AI 中文总结
该研究将哈密顿量对称性嵌入神经量子态（NQS）的变分参数化，通过几何正则化压缩参数空间，在保持基态精度的同时大幅减少参数数量、降低训练成本，提升了NQS的优化效率。
AI 中文摘要
神经量子态（NQS）是极具表达力的变分波函数，但其优化常受冗余参数与条件不佳的损失空间瓶颈制约。我们证明，将哈密顿量对称性直接嵌入变分参数化可从几何上正则化该学习问题。对于玻尔兹曼族NQS，我们通过沿物理几何轨道绑定局域泡利Z生成元来强制对称性，在优化前解析地压缩可训练系数空间。为量化所得优化几何，我们引入基于优化损失空间雅可比矩阵与海森矩阵的几何度量，该框架可评估对应高质量低能解的物理可达态空间占比。在横场伊辛模型（TFIM）与XXZ自旋链上评估该方法，结果显示对称性编译可移除绝大多数参数，同时在报告基准的分辨率内保持基态精度；在大尺寸TFIM系统中，强空间约束将数千个参数压缩至数十个，大幅提升运行时间。我们的几何诊断表明，对称性通过将可达态空间集中在低能解周围并保留宽目标盆地，生成更有利的目标感知几何。综上，结果表明对称性编译将NQS的表达力集中于目标问题相关的态，从而在不牺牲精度的前提下减小模型规模、降低训练成本。
英文摘要
Neural quantum states (NQS) offer highly expressive variational wavefunctions, but their optimization is frequently bottlenecked by redundant parameters and poorly conditioned landscapes. We demonstrate that embedding Hamiltonian symmetries directly into the variational parameterization geometrically regularizes this learning problem. For Boltzmann-family NQS, we enforce symmetries by tying local Pauli-$Z$ generators along physical geometric orbits, analytically collapsing the trainable coefficient space prior to optimization. To quantify the resulting optimization geometry, we introduce a geometric metric built on the Jacobian and Hessian of the optimization landscape. This framework evaluates the fraction of the physically accessible state space that corresponds to high-quality, low-energy solutions. Evaluating our approach on transverse-field Ising (TFIM) and XXZ spin chains shows that symmetry compilation excises the vast majority of parameters while maintaining ground-state accuracy within the resolution of the reported benchmarks. In large TFIM systems, strong spatial constraints compress thousands of parameters down to tens, delivering substantial runtime accelerations. Our geometric diagnostics indicate that symmetry produces a more favorable target-aware geometry by concentrating the reachable state space around low-energy solutions while retaining broad target basins. Together, our results indicate that symmetry compilation concentrates the expressive power of NQS on states relevant to the target problem, thereby reducing model size and training cost without sacrificing accuracy.
