Neural network quantum state with proximal optimization: a ground-state searching scheme based on variational Monte Carlo

TL;DR

This paper introduces a novel neural network quantum state optimization method using proximal optimization within variational Monte Carlo, improving stability and efficiency in ground-state searches for quantum many-body systems.

Contribution

The paper presents a new VMC-PO algorithm that reuses samples for multiple updates, reducing complexity and enhancing stability compared to traditional methods.

Findings

Achieves ground-state energies comparable to state-of-the-art methods.

Reduces numerical instabilities during network updates.

Simplifies implementation relative to stochastic reconfiguration.

Abstract

Neural network quantum states (NQS), incorporating with variational Monte Carlo (VMC) method, are shown to be a promising way to investigate quantum many-body physics. Whereas vanilla VMC methods perform one gradient update per sample, we introduce a novel objective function with proximal optimization (PO) that enables multiple updates via reusing the mismatched samples. Our VMC-PO method keeps the advantage of the previous importance sampling gradient optimization algorithm [L. Yang, {\it et al}, Phys. Rev. Research {\bf 2}, 012039(R)(2020)] that efficiently uses sampled states. PO mitigates the numerical instabilities during network updates, which is similar to stochastic reconfiguration (SR) methods, but achieves an alternative and simpler implement with lower computational complexity. We investigate the performance of our VMC-PO algorithm for ground-state searching with a 1-dimensional transverse-field Ising model and 2-dimensional Heisenberg antiferromagnet on a square lattice, and demonstrate that the reached ground-state energies are comparable to state-of-the-art results.