Minimising biases in Full Configuration Interaction Quantum Monte Carlo

TL;DR

This paper models FCIQMC as a Markov chain, analyzes population control bias in simple systems, and proposes a reweighting method to reduce bias, improving the accuracy of quantum Monte Carlo simulations.

Contribution

It constructs the Markov matrix for FCIQMC, quantifies population control bias, and introduces a reweighting scheme to mitigate bias effects.

Findings

Population control bias exists even in simple two-determinant systems.

Simulation parameters significantly influence bias magnitude.

Reweighting effectively reduces bias in FCIQMC results.

Abstract

We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov Chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to in general minimise the bias. We show a reweighting scheme to remove the bias caused by population control commonly used in Diffusion Monte Carlo [J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step.