Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

2026-05-13

AI Summary

Traditional recurrent neural networks are inherently sequential, making them difficult to parallelize and thus limiting their applicability to large-scale quantum many-body systems. This work proposes an autoregressive variational quantum state model based on a parallel scan recurrent architecture, marking the first introduction of modern parallelizable recurrent structures into neural quantum states. By effectively overcoming the scalability bottleneck of conventional recurrent models, the method integrates autoregressive modeling with variational Monte Carlo training to enable efficient simulation of both one- and two-dimensional systems. High-accuracy results are demonstrated on a 52×52 two-dimensional spin lattice, showing excellent agreement with established quantum Monte Carlo data and confirming the approach’s superior scalability and precision.

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 ansätze, 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.

Problem

• recurrent neural quantum states
• scalability
• variational Monte Carlo
• quantum many-body systems
• parallelization

Innovation

• parallel scan
• recurrent neural quantum states
• variational Monte Carlo
• autoregressive wave functions
• scalable neural networks