From symmetry to structure：constructing neural network quantum states from symmetry principles

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.