Selected configuration interaction wave functions in phaseless auxiliary field quantum Monte Carlo

TL;DR

This paper introduces efficient algorithms for integrating selected configuration interaction wave functions into phaseless auxiliary field quantum Monte Carlo, enabling larger trial states with minimal computational overhead and improved accuracy assessment.

Contribution

The authors develop scalable algorithms that incorporate large sCI trial wave functions into ph-AFQMC, significantly reducing computational costs and enabling systematic convergence studies.

Findings

Cost per sample increases only modestly with larger configurations

Able to use up to a million configurations in trial wave functions

Scalability improved by restricting to active space and error cancellation

Abstract

We present efficient algorithms for using selected configuration interaction (sCI) trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC). These advancements, geared towards optimizing computational performance for longer CI expansions, allow us to use up to a million configurations feasibly in the trial state for ph-AFQMC. In one example, we found the cost of ph-AFQMC per sample to increase only by a factor of about $3$ for a calculation with $10^4$ configurations compared to that with a single one, demonstrating the tiny computational overhead due to a longer expansion. This favorable scaling allows us to study the systematic convergence of the phaseless bias in AFQMC calculations with an increasing number of configurations and provides a means to gauge the accuracy of ph-AFQMC with other trial states. We also show how the scalability issues of sCI trial states for large system sizes could be mitigated by restricting them to a moderately sized orbital active space and leveraging the near-cancellation of out of active space phaseless errors.