量子多体模拟研究者终于有了一个计算资源友好、可扩展的递归架构方案——PSR-NQS 在 52×52 晶格上验证了精度，做变分蒙特卡洛的团队可以直接参考实现。
该研究提出并行扫描递归神经网络量子态（PSR-NQS），利用现代递归架构和并行化递归技术，克服了传统递归神经网络量子态在可扩展性上的局限。PSR-NQS 可在变分蒙特卡洛框架中高效训练，在一维和二维空间均取得准确基准结果。通过迭代再训练，该方法成功模拟了 52×52 的二维自旋晶格，与现有量子蒙特卡洛数据一致。这项工作表明递归架构能以较低计算资源实现可扩展的神经量子态模拟。
Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo
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.