{ "cells": [ { "cell_type": "markdown", "id": "9e40af77-7f0f-4dd6-ab0a-420cf396050e", "metadata": {}, "source": [ "# Bounding the subspace dimension\n", "\n", "In this walkthrough, 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 random bitstrings 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_bit_array_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", "bit_array = generate_bit_array_uniform(10_000, num_orbitals * 2, rand_seed=rng)" ] }, { "cell_type": "markdown", "id": "82b062a3-d4ca-41e2-9b00-4a394f83cbdd", "metadata": {}, "source": [ "Call SQD with increasing batch sizes." ] }, { "cell_type": "code", "execution_count": 3, "id": "e0847f28", "metadata": {}, "outputs": [], "source": [ "from qiskit_addon_sqd.fermion import diagonalize_fermionic_hamiltonian\n", "\n", "list_samples_per_batch = [50, 200, 400, 600]\n", "\n", "# SQD options\n", "max_iterations = 5\n", "\n", "# Eigenstate solver options\n", "num_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", " result = diagonalize_fermionic_hamiltonian(\n", " hcore,\n", " eri,\n", " bit_array,\n", " samples_per_batch=samples_per_batch,\n", " norb=num_orbitals,\n", " nelec=(num_elec_a, num_elec_b),\n", " num_batches=num_batches,\n", " max_iterations=max_iterations,\n", " symmetrize_spin=True,\n", " seed=rng,\n", " )\n", " energies.append(result.energy)\n", " subspace_dimensions.append(np.prod(result.sci_state.amplitudes.shape))" ] }, { "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": 4, "id": "caffd888-e89c-4aa9-8bae-4d1bb723b35e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "# Data for energies plot\n", "x1 = subspace_dimensions\n", "y1 = np.array(energies) + nuclear_repulsion_energy\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()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setting an explicit bound with `max_dim`\n", "\n", "In the sweep above, the subspace dimension was controlled only indirectly. `samples_per_batch` sets how many bitstrings are drawn into each batch, but the dimension of the resulting subspace is determined by how many *distinct* spin-alpha and spin-beta strings those bitstrings contain, and the pool of configurations available for subsampling grows from one configuration recovery iteration to the next. That is why the subspace dimensions on the horizontal axis above are irregular numbers that we did not pick.\n", "\n", "The `max_dim` argument of `diagonalize_fermionic_hamiltonian` bounds the dimension directly. It limits the number of CI strings retained in each spin sector, and since the subspace is spanned by the Cartesian product of the two sectors, its dimension is the product of the two sector dimensions:\n", "\n", "- `max_dim=d` limits both sectors to `d` strings, so the subspace dimension is at most `d ** 2`.\n", "- `max_dim=(d_a, d_b)` limits the spin-alpha and spin-beta sectors separately, so the subspace dimension is at most `d_a * d_b`. When `symmetrize_spin=True`, the two limits must be equal.\n", "- `max_dim=None`, the default, imposes no limit.\n", "\n", "When a batch contains more strings than the limit allows, the least important ones are discarded: the strings passed via `include_configurations` are kept first, followed by the strings carried over from the previous iteration (see `carryover_threshold`), and the remaining slots are filled with the sampled strings in decreasing order of how often they were sampled.\n", "\n", "Because `max_dim` caps the size of the largest diagonalization that the eigenstate solver will be asked to perform, it is a convenient way to keep the solver within a runtime and memory budget: choose `samples_per_batch` generously, and let `max_dim` decide how large the subspace is allowed to grow.\n", "\n", "Below, we repeat the study, this time holding `samples_per_batch` fixed and increasing `max_dim`." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max_dim: [100, 200, 400, 800]\n", "subspace dimension: [10000, 40000, 160000, 640000]\n" ] } ], "source": [ "list_max_dim = [100, 200, 400, 800]\n", "\n", "# Use a generous number of samples per batch, so that max_dim is what limits\n", "# the dimension of the subspace\n", "samples_per_batch = 600\n", "\n", "energies_max_dim = []\n", "subspace_dimensions_max_dim = []\n", "\n", "for max_dim in list_max_dim:\n", " result = diagonalize_fermionic_hamiltonian(\n", " hcore,\n", " eri,\n", " bit_array,\n", " samples_per_batch=samples_per_batch,\n", " norb=num_orbitals,\n", " nelec=(num_elec_a, num_elec_b),\n", " num_batches=num_batches,\n", " max_iterations=max_iterations,\n", " symmetrize_spin=True,\n", " max_dim=max_dim,\n", " seed=rng,\n", " )\n", " energies_max_dim.append(result.energy)\n", " subspace_dimensions_max_dim.append(int(np.prod(result.sci_state.amplitudes.shape)))\n", "\n", "print(f\"max_dim: {list_max_dim}\")\n", "print(f\"subspace dimension: {subspace_dimensions_max_dim}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The subspace dimension is now exactly `max_dim ** 2` in every run: it was chosen rather than discovered. Plotting both sweeps together shows that the accuracy is governed by the subspace dimension itself, whichever argument was used to arrive at it. The two curves need not coincide exactly, though. The `max_dim` runs draw 600 bitstrings per batch and then keep the most frequently sampled strings, so at a given dimension they can retain a better set of configurations than a run that reached that dimension by sampling fewer bitstrings in the first place." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 1, figsize=(12, 6))\n", "\n", "axs.plot(\n", " subspace_dimensions,\n", " np.array(energies) + nuclear_repulsion_energy,\n", " marker=\".\",\n", " markersize=20,\n", " label=\"Varying samples_per_batch\",\n", ")\n", "axs.plot(\n", " subspace_dimensions_max_dim,\n", " np.array(energies_max_dim) + nuclear_repulsion_energy,\n", " marker=\"^\",\n", " markersize=12,\n", " label=\"Varying max_dim\",\n", ")\n", "axs.axhline(y=exact_energy, color=\"red\", linestyle=\"--\", label=\"Exact\")\n", "axs.set_xscale(\"log\")\n", "axs.ticklabel_format(axis=\"y\", useOffset=False)\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", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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": "3.13.13" } }, "nbformat": 4, "nbformat_minor": 5 }