AI 中文总结
本研究针对循环神经量子态（RNN-based NQS）在曲率优化器下训练不稳定的问题，通过正则化技术稳定最小步长随机重构（minSR）方法，在多个量子模型上验证了其性能优于Adam优化器，为自回归NQS结合现代优化技术解决量子模拟问题提供了可行路径。
AI 中文摘要
神经量子态（NQS）是一种基于神经网络的强大变分框架，用于表示多体波函数并求解基态。循环神经网络（RNN）因计算成本相对较低且具备自回归特性（可实现完美采样）而极具应用前景。据报道，RNN在基于曲率的优化器（如最小步长随机重构（minSR）方法）下训练不稳定。本文针对这一问题，提出通过简单的正则化技术使minSR稳定，仅需少量样本即可实现基于RNN的NQS的鲁棒训练。在一维横场伊辛模型和一维团簇态上，本文方法的性能优于Adam优化器；在二维海森堡模型和J₁-J₂模型上，也取得了有竞争力的结果。本研究为将现代优化技术与自回归NQS结合以解决量子模拟领域的开放问题提供了可行途径。
英文摘要
Neural Quantum States (NQS) provide a powerful neural network-based variational framework for representing many-body wave functions and solving for ground states. Recurrent Neural Networks (RNNs) are particularly promising owing to their relatively low computational cost and their autoregressive property, which enables perfect sampling. Recently, RNNs have been reported to be unstable under curvature-based optimizers such as the minimum-step stochastic reconfiguration (minSR) method. In this paper, we address this perceived limitation and show that minSR can be stabilized through simple regularization techniques, enabling robust training of RNN-based NQS with only a few samples. Our approach outperforms the Adam optimizer on the one-dimensional transverse-field Ising model and the one-dimensional cluster state, and provides competitive results on the two-dimensional Heisenberg and $J_1-J_2$ models. This work offers a promising pathway for using modern optimization techniques with autoregressive NQS to address open questions in quantum simulation.
Comments24 pages, 6 figures, 2 tables
