Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo

TL;DR

This paper analyzes the population control bias in full configuration interaction quantum Monte Carlo (FCIQMC), identifies its origin, and proposes re-weighting and importance sampling techniques to reduce bias, improving accuracy in large quantum systems.

Contribution

It provides a detailed analysis of the population control bias in FCIQMC and introduces correction methods and importance sampling to mitigate this bias, enhancing result accuracy.

Findings

Bias varies with estimators, especially the shift estimator.

Re-weighting effectively reduces population control bias.

Importance sampling significantly decreases bias in sign-problem-free systems.

Abstract

Population control is an essential component of any projector Monte Carlo algorithm. This control mechanism usually introduces a bias in the sampled quantities that is inversely proportional to the population size. In this paper, we investigate the population control bias in the full configuration interaction quantum Monte Carlo method. We identify the precise origin of this bias and quantify it in general. We show that it has different effects on different estimators and that the shift estimator is particularly susceptible. We derive a re-weighting technique, similar to the one used in diffusion Monte Carlo, for correcting this bias and apply it to the shift estimator. We also show that by using importance sampling, the bias can be reduced substantially. We demonstrate the necessity and the effectiveness of applying these techniques for sign-problem-free systems where this bias is especially notable. Specifically, we show results for large one-dimensional Hubbard models and the two-dimensional Heisenberg model, where corrected FCIQMC results are comparable to the other high-accuracy results.