Understanding and Improving the Efficiency of Full Configuration Interaction Quantum Monte Carlo

TL;DR

This paper analyzes the efficiency of Full Configuration Interaction Quantum Monte Carlo, showing how parameter choices and orbital localization affect statistical error and inefficiency, with implications for computational quantum chemistry.

Contribution

It introduces a measure of inefficiency in FCIQMC and demonstrates how basis localization can significantly reduce statistical errors.

Findings

Inefficiency is minimized in a specific parameter regime.

Inefficiency increases sublinearly with Hilbert space size.

Localizing orbitals reduces statistical error beyond the sign problem effects.

Abstract

Within Full Configuration Interaction Quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per timestep and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree--Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem.