Probabilistic Computers for Neural Quantum States

TL;DR

This paper demonstrates that probabilistic computing hardware, specifically FPGA-based systems, can significantly accelerate the sampling process in neural quantum state simulations, enabling larger system sizes and deeper models.

Contribution

It introduces a novel FPGA-based probabilistic computer for neural quantum state sampling and a dual-sampling algorithm for training deep Boltzmann machines efficiently.

Findings

Accurate ground-state energies for 80x80 lattices using FPGA-based sampling.

Successful training of deep Boltzmann machines on a single FPGA for 30x30 systems.

Probabilistic hardware overcomes sampling bottlenecks in quantum many-body simulations.

Abstract

Neural quantum states efficiently represent many-body wavefunctions with neural networks, but the cost of Monte Carlo sampling limits their scaling to large system sizes. Here we address this challenge by combining sparse Boltzmann machine architectures with probabilistic computing hardware. We implement a probabilistic computer on field-programmable gate arrays (FPGAs) and use it as a fast sampler for energy-based neural quantum states. For the two-dimensional transverse-field Ising model at criticality, we obtain accurate ground-state energies for lattices up to 80$\times$80 (6400 spins) using a custom multi-FPGA cluster. Furthermore, we introduce a dual-sampling algorithm to train deep Boltzmann machines, replacing intractable marginalization with conditional sampling over auxiliary layers. This enables the training of sparse deep models and improves parameter efficiency relative to shallow networks. We further implement this algorithm on a single FPGA, demonstrating the training of deep Boltzmann machines for systems as large as $30 \times 30$ (900 spins). Together, these results demonstrate that probabilistic hardware can overcome the sampling bottleneck in variational simulation of quantum many-body systems, opening a path to larger system sizes and deeper variational architectures.