docs/how_tos/choose_subspace_dimension.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9e40af77-7f0f-4dd6-ab0a-420cf396050e",
   "metadata": {},
   "source": [
    "# Bounding the subspace dimension\n",
    "\n",
    "In this tutorial, we will show the effect of the subspace dimension in the [self-consistent configuration recovery technique](https://arxiv.org/abs/2405.05068).\n",
    "\n",
    "***A priori***, we do not know what is the correct subspace dimension to obtain a target level of accuracy. However, we do know that increasing the subspace dimension increases the accuracy of the method. Therefore, we can study the accuracy of the predictions as a function of the subspace dimension."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6755afb-ca1e-4473-974b-ba89acc8abce",
   "metadata": {},
   "source": [
    "Specify the molecule and its properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "677f54ac-b4ed-47e3-b5ba-5366d3a520f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged SCF energy = -108.835236570775\n",
      "CASCI E = -109.046671778080  E(CI) = -32.8155692383188  S^2 = 0.0000000\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "\n",
    "import pyscf\n",
    "import pyscf.cc\n",
    "import pyscf.mcscf\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "# Specify molecule properties\n",
    "open_shell = False\n",
    "spin_sq = 0\n",
    "\n",
    "# Build N2 molecule\n",
    "mol = pyscf.gto.Mole()\n",
    "mol.build(\n",
    "    atom=[[\"N\", (0, 0, 0)], [\"N\", (1.0, 0, 0)]],\n",
    "    basis=\"6-31g\",\n",
    "    symmetry=\"Dooh\",\n",
    ")\n",
    "\n",
    "# Define active space\n",
    "n_frozen = 2\n",
    "active_space = range(n_frozen, mol.nao_nr())\n",
    "\n",
    "# Get molecular integrals\n",
    "scf = pyscf.scf.RHF(mol).run()\n",
    "num_orbitals = len(active_space)\n",
    "n_electrons = int(sum(scf.mo_occ[active_space]))\n",
    "num_elec_a = (n_electrons + mol.spin) // 2\n",
    "num_elec_b = (n_electrons - mol.spin) // 2\n",
    "cas = pyscf.mcscf.CASCI(scf, num_orbitals, (num_elec_a, num_elec_b))\n",
    "mo = cas.sort_mo(active_space, base=0)\n",
    "hcore, nuclear_repulsion_energy = cas.get_h1cas(mo)\n",
    "eri = pyscf.ao2mo.restore(1, cas.get_h2cas(mo), num_orbitals)\n",
    "\n",
    "# Compute exact energy\n",
    "exact_energy = cas.run().e_tot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c58e988c-a109-44cd-a975-9df43250c318",
   "metadata": {},
   "source": [
    "Generate some dummy counts to proxy QPU samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9506e0b-ed64-48bb-a97a-ef851b604af1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit_addon_sqd.counts import generate_counts_uniform\n",
    "\n",
    "# Create a seed to control randomness throughout this workflow\n",
    "rng = np.random.default_rng(24)\n",
    "\n",
    "# Generate random samples\n",
    "counts_dict = generate_counts_uniform(10_000, num_orbitals * 2, rand_seed=rng)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "851bc98e-9c08-4e78-9472-36301abc11d8",
   "metadata": {},
   "source": [
    "Convert the counts to a bitstring matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7a102a7f-aae6-4583-ab82-ae40fcb5496a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_sqd.counts import counts_to_arrays\n",
    "\n",
    "# Convert counts into bitstring and probability arrays\n",
    "bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb704101-0fe8-4d12-b572-b1d844e35a90",
   "metadata": {},
   "source": [
    "Define an SQD function, which we will call in a loop with increasing batch sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b72c048e-fe8e-4fc2-b28b-03138249074e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_sqd.configuration_recovery import recover_configurations\n",
    "from qiskit_addon_sqd.fermion import (\n",
    "    bitstring_matrix_to_ci_strs,\n",
    "    solve_fermion,\n",
    ")\n",
    "from qiskit_addon_sqd.subsampling import postselect_and_subsample\n",
    "\n",
    "\n",
    "def configuration_recovery_loop(\n",
    "    hcore: np.ndarray,\n",
    "    eri: np.ndarray,\n",
    "    num_elec_a: int,\n",
    "    num_elec_b: int,\n",
    "    spin_sq: float,\n",
    "    iterations: int,\n",
    "    n_batches: int,\n",
    "    samples_per_batch: int,\n",
    "    max_davidson_cycles: int,\n",
    "    rng: np.random.Generator,\n",
    ") -> tuple[np.ndarray, np.ndarray]:\n",
    "    \"\"\"Perform SQD.\"\"\"\n",
    "    # Self-consistent configuration recovery loop\n",
    "    e_hist = np.zeros((iterations, n_batches))  # energy history\n",
    "    s_hist = np.zeros((iterations, n_batches))  # spin history\n",
    "    d_hist = np.zeros((iterations, n_batches))  # subspace dimension history\n",
    "    occupancy_hist = []\n",
    "    avg_occupancy = None\n",
    "    for i in range(iterations):\n",
    "        print(f\"Starting configuration recovery iteration {i}\")\n",
    "        # On the first iteration, we have no orbital occupancy information from the\n",
    "        # solver, so we just post-select from the full bitstring set based on hamming weight.\n",
    "        if avg_occupancy is None:\n",
    "            bs_mat_tmp = bitstring_matrix_full\n",
    "            probs_arr_tmp = probs_arr_full\n",
    "\n",
    "        # In following iterations, we use both the occupancy info and the target hamming\n",
    "        # weight to correct bitstrings.\n",
    "        else:\n",
    "            bs_mat_tmp, probs_arr_tmp = recover_configurations(\n",
    "                bitstring_matrix_full,\n",
    "                probs_arr_full,\n",
    "                avg_occupancy,\n",
    "                num_elec_a,\n",
    "                num_elec_b,\n",
    "                rand_seed=rng,\n",
    "            )\n",
    "\n",
    "        # Throw out samples with incorrect hamming weight and create batches of subsamples.\n",
    "        batches = postselect_and_subsample(\n",
    "            bs_mat_tmp,\n",
    "            probs_arr_tmp,\n",
    "            hamming_right=num_elec_a,\n",
    "            hamming_left=num_elec_b,\n",
    "            samples_per_batch=samples_per_batch,\n",
    "            num_batches=n_batches,\n",
    "            rand_seed=rng,\n",
    "        )\n",
    "\n",
    "        # Run eigenstate solvers in a loop. This loop should be parallelized for larger problems.\n",
    "        int_e = np.zeros(n_batches)\n",
    "        int_s = np.zeros(n_batches)\n",
    "        int_d = np.zeros(n_batches)\n",
    "        int_occs = []\n",
    "        cs = []\n",
    "        for j in range(n_batches):\n",
    "            ci_strs = bitstring_matrix_to_ci_strs(batches[j], open_shell=open_shell)\n",
    "            int_d[j] = len(ci_strs[0]) * len(ci_strs[1])\n",
    "            energy_sci, coeffs_sci, avg_occs, spin = solve_fermion(\n",
    "                batches[j],\n",
    "                hcore,\n",
    "                eri,\n",
    "                open_shell=open_shell,\n",
    "                spin_sq=spin_sq,\n",
    "                max_davidson=max_davidson_cycles,\n",
    "            )\n",
    "            energy_sci += nuclear_repulsion_energy\n",
    "            int_e[j] = energy_sci\n",
    "            int_s[j] = spin\n",
    "            int_occs.append(avg_occs)\n",
    "            cs.append(coeffs_sci)\n",
    "\n",
    "        # Combine batch results\n",
    "        avg_occupancy = tuple(np.mean(int_occs, axis=0))\n",
    "\n",
    "        # Track optimization history\n",
    "        e_hist[i, :] = int_e\n",
    "        s_hist[i, :] = int_s\n",
    "        d_hist[i, :] = int_d\n",
    "        occupancy_hist.append(avg_occupancy)\n",
    "\n",
    "    return e_hist.flatten(), d_hist.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82b062a3-d4ca-41e2-9b00-4a394f83cbdd",
   "metadata": {},
   "source": [
    "Call SQD with increasing batch sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e0847f28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting configuration recovery iteration 0\n",
      "Starting configuration recovery iteration 1\n",
      "Starting configuration recovery iteration 2\n",
      "Starting configuration recovery iteration 3\n",
      "Starting configuration recovery iteration 4\n",
      "Starting configuration recovery iteration 0\n",
      "Starting configuration recovery iteration 1\n",
      "Starting configuration recovery iteration 2\n",
      "Starting configuration recovery iteration 3\n",
      "Starting configuration recovery iteration 4\n",
      "Starting configuration recovery iteration 0\n",
      "Starting configuration recovery iteration 1\n",
      "Starting configuration recovery iteration 2\n",
      "Starting configuration recovery iteration 3\n",
      "Starting configuration recovery iteration 4\n",
      "Starting configuration recovery iteration 0\n",
      "Starting configuration recovery iteration 1\n",
      "Starting configuration recovery iteration 2\n",
      "Starting configuration recovery iteration 3\n",
      "Starting configuration recovery iteration 4\n"
     ]
    }
   ],
   "source": [
    "list_samples_per_batch = [50, 200, 400, 600]\n",
    "\n",
    "# SQD options\n",
    "iterations = 5\n",
    "\n",
    "# Eigenstate solver options\n",
    "n_batches = 10\n",
    "max_davidson_cycles = 200\n",
    "\n",
    "energies = []\n",
    "subspace_dimensions = []\n",
    "\n",
    "for samples_per_batch in list_samples_per_batch:\n",
    "    e_hist, d_hist = configuration_recovery_loop(\n",
    "        hcore,\n",
    "        eri,\n",
    "        num_elec_a,\n",
    "        num_elec_b,\n",
    "        spin_sq,\n",
    "        iterations,\n",
    "        n_batches,\n",
    "        samples_per_batch,\n",
    "        max_davidson_cycles,\n",
    "        rng=rng,\n",
    "    )\n",
    "    energies.append(np.min(e_hist))\n",
    "\n",
    "    index_min = np.argmin(e_hist)\n",
    "    subspace_dimensions.append(d_hist[index_min])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d78906b-4759-4506-9c69-85d4e67766b3",
   "metadata": {},
   "source": [
    "This plot shows that increasing the subspace dimension leads to more accurate results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "caffd888-e89c-4aa9-8bae-4d1bb723b35e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Data for energies plot\n",
    "x1 = subspace_dimensions\n",
    "y1 = energies\n",
    "\n",
    "fig, axs = plt.subplots(1, 1, figsize=(12, 6))\n",
    "\n",
    "# Plot energies\n",
    "axs.plot(x1, y1, marker=\".\", markersize=20, label=\"Estimated\")\n",
    "axs.set_xticks(x1)\n",
    "axs.set_xticklabels(x1)\n",
    "axs.axhline(y=exact_energy, color=\"red\", linestyle=\"--\", label=\"Exact\")\n",
    "axs.set_title(\"Approximated Ground State Energy vs subspace dimension\")\n",
    "axs.set_xlabel(\"Subspace dimension\")\n",
    "axs.set_ylabel(\"Energy (Ha)\")\n",
    "axs.legend()\n",
    "\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
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