Continuous-variable optimization with neural network quantum states

TL;DR

This paper explores the use of continuous-variable neural network quantum states for continuous optimization, demonstrating competitive results but highlighting scaling challenges and proposing potential improvements.

Contribution

It introduces CV-NQS for continuous optimization and evaluates their performance, revealing scaling issues and suggesting extensions to improve scalability.

Findings

CV-NQS can find ground states competitively.

Scaling of CV-NQS remains a challenge.

Proposed extensions may improve scalability.

Abstract

Inspired by proposals for continuous-variable quantum approximate optimization (CV-QAOA), we investigate the utility of continuous-variable neural network quantum states (CV-NQS) for performing continuous optimization, focusing on the ground state optimization of the classical antiferromagnetic rotor model. Numerical experiments conducted using variational Monte Carlo with CV-NQS indicate that although the non-local algorithm succeeds in finding ground states competitive with the local gradient search methods, the proposal suffers from unfavorable scaling. A number of proposed extensions are put forward which may help alleviate the scaling difficulty.