Efficient heat-bath sampling in Fock space

TL;DR

The paper presents an efficient heat-bath sampling algorithm for Fock space, significantly improving the efficiency of quantum Monte Carlo methods like S-FCIQMC, especially for larger basis sets and more electrons.

Contribution

Introduces a heat-bath sampling algorithm for Fock space that enhances the efficiency of quantum Monte Carlo methods with minimal additional computational cost.

Findings

Large efficiency gains in nitrogen dimer simulations with basis set size

Efficiency increases with the number of electrons in first-row dimers

Modest computational overhead compared to uniform sampling

Abstract

We introduce an algorithm for sampling many-body quantum states in Fock space. The algorithm efficiently samples states with probability approximately proportional to an arbitrary function of the second-quantized Hamiltonian matrix element connecting the sampled state to the current state. We apply the new sampling algorithm to the recently-developed Semistochastic Full Configuration Interaction Quantum Monte Carlo method (S-FCIQMC), a semistochastic implementation of the power method for projecting out the ground state energy in a basis of Slater determinants. The heat-bath sampling requires modest additional computational time and memory compared to uniform sampling but results in newly-spawned weights that are approximately of the same magnitude, thereby greatly improving the efficiency of projection. A comparison in efficiency between uniform and approximate heat-bath sampling is performed on the all-electron nitrogen dimer at equilibrium in Dunning's cc-pVXZ basis sets with X in {D, T, Q, 5}, demonstrating a large gain in efficiency that increases with basis set size. In addition, a comparison in efficiency is performed on three all-electron first-row dimers, B_2, N_2, and F_2, in a cc-pVQZ basis, demonstrating that the gain in efficiency compared to uniform sampling also increases dramatically with the number of electrons.