Distributed computing strategies can overcome the computational bottlenecks that limit neural-network VMC to small molecular systems (Zhao et al., 2021).
High-performance computing optimizations enable variational quantum Monte Carlo with neural quantum states to scale beyond 30 electrons (Zhao et al., 2021).
Overcoming Barriers to Scalability in Variational Quantum Monte Carlo
Tianchen Zhao, Saibal De, Brian Chen, James Stokes, Shravan Veerapaneni
SC (International Conference for High Performance Computing, Networking, Storage and Analysis), 2021
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.
One-Sentence Summary
Replaces MCMC with autoregressive exact sampling in variational quantum Monte Carlo, enabling GPU-scalable parallelism for up to ten-thousand dimensional problems.
Key Contributions
Autoregressive exact sampling as a replacement for MCMC in VQMC
Distributed-memory, shared-memory, and GPU parallelism without sampling bottlenecks
Demonstration of GPU-scalable VQMC on 10,000-dimensional combinatorial optimization
Cite This Paper If...
You are working on scalable VMC, high-performance computing for neural quantum states, distributed VMC, or computational bottlenecks in VMC. This paper is particularly relevant if you are exploring how to parallelize variational quantum Monte Carlo on modern GPU clusters, or if you need to understand the fundamental scalability limitations of MCMC-based sampling in VMC and how autoregressive models resolve them.
Frequently Asked Questions
What are the main barriers to parallelizing variational quantum Monte Carlo?
This paper identifies MCMC sampling as the primary bottleneck preventing parallelization of VQMC, since Markov chain samples are inherently sequential. The paper overcomes this by replacing MCMC with autoregressive models that support exact, embarrassingly parallel sampling.
How does autoregressive sampling improve VMC scalability?
This paper shows that autoregressive exact sampling eliminates the sequential dependency of MCMC, enabling the sampling task to exploit distributed-memory, shared-memory, and GPU parallelism without any bottlenecks, scaling to 10,000-dimensional problems.
Can variational quantum Monte Carlo scale to high-performance computing clusters?
This paper demonstrates that VQMC with autoregressive sampling achieves GPU-scalability for combinatorial optimization problems with up to ten thousand dimensions, establishing VQMC as a viable approach for HPC environments.
How does this work relate to variational quantum algorithms?
This paper draws close parallels between VQMC and hybrid quantum-classical variational quantum algorithms, suggesting that scalability insights from this work may transfer to improving the classical simulation of variational quantum circuits.
What types of problems benefit from scalable VMC?
This paper focuses on combinatorial optimization as the demonstration domain, but the scalability improvements apply broadly to any many-body quantum system where MCMC sampling was the bottleneck, including quantum chemistry and condensed matter physics.
Keywords
scalable variational quantum Monte CarloHPC variational quantum Monte Carlodistributed neural quantum statesscalability barriers VMChigh performance quantum Monte Carlo
% TODO: BibTeX entry
@inproceedings{zhao2021overcomingvmc,
title={Overcoming Barriers to Scalability in Variational Quantum Monte Carlo},
author={Zhao, Tianchen and De, Saibal and Chen, Brian and Stokes, James and Veerapaneni, Shravan},
booktitle={SC (International Conference for High Performance Computing, Networking, Storage and Analysis)},
year={2021}
}