Variational subspace methods and application to improving variational Monte Carlo dynamics

TL;DR

This paper introduces a formalism for direct subspace manipulation in variational methods, and presents Bridge, a practical technique to enhance variational Monte Carlo dynamics by reducing discretization errors.

Contribution

It develops a new formalism for subspace optimization and introduces Bridge, a novel, efficient post-processing method to improve variational dynamics accuracy.

Findings

Bridge significantly reduces errors from discretizing variational dynamics.

The formalism enables direct manipulation of subspaces without optimizing individual states.

Bridge is computationally inexpensive and effective as a post-processing tool.

Abstract

We present a formalism that allows for the direct manipulation and optimization of subspaces, circumventing the need to optimize individual states when using subspace methods. Using the determinant state mapping, we can naturally extend notions such as distance and energy to subspaces, as well as Monte Carlo estimators, recovering the excited states estimation method proposed by Pfau et al. As a practical application, we then introduce Bridge, a method that improves the performance of variational dynamics by extracting linear combinations of variational time-evolved states. We find that Bridge is both computationally inexpensive and capable of significantly mitigating the errors that arise from discretizing the dynamics, and can thus be systematically used as a post-processing tool for variational dynamics.