Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

TL;DR

This paper introduces parallel scan recurrent neural quantum states (PSR-NQS), enabling scalable and efficient variational Monte Carlo simulations for large quantum many-body systems using modern recurrent architectures.

Contribution

It develops a novel parallelizable recurrent neural network framework for quantum state simulations, achieving high accuracy and scalability in two-dimensional systems.

Findings

Achieved accurate benchmarks in 1D and 2D quantum systems.

Scaled to 52x52 spin lattices with agreement to quantum Monte Carlo data.

Demonstrated recurrent architectures as practical for large-scale quantum simulations.

Abstract

Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architectures can support fast, accurate, and computationally accessible neural quantum state simulations. Using autoregressive recurrent wave functions together with recent advances in parallelizable recurrence, we develop variational ans\"atze, called parallel scan recurrent neural quantum states (PSR-NQS), which can be trained efficiently within variational Monte Carlo in one and two spatial dimensions. We demonstrate accurate benchmark results and show that, with iterative retraining, our approach reaches two-dimensional spin lattices as large as $52\times52$ while remaining in agreement with available quantum Monte Carlo data. Our results establish recurrent architectures as a practical and promising route toward scalable neural quantum state simulations with modest computational resources.