Notebooks/KineticEnergyEstimationProblem2.ipynb

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    "# Measuring Kinetic Energy of Coupled Classical Harmonic Oscillator Systems using Classiq\n",
    "\n",
    "Authors: Viraj Dsouza, Cristina Radian, Kerem Yurtseven\n",
    "\n",
    "Date: 09.08.2024\n",
    "\n",
    "This work is designed under and for the final project of the Womanium Quantum+AI Program 2024\n",
    "\n",
    "Reference Paper: Exponential Quantum Speedup in Simulating Coupled Classical Oscillators, Babbush et.al, 2023 [1](https://arxiv.org/abs/2303.13012)\n",
    "___"
   ]
  },
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   "metadata": {},
   "source": [
    "## Problem 2\n",
    "\n",
    "In the paper of Babbush et.al [1](https://arxiv.org/abs/2303.13012), authors assert that the quantum algorithm can estimate the kinetic energy of a system with a finite error. The problem is defined as\n",
    ">Let $K$ be the $N \\times N$ symmetric matrix of spring constants $\\kappa_{jk} \\geq 0$ and assume it is $d-sparse$ (i.e., there are at most $d$ non-zero entries in each row). Let $M$ be the $N \\times N$ diagonal matrix of masses $m_j > 0$ and define the normalized state\n",
    "\\begin{equation*}\n",
    "    \\ket{\\psi(t)} := \\frac{1}{\\sqrt{2E}} \\begin{pmatrix} \\sqrt{M} \\dot{\\mathbf{x}}(t) \\\\ \\mathbf{\\mu}(t) \\end{pmatrix}\n",
    "    \\qquad(1)\n",
    "\\end{equation*}\n",
    "where $E > 0$ is a constant, and $\\mathbf{\\mu}(t) \\in \\mathbb{R}^M\\ (M := \\frac{N(N + 1)}{2})$ is a vector with $N$ entries $\\sqrt{\\kappa_{jj}} x_j(t)$ and $\\frac{N(N - 1)}{2}$ entries $\\sqrt{\\kappa_{jk}} (x_j(t) - x_k(t))$, with $k > j$. Assume we are given oracle access to $K$ and $M$, and oracle access to a unitary $W$ that prepares the initial state, i.e., $W \\ket{0} \\mapsto \\ket{\\psi(0)}$. Given $t \\geq 0$ and $\\epsilon > 0$.\n",
    "\n",
    ">Assume we have an oracle for $V \\subseteq [N]$, which is a subset of the oscillators. The oracle outputs an estimate $\\hat{k}_V(t) \\in \\mathbb{R}$ such that\n",
    "\\begin{equation*}\n",
    "|\\hat{k}_V(t) - \\frac{K_V(t)}{E}| \\leq \\epsilon\n",
    "\\qquad(2)\n",
    "\\end{equation*}\n",
    "where $K_V(t) := \\frac{1}{2} \\sum_{j \\in V} m_j \\dot{x}_j(t)$ is the kinetic energy of $V$ at time $t$.\n",
    "\n",
    "___\n"
   ]
  },
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Our Configuration\n",
    "\n",
    "![System_Config.png](attachment:System_Config.png)\n",
    "\n",
    "We use $N = 2^3$ masses and evolve it for a certain time. All masses are equal to 1, i.e $m_i = 1$. Also, the spring between each adjacent mass is 1 and initial and final masses are connected to the wall with a spring constant equal to 1. Initial states are chosen as $\\vec{x}(t) = (0,0,0,0.....0)^T$ and $\\vec{\\dot{x}}(t) = (1,0,0,0.....0)^T$\n",
    "\n",
    "In the post-processing, we get the final velocity vector and evalueate $\\hat{k_V}(t)$ as\n",
    "\\begin{equation*}\n",
    "    \\hat{k_V}(t) = \\frac{v(t)^T v(t)}{2}\n",
    "    \\qquad(3)\n",
    "\\end{equation*}\n",
    "\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pre-Processing\n",
    "\n",
    "Create necessary matrix and initial states using functions created in `ccho_helpers.py`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Import Libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "from ccho_helpers import *\n",
    "from classiq import (\n",
    "    qfunc,\n",
    "    QNum,\n",
    "    QArray,\n",
    "    QBit,\n",
    "    allocate,\n",
    "    bind,\n",
    "    repeat,\n",
    "    CX,\n",
    "    control,\n",
    "    PHASE,\n",
    "    Output,\n",
    "    prepare_amplitudes,\n",
    "    create_model,\n",
    "    set_execution_preferences,\n",
    "    synthesize,\n",
    "    execute,\n",
    "    suzuki_trotter\n",
    ") \n",
    "from classiq.execution import ExecutionPreferences, ClassiqBackendPreferences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### We take N=8 for the purpose of demonstration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial Energy:  0.5\n",
      "B matrix:  [[ 1.+0.j  1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
      " [ 0.+0.j -1.+0.j  0.+0.j  1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
      " [ 0.+0.j  0.+0.j  0.+0.j -1.+0.j  0.+0.j  1.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
      " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j -1.+0.j  0.+0.j  1.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
      " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j -1.+0.j  0.+0.j\n",
      "   1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
      " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "  -1.+0.j  0.+0.j  1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
      " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j -1.+0.j  0.+0.j  1.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
      " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j -1.+0.j  1.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j\n",
      "   0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]]\n",
      "Hamiltonian formed: [[-0.-0.j -0.-0.j -0.-0.j ... -0.-0.j -0.-0.j -0.-0.j]\n",
      " [-0.-0.j -0.-0.j -0.-0.j ... -0.-0.j -0.-0.j -0.-0.j]\n",
      " [-0.-0.j -0.-0.j -0.-0.j ... -0.-0.j -0.-0.j -0.-0.j]\n",
      " ...\n",
      " [-0.+0.j -0.+0.j -0.+0.j ... -0.-0.j -0.-0.j -0.-0.j]\n",
      " [-0.+0.j -0.+0.j -0.+0.j ... -0.-0.j -0.-0.j -0.-0.j]\n",
      " [-0.+0.j -0.+0.j -0.+0.j ... -0.-0.j -0.-0.j -0.-0.j]]\n",
      "Initial State: [[1.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
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      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]]\n"
     ]
    }
   ],
   "source": [
    "## Providing all inputs for 8 coupled SHO case and performing all the initial transformations\n",
    "\n",
    "# Number of masses\n",
    "N=2**3\n",
    "\n",
    "# Mass Matrix\n",
    "M= np.zeros([N, N])\n",
    "for i in range(N):\n",
    "    M[i][i] = 1\n",
    "\n",
    "K = np.zeros([N,N])\n",
    "for j in range(N):\n",
    "    for t in range(j, N):\n",
    "        if j == 0 or j == N-1:\n",
    "            K[j][j] = 1\n",
    "        if abs(j-t) == 1:\n",
    "            K[j][t] = 1\n",
    "            K[t][j] = 1\n",
    "\n",
    "# Initial Conditions\n",
    "x_0 = np.zeros([N,1])\n",
    "xdot_0 = np.zeros([N,1])\n",
    "xdot_0[0] = 1\n",
    "\n",
    "# F Matrix\n",
    "F= create_matrix_F(K, N)\n",
    "\n",
    "# A Matrix\n",
    "A = create_matrix_A(M, F)\n",
    "\n",
    "# Transform coordinates\n",
    "y = coordinate_transformation(M, x_0, xdot_0)\n",
    "y_0 = y[\"y_0\"]\n",
    "ydot_0 = y[\"ydot_0\"]\n",
    "\n",
    "# B Matrix\n",
    "B = create_matrix_B(M, K, A, N)\n",
    "\n",
    "# Stacking B with zeros to get square matrix N^2 x N^2\n",
    "B_padded = padding_B(B, N)\n",
    "\n",
    "# Hamiltonian\n",
    "H = create_Hamiltonian(B_padded)\n",
    "\n",
    "# Initial State\n",
    "init_state = create_init_state(B_padded, y_0, ydot_0, N)\n",
    "E0_y = calculate_energy(y_0, ydot_0, M, K)\n",
    "\n",
    "# Normalize the Initial State\n",
    "normalization = normalize_init_state(init_state)\n",
    "normalized_init_state = normalization[\"normalized_init_state\"]\n",
    "norm = normalization[\"norm\"]\n",
    "\n",
    "# Print the results\n",
    "print(\"Initial Energy: \", E0_y)\n",
    "print(\"B matrix: \", B)\n",
    "print(\"Hamiltonian formed:\", H)\n",
    "print(\"Initial State:\", init_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pauli Matrix Decomposition\n",
    "\n",
    "Create the Pauli List for the Hamiltonian. Pauli Decomposition is taken from [Classiq Library](https://github.com/Classiq/classiq-library/blob/main/algorithms/hhl/hhl/hhl.ipynb) thanks a lot to the authors!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 16384/16384 [00:13<00:00, 1258.60it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('XIIIIIZ', (-0.03125+0j)), ('XIIIIZZ', (-0.03125+0j)), ('XIIIIZX', (-0.03125+0j)), ('XIIIIXI', (-0.015625+0j)), ('XIIIIXZ', (0.015625+0j)), ('XIIIIXX', (0.015625+0j)), ('XIIIIYY', (-0.015625+0j)), ('XIIIZIZ', (-0.03125+0j)), ('XIIIZZZ', (-0.03125+0j)), ('XIIIZZX', (-0.03125+0j)), ('XIIIZXI', (-0.015625+0j)), ('XIIIZXZ', (0.015625+0j)), ('XIIIZXX', (-0.015625+0j)), ('XIIIZYY', (0.015625+0j)), ('XIIIXII', (-0.015625+0j)), ('XIIIXIZ', (0.015625+0j)), ('XIIIXZI', (0.015625+0j)), ('XIIIXZZ', (-0.015625+0j)), ('XIIIXXI', (0.015625+0j)), ('XIIIXXZ', (-0.015625+0j)), ('XIIIXXX', (-0.015625+0j)), ('XIIIXYY', (-0.015625+0j)), ('XIIIYXY', (0.015625+0j)), ('XIIIYYI', (0.015625+0j)), ('XIIIYYZ', (-0.015625+0j)), ('XIIIYYX', (-0.015625+0j)), ('XIIZIIZ', (-0.03125+0j)), ('XIIZIZZ', (-0.03125+0j)), ('XIIZIZX', (-0.03125+0j)), ('XIIZIXI', (-0.015625+0j)), ('XIIZIXZ', (0.015625+0j)), ('XIIZIXX', (0.015625+0j)), ('XIIZIYY', (-0.015625+0j)), ('XIIZZIZ', (-0.03125+0j)), ('XIIZZZZ', (-0.03125+0j)), 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('XIIXXXZ', (0.015625+0j)), ('XIIXYZY', (-0.03125+0j)), ('XIIXYYI', (-0.015625+0j)), ('XIIXYYZ', (0.015625+0j)), ('XIIYIIY', (-0.015625+0j)), ('XIIYIZY', (0.015625+0j)), ('XIIYIXY', (0.015625+0j)), ('XIIYIYI', (0.015625+0j)), ('XIIYIYZ', (-0.015625+0j)), ('XIIYIYX', (-0.015625+0j)), ('XIIYZIY', (0.015625+0j)), ('XIIYZZY', (-0.015625+0j)), ('XIIYZXY', (-0.015625+0j)), ('XIIYZYI', (-0.015625+0j)), ('XIIYZYZ', (0.015625+0j)), ('XIIYZYX', (0.015625+0j)), ('XIIYXZY', (0.03125+0j)), ('XIIYXYI', (0.015625+0j)), ('XIIYXYZ', (-0.015625+0j)), ('XIIYYII', (0.015625+0j)), ('XIIYYIZ', (-0.015625+0j)), ('XIIYYZI', (0.015625+0j)), ('XIIYYZZ', (-0.015625+0j)), ('XIIYYZX', (-0.03125+0j)), ('XIIYYXI', (-0.015625+0j)), ('XIIYYXZ', (0.015625+0j)), ('XIZIIIZ', (-0.03125+0j)), ('XIZIIZZ', (-0.03125+0j)), ('XIZIIZX', (-0.03125+0j)), ('XIZIIXI', (-0.015625+0j)), ('XIZIIXZ', (0.015625+0j)), ('XIZIIXX', (0.015625+0j)), ('XIZIIYY', (-0.015625+0j)), ('XIZIZIZ', (-0.03125+0j)), ('XIZIZZZ', (-0.03125+0j)), ('XIZIZZX', (-0.03125+0j)), ('XIZIZXI', (-0.015625+0j)), ('XIZIZXZ', (0.015625+0j)), ('XIZIZXX', (-0.015625+0j)), ('XIZIZYY', (0.015625+0j)), ('XIZIXII', (-0.015625+0j)), ('XIZIXIZ', (0.015625+0j)), ('XIZIXZI', (0.015625+0j)), ('XIZIXZZ', (-0.015625+0j)), ('XIZIXXI', (0.015625+0j)), ('XIZIXXZ', (-0.015625+0j)), ('XIZIXXX', (-0.015625+0j)), ('XIZIXYY', (-0.015625+0j)), ('XIZIYXY', (0.015625+0j)), ('XIZIYYI', (0.015625+0j)), ('XIZIYYZ', (-0.015625+0j)), ('XIZIYYX', (-0.015625+0j)), ('XIZZIIZ', (-0.03125+0j)), ('XIZZIZZ', (-0.03125+0j)), ('XIZZIZX', (-0.03125+0j)), ('XIZZIXI', (-0.015625+0j)), ('XIZZIXZ', (0.015625+0j)), ('XIZZIXX', (0.015625+0j)), ('XIZZIYY', (-0.015625+0j)), ('XIZZZIZ', (-0.03125+0j)), ('XIZZZZZ', (-0.03125+0j)), ('XIZZZZX', (-0.03125+0j)), ('XIZZZXI', (-0.015625+0j)), ('XIZZZXZ', (0.015625+0j)), ('XIZZZXX', (-0.015625+0j)), ('XIZZZYY', (0.015625+0j)), ('XIZZXII', (-0.015625+0j)), ('XIZZXIZ', (0.015625+0j)), ('XIZZXZI', (0.015625+0j)), ('XIZZXZZ', (-0.015625+0j)), ('XIZZXXI', (0.015625+0j)), ('XIZZXXZ', (-0.015625+0j)), ('XIZZXXX', (-0.015625+0j)), ('XIZZXYY', (-0.015625+0j)), ('XIZZYXY', (0.015625+0j)), ('XIZZYYI', (0.015625+0j)), ('XIZZYYZ', (-0.015625+0j)), ('XIZZYYX', (-0.015625+0j)), ('XIZXIIX', (-0.015625+0j)), ('XIZXIZX', (0.015625+0j)), ('XIZXIXI', (0.015625+0j)), ('XIZXIXZ', (-0.015625+0j)), ('XIZXIXX', (-0.015625+0j)), ('XIZXIYY', (-0.015625+0j)), ('XIZXZIX', (0.015625+0j)), ('XIZXZZX', (-0.015625+0j)), ('XIZXZXI', (-0.015625+0j)), ('XIZXZXZ', (0.015625+0j)), ('XIZXZXX', (0.015625+0j)), ('XIZXZYY', (0.015625+0j)), ('XIZXXII', (0.015625+0j)), ('XIZXXIZ', (-0.015625+0j)), ('XIZXXZI', (0.015625+0j)), ('XIZXXZZ', (-0.015625+0j)), ('XIZXXZX', (-0.03125+0j)), ('XIZXXXI', (-0.015625+0j)), ('XIZXXXZ', (0.015625+0j)), ('XIZXYZY', (-0.03125+0j)), ('XIZXYYI', (-0.015625+0j)), ('XIZXYYZ', (0.015625+0j)), ('XIZYIIY', (-0.015625+0j)), ('XIZYIZY', (0.015625+0j)), ('XIZYIXY', (0.015625+0j)), ('XIZYIYI', (0.015625+0j)), ('XIZYIYZ', (-0.015625+0j)), 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('YZZXZXY', (-0.015625+0j)), ('YZZXZYI', (-0.015625+0j)), ('YZZXZYZ', (0.015625+0j)), ('YZZXZYX', (0.015625+0j)), ('YZZXXZY', (0.03125+0j)), ('YZZXXYI', (0.015625+0j)), ('YZZXXYZ', (-0.015625+0j)), ('YZZXYII', (0.015625+0j)), ('YZZXYIZ', (-0.015625+0j)), ('YZZXYZI', (0.015625+0j)), ('YZZXYZZ', (-0.015625+0j)), ('YZZXYZX', (-0.03125+0j)), ('YZZXYXI', (-0.015625+0j)), ('YZZXYXZ', (0.015625+0j)), ('YZZYIIX', (0.015625+0j)), ('YZZYIZX', (-0.015625+0j)), ('YZZYIXI', (-0.015625+0j)), ('YZZYIXZ', (0.015625+0j)), ('YZZYIXX', (0.015625+0j)), ('YZZYIYY', (0.015625+0j)), ('YZZYZIX', (-0.015625+0j)), ('YZZYZZX', (0.015625+0j)), ('YZZYZXI', (0.015625+0j)), ('YZZYZXZ', (-0.015625+0j)), ('YZZYZXX', (-0.015625+0j)), ('YZZYZYY', (-0.015625+0j)), ('YZZYXII', (-0.015625+0j)), ('YZZYXIZ', (0.015625+0j)), ('YZZYXZI', (-0.015625+0j)), ('YZZYXZZ', (0.015625+0j)), ('YZZYXZX', (0.03125+0j)), ('YZZYXXI', (0.015625+0j)), ('YZZYXXZ', (-0.015625+0j)), ('YZZYYZY', (0.03125+0j)), ('YZZYYYI', (0.015625+0j)), ('YZZYYYZ', (-0.015625+0j))]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "## Pauli Decomposition and transforming it into Classiq syntax\n",
    "\n",
    "# Create the Pauli Matrix Decomposition of the Hamiltonian\n",
    "pauli_list = lcu_naive(H)\n",
    "\n",
    "# Transform Pauli Matrix Decomposition to Classiq compatible\n",
    "classiq_pauli_list = pauli_list_to_hamiltonian(pauli_list)\n",
    "\n",
    "print(pauli_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hamiltonian simulation\n",
    "\n",
    "We use the `suzuki_trotter` function of classiq that produces a quantum gate that approximates $e^{iHt}$, for any input **Hermitian operator** $H$. Since the Hamiltonian for this algorithm is Hermitian by definition, exponentiation methods can be used straightforwardly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the `suzuki_trotter` for each iteration for a time interval. Here, we choose our time interval as $[0,20]$ take $40$ samples with $0.5$ interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 40/40 [1:09:17<00:00, 103.94s/it]\n"
     ]
    }
   ],
   "source": [
    "## Create qfuncs and iterate the loop\n",
    "\n",
    "# Time List\n",
    "t_list = np.linspace(0,20,40)\n",
    "# Kinetic Energy at each time\n",
    "kinetic_en = []\n",
    "\n",
    "for t in tqdm.tqdm(t_list):\n",
    "\n",
    "    # Add i phase for the last half\n",
    "    @qfunc\n",
    "    def init_state_phase(state: QNum):\n",
    "        \"\"\"\n",
    "            Definition:\n",
    "                Imply -pi/2 phase to the last half (msb qubit) of the QNum state in order to add -i factor\n",
    "            Args:\n",
    "                state (QNum): Initial state with bare amplitudes\n",
    "            Outputs:\n",
    "                state (QNum): Initial state with phase\n",
    "        \"\"\"\n",
    "\n",
    "        state_in_qubit = QArray(\"state_in_qubit\")\n",
    "        msb = QArray(\"msb\", QBit)\n",
    "        \n",
    "        size = np.log2(init_state.size)\n",
    "        allocate(size, msb)\n",
    "\n",
    "        bind(state, state_in_qubit)\n",
    "        repeat(state_in_qubit.len, lambda i: CX(state_in_qubit[i], msb[i]))\n",
    "        control(msb[size-1], lambda: PHASE(np.pi/2, state_in_qubit[size-1]))\n",
    "        bind(state_in_qubit, state)\n",
    "\n",
    "    # Main function with suzuki_trotter\n",
    "    @qfunc\n",
    "    def main(state: Output[QNum]):\n",
    "        \"\"\"\n",
    "            Definition:\n",
    "                Main function to make evolution\n",
    "\n",
    "            Outputs:\n",
    "                state (Output[QNum]): Resulting state at the t = evolution_coefficient\n",
    "        \"\"\"\n",
    "            \n",
    "        prepare_amplitudes(amplitudes=list(normalized_init_state), out=state, bound=0.00000000000001)\n",
    "        init_state_phase(state)\n",
    "\n",
    "        suzuki_trotter(\n",
    "            classiq_pauli_list,\n",
    "            evolution_coefficient=t,\n",
    "            order=2,\n",
    "            repetitions=10,\n",
    "            qbv=state,\n",
    "        )\n",
    "\n",
    "    # Create model and synthesis. Use \"simulator_statevector\" to take phases into account\n",
    "    qmod = create_model(main)\n",
    "    backend_preferences = ClassiqBackendPreferences(backend_name=\"simulator_statevector\")\n",
    "    model_pref = set_execution_preferences(qmod, ExecutionPreferences(num_shots=1000, backend_preferences=backend_preferences))\n",
    "    qprog = synthesize(model_pref)\n",
    "\n",
    "    # Execute the job\n",
    "    job = execute(qprog)\n",
    "    parsed_state_vector = job.result()[0].value.parsed_state_vector\n",
    "\n",
    "    # Combine the final results\n",
    "    state_amplitudes = sum_amplitudes_by_state(parsed_state_vector, N)\n",
    "\n",
    "    # Normalize the global phase\n",
    "    normalized_final_state = normalize_final_state(state_amplitudes, parsed_state_vector)\n",
    "\n",
    "    # Eliminate small numbers\n",
    "    simplified_final_state = simplify_final_state(normalized_final_state)\n",
    "\n",
    "    # Renormalize the final state using the norm of initial state\n",
    "    final_state = norm * simplified_final_state[..., None]\n",
    "\n",
    "    # Take velocities\n",
    "    xdot_final = final_state[:N]\n",
    "\n",
    "    ke = np.matmul(xdot_final.T, xdot_final) / 2\n",
    "    \n",
    "    kinetic_en.append(ke[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\Kerem\\anaconda3\\Lib\\site-packages\\matplotlib\\collections.py:192: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  offsets = np.asanyarray(offsets, float)\n",
      "c:\\Users\\Kerem\\anaconda3\\Lib\\site-packages\\matplotlib\\cbook\\__init__.py:1340: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Kinetic Energy')"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot the Results - Create a Cubic Spline Interpolation to fit the data\n",
    "spl = scipy.interpolate.CubicSpline(t_list, kinetic_en)\n",
    "t_new = np.linspace(0,20,1000)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.suptitle(r\"Kinetic Energy vs Time - Quantum\")\n",
    "ax.scatter(t_list, kinetic_en, label=r\"Kinetic Energy Data\")\n",
    "ax.plot(t_new, spl(t_new), label=r\"Kinetic Energy Fit Line\")\n",
    "ax.legend()\n",
    "ax.set_xlabel('Time')\n",
    "ax.set_ylabel('Kinetic Energy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classical Results Comparision\n",
    "Compute classical results numerically and compare it with the quantum results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def equations_of_motion(t, init, N, M, K):\n",
    "    \"\"\"\n",
    "    Definition:\n",
    "        EOM for classical coupled oscillator system with N masses\n",
    "    Args:\n",
    "        t (array): Time array\n",
    "        init (list): Initial Conditions\n",
    "        N (int): Number of masses\n",
    "        M (array): Mass matrix (diagonal)\n",
    "        K (array): Spring constant matrix\n",
    "    Output:\n",
    "        (list): List of final equations\n",
    "    \"\"\"\n",
    "\n",
    "    x = init[:N]\n",
    "    v = init[N:]\n",
    "    dxdt = v\n",
    "    dvdt = np.zeros(N)\n",
    "    \n",
    "    for i in range(N):\n",
    "        if i == 0:\n",
    "            dvdt[i] = (-K[i, i] * x[i] + K[i, i+1] * (x[i+1] - x[i])) / M[i, i]\n",
    "        elif i == N-1:\n",
    "            dvdt[i] = (-K[i, i] * x[i] + K[i, i-1] * (x[i-1] - x[i])) / M[i, i]\n",
    "        else:\n",
    "            dvdt[i] = (-K[i, i] * x[i] + K[i, i-1] * (x[i-1] - x[i]) + K[i, i+1] * (x[i+1] - x[i])) / M[i, i]\n",
    "\n",
    "    return np.concatenate((dxdt, dvdt))\n",
    "\n",
    "# Initial conditions: [x1(0), x2(0), ..., xN(0), v1(0), v2(0), ..., vN(0)]\n",
    "initial_conditions = np.concatenate((x_0, xdot_0))\n",
    "\n",
    "# Time span for the simulation\n",
    "t_span = (0, 20)\n",
    "t_eval = np.linspace(t_span[0], t_span[1], 1000)\n",
    "\n",
    "# Solve the system of differential equations\n",
    "solution = scipy.integrate.solve_ivp(equations_of_motion, t_span, initial_conditions.flatten(), t_eval=t_eval, args=(N, M, K))\n",
    "\n",
    "# Extract the results\n",
    "t = solution.t\n",
    "x = solution.y[:N, :]\n",
    "v = solution.y[N:, :]\n",
    "\n",
    "kinetic_classic = []\n",
    "for vt in v.T:\n",
    "    e = 0\n",
    "    for vi in vt:\n",
    "        e += vi**2/2\n",
    "    kinetic_classic.append(e)\n",
    "\n",
    "# Plot position of mass 1\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(t, kinetic_classic, \"r\", label='Kinetic Energy of the System')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Kinetic Energy')\n",
    "plt.title('Kinetic Energy vs Time - Classical')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Kinetic Energy')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot classical and quantum graphs together\n",
    "fig, ax = plt.subplots()\n",
    "fig.suptitle(r\"Kinetic Energy vs Time\")\n",
    "ax.plot(t_new, spl(t_new), \"b\", label=r\"Kinetic Energy Quantum\")\n",
    "ax.plot(t, kinetic_classic, \"r\", label=r'Kinetic Energy Classical')\n",
    "ax.legend()\n",
    "ax.set_xlabel('Time')\n",
    "ax.set_ylabel('Kinetic Energy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Kinetic Energy')"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Difference between classical and quantum solutions\n",
    "classic_sample = [kinetic_classic[i*25] for i in range(40)]\n",
    "error = [(kinetic_en[i] - classic_sample[i]) for i in range(40)]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.suptitle(r\"Error in Quantum Algortihm\")\n",
    "ax.plot(t_list, error, \"g-o\", label=r\"Error\")\n",
    "ax.legend()\n",
    "ax.set_xlabel('Time')\n",
    "ax.set_ylabel('Kinetic Energy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion and Results\n",
    "\n",
    "Results show that quantum algorithm is quite good in estimating the kinetic energy of the system and simulation of **Problem 2** is simulated accurately. It can be said that for the given parameters and configuration, kinetic energy is estimated as:\n",
    "\\begin{equation*}\n",
    "|\\hat{k}_V(t) - K_V(t)| \\leq \\epsilon\n",
    "\\qquad(4)\n",
    "\\end{equation*}\n",
    "where $\\epsilon$ is $0.025$ for $t \\in [0,10]$ and $0.1$ for $t \\in [10,20]$\n",
    "\n",
    "\n",
    "Also, it is noteworthy to say that `suzuki_trotter` parameters \"order\" and \"repetition\" is important in the accuracy and to simulate for higher times with high accuracy, these parameters should be chosen higher. By doing a trade-off between simulation times and accuracy, $\\epsilon$ can be further improved. More importantly, the effect of Quantum Advantage and Quantum Speedup can be observed with higher masses or more complex cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "____"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
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 },
 "nbformat": 4,
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}