We propose and analyze a family of approximately-symmetric neural networks
for quantum spin liquid problems. These tailored architectures are
parameter-efficient, scalable, and significantly out-perform existing
symmetry-unaware neural network architectures. Utilizing the mixed-field toric
code model, we demonstrate that our approach is competitive with the
state-of-the-art tensor network and quantum Monte Carlo methods. Moreover, at
the largest system sizes (N=480), our method allows us to explore Hamiltonians
with sign problems beyond the reach of both quantum Monte Carlo and finite-size
matrix-product states. The network comprises an exactly symmetric block
following a non-symmetric block, which we argue learns a transformation of the
ground state analogous to quasiadiabatic continuation. Our work paves the way
toward investigating quantum spin liquid problems within interpretable neural
network architectures

我们提出并分析了一种近似对称的神经网络家族，用于量子自旋液体问题。我们的方法在参数效率、可扩展性方面明显优于现有的无对称神经网络体系结构，并利用混合场拓扑码模型证明我们的方法与现有的张量网络和量子蒙特卡罗方法相竞争。此外，在最大的系统尺寸（N=480）下，我们的方法可以探索存在量子蒙特卡罗和有限尺寸矩阵乘积态无法解决的带有符号问题的哈密顿量。该网络包含一个完全对称的块以及一个非对称的块，我们认为它学习了类似准绝热延续的基态变换。我们的工作为在可解释的神经网络架构下研究量子自旋液体问题铺平了道路。