",
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "45964c1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorcircuit as tc\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "from tensorcircuit.applications.optimization import (\n",
    "    QUBO_QAOA,\n",
    "    QUBO_QAOA_cvar,\n",
    "    cvar_loss,\n",
    ")\n",
    "from tensorcircuit.templates.ansatz import QAOA_ansatz_for_Ising\n",
    "from tensorcircuit.templates.conversions import QUBO_to_Ising\n",
    "\n",
    "K = tc.set_backend(\"tensorflow\")\n",
    "tf.random.set_seed(530)\n",
    "tc.set_dtype(\"float32\")\n",
    "tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "dbdf2a73",
   "metadata": {},
   "source": [
    "The function `QUBO_to_Ising` is defined to convert the Q-matrix to an Ising Hamiltonian. Let's test this function using our example. The result matches exactly with what we derived."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "1f396a77",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pauli terms in this QUBO problem are: [[1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]\n",
      "And the corresponding weights are: [ 3.5 -2.  -1. ]\n",
      "The offset is: -0.5\n"
     ]
    }
   ],
   "source": [
    "# Example usage\n",
    "Q = np.array([[-5, -2], [-2, 6]])  # Example Q-matrix\n",
    "pauli_terms, weights, offset = QUBO_to_Ising(Q)\n",
    "print(\"The Pauli terms in this QUBO problem are:\", pauli_terms)\n",
    "print(\"And the corresponding weights are:\", weights)\n",
    "print(\"The offset is:\", offset)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "192d6c47",
   "metadata": {},
   "source": [
    "## Solve this problem\n",
    "\n",
    "We are going to use the QUBO problem solver, `QUBO_QAOA`, to solve this problem. A 2-layer QAOA ansatz is employed and will be trained for 500 iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "2bc533da-b4f2-4ffb-b486-c65880a30a6d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.Adam` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.Adam`.\n"
     ]
    }
   ],
   "source": [
    "iterations = 500\n",
    "nlayers = 2\n",
    "\n",
    "loss_list = []\n",
    "\n",
    "\n",
    "def record_loss(loss, params):\n",
    "    loss_list.append(loss)\n",
    "\n",
    "\n",
    "# Run QUBO_QAOA function to obtain the final parameters\n",
    "final_params = QUBO_QAOA(Q, nlayers, iterations, callback=record_loss)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e93d8cbe-2884-4f0a-80f8-3b600194927b",
   "metadata": {},
   "source": [
    "Note that with 2 layers and 500 iterations, the objective function does not in this case (although it depends on the initial parameters) converge to the true value of $-4.5$. However, we see below that the final wavefunction does have a significant overlap with the desired state $|10\\rangle$, and then the output of the QAOA algorithm will, with high probability, give the best result.\n",
    "\n",
    "Define a function and print a table of results, where all quantum states are listed in the order of possibilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "b25ba588",
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_result_prob(c, wrap=False, reverse=False):\n",
    "    states = []\n",
    "    n_qubits = c._nqubits\n",
    "    # Generate all possible binary states for the given number of qubits\n",
    "    for i in range(2**n_qubits):\n",
    "        a = f\"{bin(i)[2:]:0>{n_qubits}}\"\n",
    "        states.append(a)\n",
    "\n",
    "    # Calculate the probabilities of each state using the circuit's probability method\n",
    "    probs = K.numpy(c.probability()).round(decimals=4)\n",
    "\n",
    "    # Sort the states and probabilities in descending order based on the probabilities\n",
    "    sorted_indices = np.argsort(probs)[::-1]\n",
    "    if reverse == True:\n",
    "        sorted_indices = sorted_indices[::-1]\n",
    "    state_sorted = np.array(states)[sorted_indices]\n",
    "    prob_sorted = np.array(probs)[sorted_indices]\n",
    "\n",
    "    print(\"\\n-------------------------------------\")\n",
    "    print(\"    selection\\t  |\\tprobability\")\n",
    "    print(\"-------------------------------------\")\n",
    "    if wrap == False:\n",
    "        for i in range(len(states)):\n",
    "            print(\"%10s\\t  |\\t  %.4f\" % (state_sorted[i], prob_sorted[i]))\n",
    "            # Print the sorted states and their corresponding probabilities\n",
    "    elif wrap == True:\n",
    "        for i in range(4):\n",
    "            print(\"%10s\\t  |\\t  %.4f\" % (state_sorted[i], prob_sorted[i]))\n",
    "        print(\"               ... ...\")\n",
    "        for i in range(-4, -1):\n",
    "            print(\"%10s\\t  |\\t  %.4f\" % (state_sorted[i], prob_sorted[i]))\n",
    "    print(\"-------------------------------------\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "da315228",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "-------------------------------------\n",
      "    selection\t  |\tprobability\n",
      "-------------------------------------\n",
      "        10\t  |\t  0.8848\n",
      "        11\t  |\t  0.1051\n",
      "        01\t  |\t  0.0093\n",
      "        00\t  |\t  0.0008\n",
      "-------------------------------------\n"
     ]
    }
   ],
   "source": [
    "c = QAOA_ansatz_for_Ising(final_params, nlayers, pauli_terms, weights)\n",
    "\n",
    "print_result_prob(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "294ea9ce-5064-4176-94d0-8dbb7d1707f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_output(c):\n",
    "    n = c._nqubits\n",
    "    N = 2**n\n",
    "\n",
    "    # Generate labels for the x-axis representing the binary states\n",
    "    x_label = r\"$\\left|{0:0\" + str(n) + r\"b}\\right>$\"\n",
    "    labels = [x_label.format(i) for i in range(N)]\n",
    "\n",
    "    # Create a bar plot with the probabilities of each state\n",
    "    plt.bar(range(N), c.probability())\n",
    "\n",
    "    # Set the x-axis ticks to the generated labels and rotate them for better visibility\n",
    "    plt.xticks(range(N), labels, rotation=70)"
   ]
  },
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   "execution_count": 85,
   "id": "fc1353ab-7a7a-4cdc-931c-3b90417c4961",
   "metadata": {
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   "outputs": [
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rujNSU1MTkyZNipaWlu5jpZRoaWmJxsa+/Q90yJAhUVNTEzt37jzsOYMHD47a2toeAwAMTBXFyMiRI2PQoEHR0dHR43hHR0fU19f36fdYunRptLe39wia/2/evHmxa9eu7mlra6tkmQBAP/JL/W6az33uc/GHf/iHcfXVV8frr79+2POWLFkSw4cP756GhoZf4ioBgF+mQZWcvGPHjjhw4EDU1dX1OF5XVxdbt2494rU33HBDfP7zn4/3v//9sXHjxiOe29nZGZ2dnZUsDQDopyq6M7J///5Yt25dNDU1dR+rqqqKpqamaG09/BvK5s6dG3/xF38RU6dOjXXr1h39agGAAaeiOyMREc3NzbF8+fJYu3ZtPP300zF79uwYOnRoLFu2LCIili9fHm1tbTF//vyIiPjsZz8bixYtig9/+MOxZcuW7rsq//M//xM/+9nP3sI/CgDQH1UcIytXroxRo0bFokWLor6+PtavXx9Tp06Nbdu2RUTEmDFj4uDBg93n/9mf/Vmceuqp8eCDD/b4fW6++eZYuHDhMS4fAOjvKv6ckQw+ZwT4v3zOSB6fM0IljsvnjAAAvNXECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQSowAAKnECACQalD2AgAgIuKOja3ZSzhp3XBJY+rjuzMCAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQSIwBAKjECAKQadDQXzZo1K+bOnRv19fWxYcOG+OQnPxnPPPPMYc+fNm1aLF68OM4777z4/ve/H5/73OfiW9/61lEvGvrijo2t2Us4ad1wSWP2EoB+pOI7I9OnT4/m5uZYuHBhTJw4MTZs2BCrVq2KUaNG9Xp+Y2NjrFixIr72ta/Fu9/97njooYfioYceine84x3HvHgAoP+rOEbmzJkT99xzT9x7772xadOmmDlzZuzZsydmzJjR6/mf/vSn41//9V/j9ttvjxdeeCFuvPHGePbZZ+P6668/5sUDAP1fRS/T1NTUxKRJk2LJkiXdx0op0dLSEo2Nvd+WbWxsjObm5h7HVq1aFb//+79/2McZPHhwnHrqqd3/vba2tsd/Ql8Mrj4lewknreP9XLW3eY7n3trXPMdrX/v6+1YUIyNHjoxBgwZFR0dHj+MdHR0xfvz4Xq+pr6/v9fz6+vrDPs68efPi5ptvPuR4W1tbJcsFkly/a1f2EjhO7O3AdLz3tba2Nnbv3n3Yrx/VG1iPtyVLlhxyN2XEiBGxc+fOpBWdmGpra6OtrS0aGhqOuMn0L/Z14LK3A5e9Pbza2tpob28/4jkVxciOHTviwIEDUVdX1+N4XV1dbN26tddrtm7dWtH5ERGdnZ3R2dnZ45jNPbzdu3f7+xmA7OvAZW8HLnt7qL78fVT0Btb9+/fHunXroqmpqftYVVVVNDU1RWtr799G2dra2uP8iIjf+q3fOuz5AMDJp1Qy06dPL3v37i0f/ehHy/jx48tXv/rVsnPnznLWWWeViCjLly8vt912W/f5jY2NpbOzs8yZM6eMGzeu3HTTTeX1118v73jHOyp6XHPo1NbWllJKqa2tTV+Lsa/G3p7MY2+PeSq/6BOf+ETZsmVL2bdvX1m9enWZMmVK99cef/zxsmzZsh7nT5s2rbzwwgtl3759ZePGjeUDH/hA9h96QMzgwYPLTTfdVAYPHpy+FmNfjb09mcfeHttU/eIXAAAp/GwaACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACDVCfmD8ji8c889Ny688MLYsmVLtLe3xznnnBOvvfZa7NixI3tpHCN7OzDZ14HL3r51xEg/Mnr06Pj4xz8ekydPjne+851RSok1a9bEeeedF2eddVbcddddcdddd8W+ffuyl0qF7O3AZF8HLnv71vIJrP3MmDFj4qyzzorvf//7MW7cuGhoaIiXX3453vWud8XHPvaxePbZZ+NLX/pSvPzyy9lLpUL2dmCyrwOXvX1rpX8mvXlr5tJLLy3//M//XJ544oly+eWXp6/H2FtjX0/WsbcVT/oCzFs4tbW15Y477ijPPPNMmTNnThkyZEj6mkzfpqqqyt6ehGNf++94zr6Ff5e/+AX9wBlnnBF/8id/EmeeeWacdtppsXnz5vjmN78ZL7300iHnXnvttfHhD384mpqaElbK8WRv+w/PWSLsbV+IkX7i3HPPjfvvvz/Gjh0b27dvjx07dsSIESNiyJAh0draGn/7t38bTz/9dFRVVUUpP9/ShoaGaGtr63GME8+wYcNiwoQJ8b3vfS9effXVPu2VvT3xec4OXJ6zx0f67RlzhFtXv7gNeOedd5bHH3+8nH322SUiyujRo8sVV1xRvvCFL5THHnusPPbYY+Vtb3tb+npN36e6urpERLn11ltLV1dX+cY3vlH+9E//tFx88cVl6NChPc6tr68v119/fTn11FPT122OPJ6zA3c8Z4/rpC/A9GG+853vlOuvv77Xr1188cVl7dq15dvf/nb3k8X0n3n22WfLsmXLyoMPPlj27dtXdu7cWVasWFGmTZtWxo4dW0455ZSyYMGC8swzz6Sv1fR9PGcH7njOHpdJX4B5k6muri5f/OIXy/PPP1/Gjh3b6zmNjY3l+eefL7/2a7+Wvl7T92loaCiPPvpomTZtWvexj3zkI+W73/1u6erqKlu2bCl33nln6ejoKHPnzi0RUU455ZT0dZsjj+fswB3P2eM26QswfZhx48aV1atXl/vvv79MmTKl1NTU9Pj6r/7qr5Y9e/aUYcOGpa/V9H3OOOOM8qEPfag0NjYe8rURI0aUz372s+XHP/5x6erqOuQ2sDmxZ9y4caW1tbX8/d//vefsAJo3nrO//uu/fsjXPGePfryBtZ+oqqqKK664IpYuXRrvfve744knnogHH3wwXnrppZgwYUK8973vjQMHDsQHP/jBqK6ujoMHD2YvmT465ZRToqurKyIiqquro6amJrq6uuLAgQMREXHHHXfExIkT4/LLL7e3/cxVV10VS5cujYsuuij+/d//PR566KHYvHmz52w/V1398x/r9saeVVdXR1VVVffz2HP26KQXkTnynHbaaWXIkCHlnHPOKTU1NWXSpEnly1/+ctm6dWvZsmVLee6558rtt9/efTvYa9D9Z4YMGVKGDRtWJk2aVM4888weX6uuri6nn356+cEPflD++I//2N7243n/+99fvv71r5ef/vSn5Yc//KHn7ACe008/vfzwhz/0nK180hdgepk33pH/27/926WlpaX893//d1m/fn1pbW0tf/3Xf13e+973logo559/fqmvr09frzn6vX311VfL2rVry1NPPVWWL19ePvjBD3bf0h88eHCZMmVK+ppN3+fNXnYZP378IeFp+sf09SW1yZMnp6+1v42XaU5gp59+erz44ovx4IMPxje+8Y0455xzYuzYsTFhwoQYPXp0PPXUUzF37tzYu3dv9lKpUG97O2bMmJgwYULU1dXFmjVr4sYbb4ydO3dmL5UKDBkyJP7qr/4qHnvssVi9enW0t7f3+oPSRo8eHe3t7Qkr5Gj1dW/r6+tj69atCSvs/9KLyPQ+n/nMZ8ratWsPuc130UUXldmzZ5eXX365/Mu//Is3SfXD6cvePvzww97c2E/mjbtdn/rUp0pXV1fZu3dvaW9vL1/96lfL1KlTy+jRo8ugQYNKRJSRI0eWlpYWnzHST6aSvT3zzDPLt7/9bXt7dJO+AHOY+fM///OyatWqctppp/X69UsvvbT84Ac/KJdeemn6Wo29NVG+/vWvlyVLlpRRo0aVT3ziE+W5554rXV1d5fnnny+LFy8uU6ZMKXPnzi2vvvpq+lqNvT3BJn0B5jBzySWXlB07dpSbb765jBw58pCvV1dXl3Xr1pVPfepT6Ws19vZkn8GDB5fPf/7zZcGCBT2On3feeWXp0qWlvb297Nmzp3R1dZXbbrutRPj8if4y9vaXMukLMEeYWbNmlfb29rJq1aryoQ99qJx99tmltra2nHbaaWXKlCllz5495e1vf3v6Oo29NVHOOeeccsEFF5SIKDU1NYf8VNdrrrmmdHV1lXPPPTd9rcbenmCTvgDzJvObv/mb5Vvf+lbZt29f2b59e3n44YfL6tWry5YtW8pdd91VIt78R1mbE3Ps7cCdN/atqqqq+71BCxYsKD/5yU/saz8fe3sc/k5/8QtOMHV1dXHFFVfEAw88EPv374+IiLPOOiuuuuqquOyyy+LFF1+MNWvWRGtra+zZs8dPguxH7O3AVF9fH5dddlk88MAD3R9YFxE9PvTqM5/5TGzfvj3uv//+Hh92x4nN3h5/YuQEdeGFF8Ytt9wSZ5xxRvzXf/1XrFy5Mr7zne90f90/UP2XvR2Y/u++btq0KR544IF48skne5wzdOjQ+NnPfpa0Qo6WvT3+xMgJbtiwYXH11VfH7/7u78av/MqvRGtra/zjP/5jfO9738teGsfI3g5M/3dfzzjjjHjyySdj5cqV8eKLL2YvjWNkb48fMXIC+///D3nMmDHxB3/wB/G+970vhg8fHh/5yEfilVdeSVwhR8veDkz2deCyt8df+htXTOXzrne9K30Nxt4a+2rs7Vsx7owAAKmqsxcAAJzcxAgAkEqMAACpxAgAkEqMAACpxAgAkEqMAACpxAgAkEqMAACpxAgAkEqMAACp/hfD9CqCsTZO9wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_output(c)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c48e4a38",
   "metadata": {},
   "source": [
    "## Improve the performance with CVaR\n",
    "\n",
    "Conditional Value-at-Risk (CVaR) is a risk measure that quantifies the potential loss beyond a certain threshold (alpha), considering the tail end of the distribution. As proposed by [Barkoutsos et al. (2020)](https://arxiv.org/abs/1907.04769), incorporating CVaR as an objective function in QAOA allows for addressing risk-averse optimization problems effectively. By optimizing for CVaR, the algorithm focuses on minimizing the expected value of the worst-case scenario, rather than solely optimizing for the mean or expected value, which usually leads to faster convergence to a more accurate result.\n",
    "\n",
    "To showcase the performance of CVaR, a more complicated QUBO problem is used. This QUBO problem is described as a randomly generated symmetric Q matrix. The Q matrix is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "02ec55b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = np.array(\n",
    "    [\n",
    "        [-60.3657, 11.68835, 12.23445, 11.7274, 11.9959, 11.80955],\n",
    "        [11.68835, -59.7527, 11.6231, 13.23295, 11.96335, 12.44725],\n",
    "        [12.23445, 11.6231, -59.69535, 11.29525, 12.00035, 11.78495],\n",
    "        [11.7274, 13.23295, 11.29525, -59.12165, 12.1006, 12.5461],\n",
    "        [11.9959, 11.96335, 12.00035, 12.1006, -60.45515, 12.07545],\n",
    "        [11.80955, 12.44725, 11.78495, 12.5461, 12.07545, -59.9126],\n",
    "    ]\n",
    ")\n",
    "pauli_terms, weights, offset = QUBO_to_Ising(Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76879a55",
   "metadata": {},
   "source": [
    "Then let's define a function to classically brute-force calculate all feasible combinations of stocks and their associated cost. The results are printed below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "46e9cbd9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "-------------------------------------\n",
      "    selection\t  |\t  cost\n",
      "-------------------------------------\n",
      "    110010\t  |\t-109.2784\n",
      "    100011\t  |\t-108.9717\n",
      "    011010\t  |\t-108.7296\n",
      "    111000\t  |\t-108.7219\n",
      "    101100\t  |\t-108.6685\n",
      "    001110\t  |\t-108.4798\n",
      "    001011\t  |\t-108.3416\n",
      "    101001\t  |\t-108.3157\n",
      "     ...\t  |\t  ...\n",
      "-------------------------------------\n"
     ]
    }
   ],
   "source": [
    "def print_Q_cost(Q, wrap=False, reverse=False):\n",
    "    n_stocks = len(Q)\n",
    "    states = []\n",
    "    for i in range(2**n_stocks):\n",
    "        a = f\"{bin(i)[2:]:0>{n_stocks}}\"\n",
    "        n_ones = 0\n",
    "        for j in a:\n",
    "            if j == \"1\":\n",
    "                n_ones += 1\n",
    "        states.append(a)\n",
    "\n",
    "    cost_dict = {}\n",
    "    for selection in states:\n",
    "        x = np.array([int(bit) for bit in selection])\n",
    "        cost_dict[selection] = np.dot(x, np.dot(Q, x))\n",
    "    cost_sorted = dict(sorted(cost_dict.items(), key=lambda item: item[1]))\n",
    "    if reverse == True:\n",
    "        cost_sorted = dict(\n",
    "            sorted(cost_dict.items(), key=lambda item: item[1], reverse=True)\n",
    "        )\n",
    "    num = 0\n",
    "    print(\"\\n-------------------------------------\")\n",
    "    print(\"    selection\\t  |\\t  cost\")\n",
    "    print(\"-------------------------------------\")\n",
    "    for k, v in cost_sorted.items():\n",
    "        print(\"%10s\\t  |\\t%.4f\" % (k, v))\n",
    "        num += 1\n",
    "        if (num >= 8) & (wrap == True):\n",
    "            break\n",
    "    print(\"     ...\\t  |\\t  ...\")\n",
    "    print(\"-------------------------------------\")\n",
    "\n",
    "\n",
    "print_Q_cost(Q, wrap=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04d4ea38",
   "metadata": {},
   "source": [
    "The QAOA with CVaR and three different alpha (1, 0.25, 0.1) will be run and a callback function will be used to record the parameters during the solving procedure. When alpha is $1$, the complete measurement results are accepted and the model changes to the standard QAOA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "d3b386d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the number of layers to 2\n",
    "nlayers = 2\n",
    "\n",
    "# Define a list of alpha values\n",
    "alpha_list = [0.1, 0.25, 1]\n",
    "\n",
    "\n",
    "# Define the callback function to record parameter values\n",
    "def record_param(xk):\n",
    "    xk_list.append(xk)\n",
    "\n",
    "\n",
    "# Generate initial parameters randomly for all alpha\n",
    "init_params = K.implicit_randn(shape=[2 * nlayers], stddev=0.5)\n",
    "\n",
    "# Create an empty list to store parameter values for each alpha\n",
    "params_list = []\n",
    "\n",
    "# Iterate over each alpha value\n",
    "for alpha in alpha_list:\n",
    "    # Create a new empty list for callback function\n",
    "    xk_list = []\n",
    "\n",
    "    # Run the QUBO_QAOA_cvar function with the specified parameters\n",
    "    final_params = QUBO_QAOA_cvar(\n",
    "        Q,\n",
    "        nlayers,\n",
    "        alpha=alpha,\n",
    "        callback=record_param,\n",
    "        maxiter=100,\n",
    "        init_params=init_params,\n",
    "    )\n",
    "\n",
    "    # Append the parameter values for the current alpha to the params_list\n",
    "    params_list.append(xk_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "b3da7c48",
   "metadata": {},
   "outputs": [],
   "source": [
    "best = 50  # Represents the binary number 110010\n",
    "prob_list = []  # Create an empty list to store probabilities\n",
    "loss_list = []  # Create an empty list to store loss values\n",
    "\n",
    "# Iterate three times\n",
    "for i in range(3):\n",
    "    c = QAOA_ansatz_for_Ising(init_params, nlayers, pauli_terms, weights)\n",
    "    loss = [cvar_loss(nlayers, Q, 1000, alpha_list[i], True, init_params)]\n",
    "    prob = [c.probability()[best].numpy()]\n",
    "\n",
    "    # Iterate 100 times\n",
    "    for j in range(100):\n",
    "        if j < len(params_list[i]) - 1:\n",
    "            params = params_list[i][j]\n",
    "        else:\n",
    "            pass\n",
    "        c = QAOA_ansatz_for_Ising(params, nlayers, pauli_terms, weights)\n",
    "        loss.append(cvar_loss(nlayers, Q, 1000, alpha_list[i], True, params))\n",
    "        prob.append(c.probability()[best].numpy())\n",
    "\n",
    "    loss_list.append(loss)  # Append the loss values to the loss_list\n",
    "    prob_list.append(prob)  # Append the probability values to the prob_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "d1f375ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for loss in loss_list:\n",
    "    plt.plot(loss)\n",
    "plt.legend([\"alpha = 0.1\", \"alpha = 0.25\", \"alpha = 1\"])\n",
    "plt.xlabel(\"iterations\")\n",
    "p = plt.ylabel(\"cost\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a88dda3",
   "metadata": {},
   "source": [
    "The depicted figure illustrates that utilizing CVaR results in quicker convergence towards a lower loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "f81fdeae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for prob in prob_list:\n",
    "    plt.plot(prob)\n",
    "plt.legend([\"alpha = 0.1\", \"alpha = 0.25\", \"alpha = 1\"])\n",
    "plt.xlabel(\"iterations\")\n",
    "p = plt.ylabel(\"probability of the best answer\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ae45348",
   "metadata": {},
   "source": [
    "The data presented in this figure indicates that QAOA with CVaR typically shows a higher probability of obtaining the correct measurement outcome."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tc_dev",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}