Reducing the Cost of Energy Differences in Variational Monte Carlo with Spotlight Sampling

TL;DR

This paper introduces spotlight sampling, an approximate method that significantly reduces the computational cost of variational Monte Carlo for energy difference calculations, achieving near-linear scaling with system size.

Contribution

The paper presents a novel spotlight sampling approach that employs approximate fragmented Hamiltonians and correlated sampling to lower the cost scaling of variational Monte Carlo.

Findings

Achieves near-linear cost scaling in tests on various molecules.

Demonstrates explicit cost crossover with standard variational Monte Carlo.

Potential for sub-linear scaling under certain conditions.

Abstract

We investigate an approximate sampling scheme that can significantly reduce the cost scaling of variational Monte Carlo when it is employed to predict the energy differences associated with local chemical changes. Inspired by side-chaining and embedding methods, this spotlight sampling approach adopts an approximate fragmented Hamiltonian and correlated sampling to reduce cost scaling to the point that it is essentially linear with system size, with the potential to go sub-linear if certain conditions are met. In tests on bond stretching energies in alcohols, hydrogen dimer chains, and molecules with various degrees of $\pi$-system delocalization, we observe the anticipated linear scaling as well as an explicit cost crossover with standard variational Monte Carlo.