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从对称性出发：构造蕴含物理结构的神经网络量子态
From symmetry to structure：constructing neural network quantum states from symmetry principles
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摘要: 量子多体系统波函数复杂度随粒子数呈指数增长，传统数值方法难以有效求解强关联体系问题。神经网络量子态(NQS)为波函数表征提供了全新变分范式，但单纯黑箱网络存在训练成本高、物理约束缺失等缺陷。文章以对称性为核心主线，综述其在神经网络量子态结构设计中的嵌入方法，涵盖交换对称性、反对称性、空间对称、粒子守恒、规范对称等关键类型。研究表明，将对称性内蕴于神经网络量子态可显著降低模型参数量、提升训练效率，赋予其物理可解释性，成为衔接量子多体物理与机器学习的核心桥梁。Abstract: The complexity of quantum many-body wavefunctions grows exponentially with system size, making strongly correlated systems challenging for traditional numerical methods. The neural network quantum state (NQS) algorithm provides a new variational paradigm for wavefunction representation, yet purely black-box neural architectures often suffer from high training costs and the lack of physical constraints. Centered on symmetry principles, this article reviews how various symmetries can be embedded into NQS architectures, including exchange symmetry, antisymmetry, spatial symmetry, particle-number conservation, and gauge symmetry. Existing studies show that incorporating symmetries intrinsically into NQS can substantially reduce the number of model parameters, improve training efficiency, and enhance physical interpretability, establishing a key bridge between quantum many-body physics and machine learning.
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