{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Minimum eigenvalue estimation of a spin (qubit) Hamiltonian\n",
    "\n",
    "In this tutorial we implement a [Qiskit pattern](https://docs.quantum.ibm.com/guides/intro-to-patterns) showing how to post-process quantum samples to approximate the minimum eigenvalue and spin-spin correlators for a ``22``-site XX-Z spin-1/2 chain. We will follow a sample-based quantum diagonalization approach [[1]](https://arxiv.org/abs/2405.05068).\n",
    "\n",
    "While a Qiskit pattern typically involves 4 steps, the aim of this tutorial is to focus on the post-processing of the samples obtained from a quantum circuit whose support coincides with that of the eigenstate corresponding to the minimum eigenvalue. Consequently, we generate a synthetic set of bitstrings to define the subspace and do not design an ansatz nor sample from a quantum circuit in this tutorial.\n",
    "\n",
    "The pattern we will implement is as follows:\n",
    "\n",
    "1. **Step 1: Map to quantum problem**\n",
    "    - Specify a Hamiltonian as a Pauli operator\n",
    "2. **Step 2: Optimize the problem**\n",
    "    - N/A\n",
    "3. **Step 3: Execute experiments**\n",
    "    - N/A: Will generate synthetic quantum samples\n",
    "4. **Step 4: Post-process results**\n",
    "   - Project the Hamiltonian onto the subspace spanned by the samples\n",
    "   - Diagonalize the Hamiltonian in the subspace to approximate the minimum eigenstate\n",
    "   - Calculate spin-spin correlators for each site, $l$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: Map to quantum problem\n",
    "\n",
    "The Hamiltonian of interest can be written as:\n",
    "\n",
    "$$\n",
    "H = \\sum_i \\alpha_i P_i,\n",
    "$$\n",
    "\n",
    "with $\\alpha_i$ being real coefficients and $P_i$ Pauli strings. A wide class\n",
    "of many-body Hamiltonians can be written as the linear combination of polynomially-many \n",
    "Pauli strings, including interacting-electron Hamiltonians, spin Hamiltonians, etc.\n",
    "\n",
    "In particular, we consider the properties of the antiferromagnetic XX-Z spin-1/2 chain\n",
    "with $L = 22$ sites:\n",
    "$$\n",
    "H = \\sum_{\\langle i, j \\rangle} J_{xy}\\left( \\sigma^x_i\\sigma^x_j + \\sigma^y_i\\sigma^y_j \\right) + \\sigma^z_i\\sigma^z_j.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIXX', 'IIIIIIIIIIIIIIIIIIIIYY', 'IIIIIIIIIIIIIIIIIIIIZZ', 'IIIIIIIIIIIIIIIIIIXXII', 'IIIIIIIIIIIIIIIIIIYYII', 'IIIIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIXXIIII', 'IIIIIIIIIIIIIIIIYYIIII', 'IIIIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIXXIIIIII', 'IIIIIIIIIIIIIIYYIIIIII', 'IIIIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIXXIIIIIIII', 'IIIIIIIIIIIIYYIIIIIIII', 'IIIIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIXXIIIIIIIIII', 'IIIIIIIIIIYYIIIIIIIIII', 'IIIIIIIIIIZZIIIIIIIIII', 'IIIIIIIIXXIIIIIIIIIIII', 'IIIIIIIIYYIIIIIIIIIIII', 'IIIIIIIIZZIIIIIIIIIIII', 'IIIIIIXXIIIIIIIIIIIIII', 'IIIIIIYYIIIIIIIIIIIIII', 'IIIIIIZZIIIIIIIIIIIIII', 'IIIIXXIIIIIIIIIIIIIIII', 'IIIIYYIIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIIIII', 'IIXXIIIIIIIIIIIIIIIIII', 'IIYYIIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIIIII', 'XXIIIIIIIIIIIIIIIIIIII', 'YYIIIIIIIIIIIIIIIIIIII', 'ZZIIIIIIIIIIIIIIIIIIII', 'XIIIIIIIIIIIIIIIIIIIIX', 'YIIIIIIIIIIIIIIIIIIIIY', 'ZIIIIIIIIIIIIIIIIIIIIZ', 'IIIIIIIIIIIIIIIIIIIXXI', 'IIIIIIIIIIIIIIIIIIIYYI', 'IIIIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIXXIII', 'IIIIIIIIIIIIIIIIIYYIII', 'IIIIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIXXIIIII', 'IIIIIIIIIIIIIIIYYIIIII', 'IIIIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIXXIIIIIII', 'IIIIIIIIIIIIIYYIIIIIII', 'IIIIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIXXIIIIIIIII', 'IIIIIIIIIIIYYIIIIIIIII', 'IIIIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIXXIIIIIIIIIII', 'IIIIIIIIIYYIIIIIIIIIII', 'IIIIIIIIIZZIIIIIIIIIII', 'IIIIIIIXXIIIIIIIIIIIII', 'IIIIIIIYYIIIIIIIIIIIII', 'IIIIIIIZZIIIIIIIIIIIII', 'IIIIIXXIIIIIIIIIIIIIII', 'IIIIIYYIIIIIIIIIIIIIII', 'IIIIIZZIIIIIIIIIIIIIII', 'IIIXXIIIIIIIIIIIIIIIII', 'IIIYYIIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIIIII', 'IXXIIIIIIIIIIIIIIIIIII', 'IYYIIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIIIII'],\n",
      "              coeffs=[0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j,\n",
      " 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j,\n",
      " 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j,\n",
      " 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j,\n",
      " 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j,\n",
      " 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j,\n",
      " 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j,\n",
      " 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j, 0.3+0.j, 1. +0.j, 0.3+0.j,\n",
      " 0.3+0.j, 1. +0.j])\n"
     ]
    }
   ],
   "source": [
    "from qiskit.transpiler import CouplingMap\n",
    "from qiskit_addon_utils.problem_generators import generate_xyz_hamiltonian\n",
    "\n",
    "num_spins = 22\n",
    "coupling_map = CouplingMap.from_ring(num_spins)\n",
    "hamiltonian = generate_xyz_hamiltonian(coupling_map, coupling_constants=(0.3, 0.3, 1.0))\n",
    "print(hamiltonian)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: Optimize problem (N/A)\n",
    "\n",
    "This tutorial is focused on post-processing samples taken from a QPU. Discussion on generating an ansatz and optimizing it for QPU execution is out of scope."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: Execute experiments\n",
    "\n",
    "This tutorial is focused on post-processing samples taken from a QPU. Discussion on running a specific state-preparation ansatz for a given Hamiltonian is out of scope. Since we don't have a specific circuit for which to evaluate the Hamiltonian, we will generate a set of synthetic samples which cover all possible pairs of domain walls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "bitstring_matrix = np.array([[i % 2 == 0 for i in range(num_spins)]], dtype=bool)\n",
    "bitstring_matrix = np.concatenate((bitstring_matrix, np.roll(bitstring_matrix, 1, axis=1)))\n",
    "for i in range(num_spins):\n",
    "    for j in range(num_spins // 2):\n",
    "        domain_wall = bitstring_matrix[0].copy()\n",
    "        domain_wall[i] -= 1\n",
    "        domain_wall[(i + 1 + j * 2) % num_spins] -= 1\n",
    "        bitstring_matrix = np.concatenate((bitstring_matrix, np.expand_dims(domain_wall, axis=0)))\n",
    "        domain_wall = bitstring_matrix[1].copy()\n",
    "        domain_wall[i] -= 1\n",
    "        domain_wall[(i + 1 + j * 2) % num_spins] -= 1\n",
    "        bitstring_matrix = np.concatenate((bitstring_matrix, np.expand_dims(domain_wall, axis=0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4: Post-process the results\n",
    "\n",
    "Using the [scipy.sparse.linalg.eigsh](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html#eigsh) arguments, we request ``\"k\": 4`` to specify we want ``4`` eigenstates, and we set ``\"which\": \"SA\"`` to specify we want the smallest algebraic eigenstates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Projecting term 1 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIIIIXX ...\n",
      "Projecting term 2 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIIIIYY ...\n",
      "Projecting term 3 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIIZZ ...\n",
      "Projecting term 4 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIIXXII ...\n",
      "Projecting term 5 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIIYYII ...\n",
      "Projecting term 6 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIZZII ...\n",
      "Projecting term 7 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIXXIIII ...\n",
      "Projecting term 8 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIYYIIII ...\n",
      "Projecting term 9 out of 66: (1+0j) * IIIIIIIIIIIIIIIIZZIIII ...\n",
      "Projecting term 10 out of 66: (0.3+0j) * IIIIIIIIIIIIIIXXIIIIII ...\n",
      "Projecting term 11 out of 66: (0.3+0j) * IIIIIIIIIIIIIIYYIIIIII ...\n",
      "Projecting term 12 out of 66: (1+0j) * IIIIIIIIIIIIIIZZIIIIII ...\n",
      "Projecting term 13 out of 66: (0.3+0j) * IIIIIIIIIIIIXXIIIIIIII ...\n",
      "Projecting term 14 out of 66: (0.3+0j) * IIIIIIIIIIIIYYIIIIIIII ...\n",
      "Projecting term 15 out of 66: (1+0j) * IIIIIIIIIIIIZZIIIIIIII ...\n",
      "Projecting term 16 out of 66: (0.3+0j) * IIIIIIIIIIXXIIIIIIIIII ...\n",
      "Projecting term 17 out of 66: (0.3+0j) * IIIIIIIIIIYYIIIIIIIIII ...\n",
      "Projecting term 18 out of 66: (1+0j) * IIIIIIIIIIZZIIIIIIIIII ...\n",
      "Projecting term 19 out of 66: (0.3+0j) * IIIIIIIIXXIIIIIIIIIIII ...\n",
      "Projecting term 20 out of 66: (0.3+0j) * IIIIIIIIYYIIIIIIIIIIII ...\n",
      "Projecting term 21 out of 66: (1+0j) * IIIIIIIIZZIIIIIIIIIIII ...\n",
      "Projecting term 22 out of 66: (0.3+0j) * IIIIIIXXIIIIIIIIIIIIII ...\n",
      "Projecting term 23 out of 66: (0.3+0j) * IIIIIIYYIIIIIIIIIIIIII ...\n",
      "Projecting term 24 out of 66: (1+0j) * IIIIIIZZIIIIIIIIIIIIII ...\n",
      "Projecting term 25 out of 66: (0.3+0j) * IIIIXXIIIIIIIIIIIIIIII ...\n",
      "Projecting term 26 out of 66: (0.3+0j) * IIIIYYIIIIIIIIIIIIIIII ...\n",
      "Projecting term 27 out of 66: (1+0j) * IIIIZZIIIIIIIIIIIIIIII ...\n",
      "Projecting term 28 out of 66: (0.3+0j) * IIXXIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 29 out of 66: (0.3+0j) * IIYYIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 30 out of 66: (1+0j) * IIZZIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 31 out of 66: (0.3+0j) * XXIIIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 32 out of 66: (0.3+0j) * YYIIIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 33 out of 66: (1+0j) * ZZIIIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 34 out of 66: (0.3+0j) * XIIIIIIIIIIIIIIIIIIIIX ...\n",
      "Projecting term 35 out of 66: (0.3+0j) * YIIIIIIIIIIIIIIIIIIIIY ...\n",
      "Projecting term 36 out of 66: (1+0j) * ZIIIIIIIIIIIIIIIIIIIIZ ...\n",
      "Projecting term 37 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIIIXXI ...\n",
      "Projecting term 38 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIIIYYI ...\n",
      "Projecting term 39 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIIIZZI ...\n",
      "Projecting term 40 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIXXIII ...\n",
      "Projecting term 41 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIIIYYIII ...\n",
      "Projecting term 42 out of 66: (1+0j) * IIIIIIIIIIIIIIIIIZZIII ...\n",
      "Projecting term 43 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIXXIIIII ...\n",
      "Projecting term 44 out of 66: (0.3+0j) * IIIIIIIIIIIIIIIYYIIIII ...\n",
      "Projecting term 45 out of 66: (1+0j) * IIIIIIIIIIIIIIIZZIIIII ...\n",
      "Projecting term 46 out of 66: (0.3+0j) * IIIIIIIIIIIIIXXIIIIIII ...\n",
      "Projecting term 47 out of 66: (0.3+0j) * IIIIIIIIIIIIIYYIIIIIII ...\n",
      "Projecting term 48 out of 66: (1+0j) * IIIIIIIIIIIIIZZIIIIIII ...\n",
      "Projecting term 49 out of 66: (0.3+0j) * IIIIIIIIIIIXXIIIIIIIII ...\n",
      "Projecting term 50 out of 66: (0.3+0j) * IIIIIIIIIIIYYIIIIIIIII ...\n",
      "Projecting term 51 out of 66: (1+0j) * IIIIIIIIIIIZZIIIIIIIII ...\n",
      "Projecting term 52 out of 66: (0.3+0j) * IIIIIIIIIXXIIIIIIIIIII ...\n",
      "Projecting term 53 out of 66: (0.3+0j) * IIIIIIIIIYYIIIIIIIIIII ...\n",
      "Projecting term 54 out of 66: (1+0j) * IIIIIIIIIZZIIIIIIIIIII ...\n",
      "Projecting term 55 out of 66: (0.3+0j) * IIIIIIIXXIIIIIIIIIIIII ...\n",
      "Projecting term 56 out of 66: (0.3+0j) * IIIIIIIYYIIIIIIIIIIIII ...\n",
      "Projecting term 57 out of 66: (1+0j) * IIIIIIIZZIIIIIIIIIIIII ...\n",
      "Projecting term 58 out of 66: (0.3+0j) * IIIIIXXIIIIIIIIIIIIIII ...\n",
      "Projecting term 59 out of 66: (0.3+0j) * IIIIIYYIIIIIIIIIIIIIII ...\n",
      "Projecting term 60 out of 66: (1+0j) * IIIIIZZIIIIIIIIIIIIIII ...\n",
      "Projecting term 61 out of 66: (0.3+0j) * IIIXXIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 62 out of 66: (0.3+0j) * IIIYYIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 63 out of 66: (1+0j) * IIIZZIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 64 out of 66: (0.3+0j) * IXXIIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 65 out of 66: (0.3+0j) * IYYIIIIIIIIIIIIIIIIIII ...\n",
      "Projecting term 66 out of 66: (1+0j) * IZZIIIIIIIIIIIIIIIIIII ...\n",
      "Diagonalizing Hamiltonian in the subspace...\n"
     ]
    }
   ],
   "source": [
    "from qiskit_addon_sqd.qubit import solve_qubit\n",
    "\n",
    "scipy_kwargs = {\"k\": 4, \"which\": \"SA\"}\n",
    "eigenvals, eigenstates = solve_qubit(bitstring_matrix, hamiltonian, verbose=True, **scipy_kwargs)\n",
    "\n",
    "min_eval = eigenstates[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-23.45253539 -23.45253539 -18.         -18.        ]\n"
     ]
    }
   ],
   "source": [
    "print(eigenvals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute spin-spin correlators\n",
    "\n",
    "Let's compute spin-spin correlators along the $x$, $y$ and $z$ axes:\n",
    "$$\n",
    "C^x(l) = \\frac{1}{L} \\sum_{i = 1}^L \\langle \\sigma^x_i \\sigma^x_{i + l} \\rangle- \n",
    "\\langle \\sigma^x_i\\rangle \\langle \\sigma^x_{i + l} \\rangle\n",
    "$$\n",
    "$$\n",
    "C^y(l) = \\frac{1}{L} \\sum_{i = 1}^L \\langle \\sigma^y_i \\sigma^y_{i + l} \\rangle-\n",
    "\\langle \\sigma^y_i \\rangle \\langle \\sigma^y_{i + l} \\rangle\n",
    "$$\n",
    "$$\n",
    "C^z(l) = \\frac{1}{L} \\sum_{i = 1}^L \\langle \\sigma^z_i \\sigma^z_{i + l} \\rangle-\n",
    "\\langle \\sigma^z_i\\rangle \\langle \\sigma^z_{i + l} \\rangle\n",
    "$$\n",
    "\n",
    "In order to compute the connected spin-spin correlators we first need to compute the  magnetization on each site along the three axes.\n",
    "\n",
    "**In order to project qubit operators using [qiskit_addon_sqd.qubit.project_operator_to_subspace](https://qiskit.github.io/qiskit-addon-sqd/stubs/qiskit_addon_sqd.qubit.project_operator_to_subspace.html#qiskit_addon_sqd.qubit.project_operator_to_subspace), the ``bitstring_matrix`` must first be sorted and de-duplicated, or the function will return unexpected results.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_sqd.qubit import sort_and_remove_duplicates\n",
    "\n",
    "# NOTE: It is essential for the projection code to have the bitstrings sorted!\n",
    "bitstring_matrix = sort_and_remove_duplicates(bitstring_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info import SparsePauliOp\n",
    "from qiskit_addon_sqd.qubit import project_operator_to_subspace\n",
    "\n",
    "s_x = np.zeros(num_spins)\n",
    "s_y = np.zeros(num_spins)\n",
    "s_z = np.zeros(num_spins)\n",
    "\n",
    "for i in range(num_spins):\n",
    "    # Sigma_x\n",
    "    pstr = [\"I\" for _ in range(num_spins)]\n",
    "    pstr[i] = \"X\"\n",
    "    pauli_op = SparsePauliOp(\"\".join(pstr))\n",
    "    sparse_op = project_operator_to_subspace(bitstring_matrix, pauli_op)\n",
    "    s_x[i] += np.real(np.conjugate(min_eval).T @ sparse_op @ min_eval)\n",
    "\n",
    "    # Sigma_y\n",
    "    pstr = [\"I\" for i in range(num_spins)]\n",
    "    pstr[i] = \"Y\"\n",
    "    pauli_op = SparsePauliOp(\"\".join(pstr))\n",
    "    sparse_op = project_operator_to_subspace(bitstring_matrix, pauli_op)\n",
    "    s_y[i] += np.real(np.conjugate(min_eval).T @ sparse_op @ min_eval)\n",
    "\n",
    "    # Sigma_z\n",
    "    pstr = [\"I\" for i in range(num_spins)]\n",
    "    pstr[i] = \"Z\"\n",
    "    pauli_op = SparsePauliOp(\"\".join(pstr))\n",
    "    sparse_op = project_operator_to_subspace(bitstring_matrix, pauli_op)\n",
    "    s_z[i] += np.real(np.conjugate(min_eval).T @ sparse_op @ min_eval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(s_x, marker=\".\", markersize=20, label=\"x\")\n",
    "plt.plot(s_y, marker=\".\", linestyle=\"--\", markersize=10, label=\"y\")\n",
    "plt.plot(s_z, marker=\".\", markersize=10, label=\"z\")\n",
    "\n",
    "plt.legend(\n",
    "    [r\"$\\langle\\sigma^x_i\\rangle$\", r\"$\\langle\\sigma^y_i\\rangle$\", r\"$\\langle\\sigma^z_i\\rangle$\"]\n",
    ")\n",
    "plt.xlabel(\"site, $i$\")\n",
    "plt.ylabel(\"single-site magnetization\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have computed the average magnetization on each site, we can compute the \n",
    "connected correlators as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_distance = num_spins // 2\n",
    "\n",
    "c_x = np.zeros(max_distance)\n",
    "c_y = np.zeros(max_distance)\n",
    "c_z = np.zeros(max_distance)\n",
    "distance_counts = np.zeros(max_distance)\n",
    "\n",
    "for i in range(num_spins):\n",
    "    for j in range(i + 1, num_spins):\n",
    "        j_wrap = j % num_spins  # Connect qubits N and 0\n",
    "        distance = min([abs(i - j), abs(i + (num_spins - j))])\n",
    "\n",
    "        # Sigma_x Sigma_x\n",
    "        pstr = [\"I\" for _ in range(num_spins)]\n",
    "        pstr[i] = \"X\"\n",
    "        pstr[j_wrap] = \"X\"\n",
    "        pauli_op = SparsePauliOp(\"\".join(pstr))\n",
    "        sparse_op = project_operator_to_subspace(bitstring_matrix, pauli_op)\n",
    "        c_x[distance - 1] += (\n",
    "            np.real(np.conjugate(min_eval).T @ sparse_op @ min_eval) - s_x[i] * s_x[j_wrap]\n",
    "        )\n",
    "\n",
    "        # Sigma_y Sigma_y\n",
    "        pstr = [\"I\" for _ in range(num_spins)]\n",
    "        pstr[i] = \"Y\"\n",
    "        pstr[j_wrap] = \"Y\"\n",
    "        pauli_op = SparsePauliOp(\"\".join(pstr))\n",
    "        sparse_op = project_operator_to_subspace(bitstring_matrix, pauli_op)\n",
    "        c_y[distance - 1] += (\n",
    "            np.real(np.conjugate(min_eval).T @ sparse_op @ min_eval) - s_y[i] * s_y[j_wrap]\n",
    "        )\n",
    "\n",
    "        # Sigma_z Sigma_z\n",
    "        pstr = [\"I\" for _ in range(num_spins)]\n",
    "        pstr[i] = \"Z\"\n",
    "        pstr[j_wrap] = \"Z\"\n",
    "        pauli_op = SparsePauliOp(\"\".join(pstr))\n",
    "        sparse_op = project_operator_to_subspace(bitstring_matrix, pauli_op)\n",
    "        c_z[distance - 1] += (\n",
    "            np.real(np.conjugate(min_eval).T @ sparse_op @ min_eval) - s_z[i] * s_z[j_wrap]\n",
    "        )\n",
    "\n",
    "        distance_counts[distance - 1] += 1\n",
    "c_x /= distance_counts\n",
    "c_y /= distance_counts\n",
    "c_z /= distance_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the Z correlation shows true long range order (the correlator does not decay to 0). The X,Y correlators decay to 0 with distance between spin pairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(1, max_distance + 1), np.abs(c_x), marker=\".\", markersize=20, label=\"xx\")\n",
    "plt.plot(\n",
    "    np.arange(1, max_distance + 1),\n",
    "    np.abs(c_y),\n",
    "    marker=\".\",\n",
    "    linestyle=\"--\",\n",
    "    markersize=10,\n",
    "    label=\"yy\",\n",
    ")\n",
    "plt.plot(np.arange(1, max_distance + 1), np.abs(c_z), marker=\".\", markersize=10, label=\"zz\")\n",
    "\n",
    "plt.legend([r\"$C^x(\\ell)$\", r\"$C^y(\\ell)$\", r\"$C^z(\\ell)$\"])\n",
    "plt.xlabel(r\"site, $\\ell$\")\n",
    "plt.ylabel(\"spin-spin correlators\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "[1] Robledo-Moreno, Javier, et al. [\"Chemistry beyond exact solutions on a quantum-centric supercomputer.\"](https://arxiv.org/abs/2405.05068) arXiv preprint arXiv:2405.05068 (2024)."
   ]
  }
 ],
 "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": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}