Looking elsewhere: improving variational Monte Carlo gradients by importance sampling

TL;DR

This paper introduces an importance sampling strategy to improve variational Monte Carlo gradients for neural-network quantum states, significantly reducing computational costs especially for peaked wavefunctions in quantum chemistry.

Contribution

The authors propose an adaptive importance sampling method that targets gradient estimation without extra hyperparameters, enhancing VMC efficiency for complex quantum states.

Findings

Reduces VMC computational cost up to 100x for peaked wavefunctions.

Systematic improvements in ground-state searches across various Hamiltonians.

Enhanced infidelity minimization in neural quantum dynamics.

Abstract

Neural-network quantum states (NQS) offer a powerful and expressive ansatz for representing quantum many-body wave functions. However, their training via Variational Monte Carlo (VMC) methods remains challenging. It is well known that some scenarios - such as sharply peaked wave functions emerging in quantum chemistry - lead to high-variance gradient estimators hindering the effectiveness of variational optimizations. In this work we investigate a systematic strategy to tackle those sampling issues by means of adaptively tuned importance sampling. Our approach is explicitly designed to (i) target the gradient estimator instead of the loss function, (ii) not introduce additional hyperparameters and (iii) be computationally inexpensive. We benchmarked our approach across the ground-state search of a wide variety of hamiltonians, including frustrated spin systems and ab-initio quantum chemistry. We also show systematic improvements on the infidelity minimization in the context of neural projected quantum dynamics. Overall, our approach can reduce the computational cost of vanilla VMC considerably, up to a factor of 100x when targeting highly peaked quantum chemistry wavefunctions.