Rayleigh-Gauss-Newton optimization with enhanced sampling for variational Monte Carlo

TL;DR

This paper introduces the Rayleigh-Gauss-Newton optimization method and enhanced sampling techniques to improve the training efficiency and accuracy of neural network-based variational Monte Carlo for quantum systems.

Contribution

It proposes a novel superlinear convergence optimizer and robust sampling strategies, demonstrating significant improvements in ground-state energy estimation.

Findings

Superlinear convergence of RGN optimizer.

Reduced sampling error with parallel tempering.

High-accuracy energy estimates on large lattice models.

Abstract

Variational Monte Carlo (VMC) is an approach for computing ground-state wavefunctions that has recently become more powerful due to the introduction of neural network-based wavefunction parametrizations. However, efficiently training neural wavefunctions to converge to an energy minimum remains a difficult problem. In this work, we analyze optimization and sampling methods used in VMC and introduce alterations to improve their performance. First, based on theoretical convergence analysis in a noiseless setting, we motivate a new optimizer that we call the Rayleigh-Gauss-Newton method, which can improve upon gradient descent and natural gradient descent to achieve superlinear convergence at no more than twice the computational cost. Second, in order to realize this favorable comparison in the presence of stochastic noise, we analyze the effect of sampling error on VMC parameter updates and experimentally demonstrate that it can be reduced by the parallel tempering method. In particular, we demonstrate that RGN can be made robust to energy spikes that occur when the sampler moves between metastable regions of configuration space. Finally, putting theory into practice, we apply our enhanced optimization and sampling methods to the transverse-field Ising and XXZ models on large lattices, yielding ground-state energy estimates with remarkably high accuracy after just 200 parameter updates.