Diffusion Monte Carlo: Exponential scaling of computational cost for large systems

TL;DR

This paper analyzes the scaling behavior of diffusion Monte Carlo for large quantum systems, revealing that the correlation within walker populations causes exponential growth in computational cost for systems with hundreds of atoms.

Contribution

It identifies the correlation among walkers as the main factor leading to exponential scaling in diffusion Monte Carlo for large systems.

Findings

Correlation within walkers causes exponential scaling

Scaling becomes significant for systems over several hundred atoms

Estimation of the scaling factor is straightforward for specific systems

Abstract

The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the diffusion Monte Carlo method for large quantum systems. We identify the correlation within the population of walkers as the dominant scaling factor for large systems. While this factor is negligible for small and medium sized systems that are typically studied, it ultimately shows exponential scaling. The scaling factor can be estimated straightforwardly for each specific system and we find that is typically only becomes relevant for systems containing more than several hundred atoms.