{ "cells": [ { "cell_type": "markdown", "id": "frontmatter", "metadata": {}, "source": [ "---\n", "title: \"Limitando a dimensão do subespaço\"\n", "description: \"Limitação da dimensão do subespaço para a versão mais recente da diagonalização quântica baseada em amostras (SQD)\"\n", "---\n", "\n" ] }, { "cell_type": "markdown", "id": "9e40af77-7f0f-4dd6-ab0a-420cf396050e", "metadata": {}, "source": [ "\n", "\n", "# Limitando a dimensão do subespaço\n", "\n", "{/* cspell:ignore hcore */}\n", "\n", "Neste passo a passo, mostraremos o efeito da dimensão do subespaço na [técnica de recuperação de configuração autoconsistente](https://arxiv.org/abs/2405.05068).\n", "\n", "*A priori*, não sabemos qual é a dimensão correta do subespaço para atingir um nível alvo de precisão. No entanto, sabemos que aumentar a dimensão do subespaço aumenta a precisão do método. Portanto, podemos estudar a precisão das previsões em função da dimensão do subespaço.\n", "\n" ] }, { "cell_type": "markdown", "id": "a6755afb-ca1e-4473-974b-ba89acc8abce", "metadata": {}, "source": [ "Especifique a molécula e suas propriedades.\n", "\n" ] }, { "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": [ "Gere algumas sequências de bits aleatórias para simular amostras da QPU.\n", "\n" ] }, { "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(\n", " 10_000, num_orbitals * 2, rand_seed=rng\n", ")" ] }, { "cell_type": "markdown", "id": "82b062a3-d4ca-41e2-9b00-4a394f83cbdd", "metadata": {}, "source": [ "Chame a função SQD com tamanhos de lote crescentes.\n", "\n" ] }, { "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": [ "Este gráfico mostra que o aumento da dimensão do subespaço leva a resultados mais precisos.\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "caffd888-e89c-4aa9-8bae-4d1bb723b35e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " $\"Output$ " ] }, "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": {}, "id": "a1b8767d", "source": "© IBM Corp., 2017-2026" } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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" } }, "nbformat": 4, "nbformat_minor": 5 }