Towards Neural Variational Monte Carlo That Scales Linearly with System Size

TL;DR

This paper introduces VQ-NQS, a neural network architecture that reduces the computational complexity of neural variational Monte Carlo methods, enabling more scalable simulations of quantum many-body systems.

Contribution

The paper proposes VQ-NQS, a novel neural network architecture that leverages vector-quantization to achieve linear scaling in system size for quantum Monte Carlo simulations.

Findings

VQ-NQS accurately reproduces ground states of 2D Heisenberg models.

Achieves approximately 10-fold reduction in FLOPs for local-energy calculations.

Demonstrates potential for scaling to larger quantum systems.

Abstract

Quantum many-body problems are some of the most challenging problems in science and are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, coupled with the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. However, the run-time of this approach scales quadratically with the number of simulated particles, constraining the practically usable NN to - in machine learning terms - minuscule sizes (<10M parameters). Considering the many breakthroughs brought by extreme NN in the +1B parameters scale to other domains, lifting this constraint could significantly expand the set of quantum systems we can accurately simulate on classical computers, both in size and complexity. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm - the source of the quadratic scaling. In our preliminary experiments, we demonstrate VQ-NQS ability to reproduce the ground state of the 2D Heisenberg model across various system sizes, while reporting a significant reduction of about ${\times}10$ in the number of FLOPs in the local-energy calculation.