{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "377f84b3-1d02-4d7e-a061-db7c9d3c643d",
   "metadata": {},
   "source": [
    "# Heisenberg spin model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0a64e811-4cb3-45fa-a117-c8fda21da412",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse.linalg as spla\n",
    "from qiskit.transpiler import CouplingMap\n",
    "import fulqrum as fq"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fded0c03-fb6f-4987-a450-18a2898c07e6",
   "metadata": {},
   "source": [
    "## Construct operator\n",
    "\n",
    "Here we construct a 16-qubit Heisenberg spin model over a square-grid using a Qiskit `CouplingMap` to define the grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ee42f198-4ded-405e-bbdf-fb5dc2aad1fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build 16-qubit coupling map\n",
    "cmap = CouplingMap.from_grid(4, 4)\n",
    "num_qubits = cmap.size()\n",
    "\n",
    "# Generate Hamiltonian\n",
    "H = fq.QubitOperator(num_qubits, [])\n",
    "touched_edges = set({})\n",
    "coeffs = [-1 / 2, -1 / 2, -1]\n",
    "for edge in cmap.get_edges():\n",
    "    if edge[::-1] not in touched_edges:  # Only add edge once to Hamiltonian\n",
    "        touched_edges.add(edge)\n",
    "        H += fq.QubitOperator(\n",
    "            num_qubits,\n",
    "            [(\"XX\", edge, coeffs[0]), (\"YY\", edge, coeffs[1]), (\"ZZ\", edge, coeffs[2])],\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67263766-eee7-44ea-bff7-60784edaf8d3",
   "metadata": {},
   "source": [
    "## Construct subspace\n",
    "\n",
    "In lieu of actually running on hardware or a simulator, here we generate a fake set of bit-strings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "66207ada-5512-458a-86b0-880ca9c34437",
   "metadata": {},
   "outputs": [],
   "source": [
    "counts = []\n",
    "for kk in range(2**num_qubits):\n",
    "    counts.append(bin(kk)[2:].zfill(num_qubits))\n",
    "\n",
    "S = fq.Subspace([counts])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca2c4986-604b-4de4-8ac3-2aeae4da5754",
   "metadata": {},
   "source": [
    "## Create subspace Hamiltonian and initial vector\n",
    "\n",
    "The Hamiltonian and subspace are combined into a `SubspaceHamiltonian` object for eigensolving.  Here we also set the initial vector for reproducibility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1715e9ec-4fe5-47b7-89c7-4431dd0da9f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "Hsub = fq.SubspaceHamiltonian(H, S)\n",
    "v0 = np.ones(S.size(), dtype=Hsub.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fe5982a-150d-450f-b1f7-08e347ddaa74",
   "metadata": {},
   "source": [
    "## Perform diagonalization\n",
    "\n",
    "Here we perform the diagonalization twice; first matrix-free and then using a CSR matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69783948-7610-433d-ae7f-0a53a73ce664",
   "metadata": {},
   "source": [
    "### Matrix-free"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "69f07f94-bd9c-4eee-82b3-c305837e23d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "evals, evecs = spla.eigsh(Hsub, k=1, which=\"SA\", v0=v0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1aca958-c4d8-4552-8d1d-531a79b41a65",
   "metadata": {},
   "source": [
    "### CSR-matrix solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a53aa19e-7f7b-4147-bd12-63af203da29b",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = Hsub.to_csr_linearoperator_fast()\n",
    "evals2, evecs2 = spla.eigsh(M, k=1, which=\"SA\", v0=v0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a45b9c10-2eb2-4fb1-83a2-3f79a943fdc9",
   "metadata": {},
   "source": [
    "### Compare solutions\n",
    "\n",
    "First compare relative error in found eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "fa0f8487-94e6-4c72-827f-79948d7eb68d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.4802973661668783e-16)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs((evals[0] - evals2[0]) / evals[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc5c3c10-909d-4469-b34b-2eb9c581cf44",
   "metadata": {},
   "source": [
    "Show that the two eigenstates agree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a9190258-f4c2-4c49-b710-dbbf7e37a851",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0000000000000000': 0.7071067811865476,\n",
       " '1111111111111111': 0.7071067811865476}"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hsub.interpret_vector(evecs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "8618b3be-822a-4c18-867c-f0bee30babdf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0000000000000000': 0.7071067811865477,\n",
       " '1111111111111111': 0.7071067811865477}"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hsub.interpret_vector(evecs2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27e5f6f8-f13c-4a44-9e46-1610daaf8b79",
   "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": "3.13.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}