用并行化循环网络实现高效量子态模拟，突破传统序列限制。
Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo
- 引入并行扫描循环结构，让递归神经网络可高效并行计算。
- 在1D和2D自旋晶格上实现52×52规模的精确模拟，结果与QMC一致。
- 适合追求低资源消耗的量子多体系统模拟研究者使用。
神经网络量子态已成为量子多体系统的重要变分框架，近期进展常依赖大规模并行架构（如Transformer）。然而，循环神经网络量子态通常被认为具有固有的顺序性，难以扩展。本文重新审视这一观点，表明现代循环架构可支持快速、准确且计算可行的神经量子态模拟。通过结合自回归循环波函数与可并行化递归的最新进展，我们提出一种并行扫描循环神经量子态（PSR-NQS）变分形式，可在一维和二维空间中高效训练。实验表明其具备高精度基准性能，并通过迭代重训练实现了高达52×52的二维自旋晶格模拟，结果与现有量子蒙特卡洛数据高度一致。这些结果证明循环架构是资源消耗适中下的可扩展神经量子态模拟的可行且有前景路径。
原文摘要 · Abstract (English)
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.
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