{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Well-Studied Task Execution Quality Metrics\n",
    "\n",
    "This tutorial covers benchmarks for algorithm-specific and task-specific metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qcmet import QFT\n",
    "from qcmet.devices import IdealSimulator, NoisySimulator, AerSimulator\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The well-studied task execution quality metrics consist of:\n",
    "\n",
    "- Variational quantum eigensolver (VQE)\n",
    "  -  Specific implementation for the 1D Fermi-Hubbard model (VQE1DFermiHubbard)\n",
    "\n",
    "- Hamiltonian simulation\n",
    "  - Specific implementation for the 1D Fermi-Hubbard model (Simulation1DFermiHubbard)\n",
    "\n",
    "- Quantum fourier transform (QFT)\n",
    "\n",
    "- QScore\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Fourier Transform (QFT)\n",
    "\n",
    "The QFT benchmark measures how well a quantum computer can implement the Quantum Fourier Transform algorithm.\n",
    "\n",
    "The QFT is a key subroutine in many quantum algorithms including:\n",
    "- Shor's algorithm for factoring\n",
    "- Quantum phase estimation\n",
    "- Hidden subgroup problem solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generated 1 QFT circuits\n"
     ]
    }
   ],
   "source": [
    "# Setup QFT benchmark\n",
    "qft = QFT(\n",
    "    qubits=4,  # QFT on 4 qubits\n",
    ")\n",
    "\n",
    "# Generate circuits\n",
    "qft.generate_circuits()\n",
    "print(f\"Generated {len(qft.circuits)} QFT circuits\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "QFT circuit structure:\n",
      "        ┌───┐┌───┐                                                       »\n",
      "   q_0: ┤ X ├┤ H ├─■────────■─────────────■──────────────────────────────»\n",
      "        ├───┤└───┘ │P(π/2)  │       ┌───┐ │                              »\n",
      "   q_1: ┤ X ├──────■────────┼───────┤ H ├─┼────────■────────■────────────»\n",
      "        ├───┤               │P(π/4) └───┘ │        │P(π/2)  │       ┌───┐»\n",
      "   q_2: ┤ X ├───────────────■─────────────┼────────■────────┼───────┤ H ├»\n",
      "        └───┘                             │P(π/8)           │P(π/4) └───┘»\n",
      "   q_3: ──────────────────────────────────■─────────────────■────────────»\n",
      "                                                                         »\n",
      "meas: 4/═════════════════════════════════════════════════════════════════»\n",
      "                                                                         »\n",
      "«                          ┌───────┐                                     »\n",
      "«   q_0: ───────────────X──┤ Rz(π) ├─────X───────────────────────────────»\n",
      "«                       │ ┌┴───────┴┐    │                               »\n",
      "«   q_1: ───────────X───┼─┤ Rz(π/2) ├─X──┼──────────────────────■────────»\n",
      "«                   │   │ ├─────────┤ │  │                ┌───┐ │        »\n",
      "«   q_2: ─■─────────X───┼─┤ Rz(π/4) ├─X──┼───────■────────┤ H ├─┼────────»\n",
      "«         │P(π/2) ┌───┐ │ ├─────────┤    │ ┌───┐ │P(-π/2) └───┘ │P(-π/4) »\n",
      "«   q_3: ─■───────┤ H ├─X─┤ Rz(π/8) ├────X─┤ H ├─■──────────────■────────»\n",
      "«                 └───┘   └─────────┘      └───┘                         »\n",
      "«meas: 4/════════════════════════════════════════════════════════════════»\n",
      "«                                                                        »\n",
      "«                                                     ┌───┐ ░ ┌─┐         \n",
      "«   q_0: ───────────■──────────────■─────────■────────┤ H ├─░─┤M├─────────\n",
      "«                   │        ┌───┐ │         │P(-π/2) └───┘ ░ └╥┘┌─┐      \n",
      "«   q_1: ─■─────────┼────────┤ H ├─┼─────────■──────────────░──╫─┤M├──────\n",
      "«         │P(-π/2)  │        └───┘ │P(-π/4)                 ░  ║ └╥┘┌─┐   \n",
      "«   q_2: ─■─────────┼──────────────■────────────────────────░──╫──╫─┤M├───\n",
      "«                   │P(-π/8)                                ░  ║  ║ └╥┘┌─┐\n",
      "«   q_3: ───────────■───────────────────────────────────────░──╫──╫──╫─┤M├\n",
      "«                                                           ░  ║  ║  ║ └╥┘\n",
      "«meas: 4/══════════════════════════════════════════════════════╩══╩══╩══╩═\n",
      "«                                                              0  1  2  3 \n"
     ]
    }
   ],
   "source": [
    "# Look at QFT circuit\n",
    "print(\"QFT circuit structure:\")\n",
    "print(qft.circuits[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "QFT Results:\n",
      "  fidelity: [1.0]\n",
      "  normalized_fidelity: [1.0]\n"
     ]
    }
   ],
   "source": [
    "# Run on device\n",
    "device = AerSimulator()\n",
    "qft.run(device, num_shots=2048)\n",
    "\n",
    "# Analyze\n",
    "results_qft = qft.analyze()\n",
    "print(\"\\nQFT Results:\")\n",
    "for key, value in results_qft.items():\n",
    "    print(f\"  {key}: {value}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing QFT Performance Across Simulators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Testing QFT on Ideal simulator...\n",
      "  Fidelity: [1.0]\n",
      "\n",
      "Testing QFT on Noisy simulator...\n",
      "  Fidelity: [0.9926757812499999]\n"
     ]
    }
   ],
   "source": [
    "# Test QFT on different devices\n",
    "devices = {\n",
    "    'Ideal': IdealSimulator(),\n",
    "    'Noisy': NoisySimulator(),\n",
    "}\n",
    "\n",
    "qft_comparison = {}\n",
    "\n",
    "for device_name, device in devices.items():\n",
    "    print(f\"\\nTesting QFT on {device_name} simulator...\")\n",
    "\n",
    "    qft_test = QFT(qubits=4)\n",
    "    qft_test.generate_circuits()\n",
    "    qft_test.run(device, num_shots=2048)\n",
    "    result = qft_test.analyze()\n",
    "\n",
    "    qft_comparison[device_name] = result\n",
    "    print(f\"  Fidelity: {result.get('fidelity', 'N/A')}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What the Numbers Mean\n",
    "\n",
    "**Fidelity**: Measure of how close the output state from your real QFT circuit is to the ideal QFT output\n",
    "- The higher the fidelity, the better the performance of QFT by the device.\n",
    "\n",
    "**Normalised Fidelity**: Measure of how close the output state from your real QFT circuit is to the ideal QFT output normalized against a fully depolarized output distribution.\n",
    "- The higher the normalised fidelity, the better the performance of QFT by the device.\n",
    "- F will be between 0 and 1. \n",
    "- F = 1 indicates that the output states are identical to the ideal states.\n",
    "- F = 0 indicates that the output states are orthogonal to the ideal states.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other Benchmarks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "QCMet furthermore implements the QScore, VQE (1D Fermi-Hubbard), and Hamiltonian simulation (1D Fermi-Hubbard) as well studied task benchmarks. See the respective implementations for further details."
   ]
  }
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