Overcoming barriers to scalability in variational quantum Monte Carlo

TL;DR

This paper demonstrates how replacing MCMC sampling with autoregressive models in VQMC enables scalable, parallelized quantum Monte Carlo computations, achieving GPU scalability for high-dimensional problems.

Contribution

It introduces the use of autoregressive models with exact sampling to overcome parallelization barriers in VQMC, enhancing scalability.

Findings

Achieved GPU scalability for VQMC in high-dimensional problems

Demonstrated parallelization of sampling step using autoregressive models

Solved up to ten-thousand dimensional combinatorial optimization problems

Abstract

The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and the emerging hybrid quantum-classical computational paradigm of variational quantum algorithms. VQMC overcomes the curse of dimensionality by performing alternating steps of Monte Carlo sampling from a parametrized quantum state followed by gradient-based optimization. While VQMC has been applied to solve high-dimensional problems, it is known to be difficult to parallelize, primarily owing to the Markov Chain Monte Carlo (MCMC) sampling step. In this work, we explore the scalability of VQMC when autoregressive models, with exact sampling, are used in place of MCMC. This approach can exploit distributed-memory, shared-memory and/or GPU parallelism in the sampling task without any bottlenecks. In particular, we demonstrate the GPU-scalability of VQMC for solving up to ten-thousand dimensional combinatorial optimization problems.