用物理启发的隐空间虚时演化，让量子态神经网络更透明高效。
Physics-inspired transformer quantum states via latent imaginary-time evolution
- 将Transformer量子态视为隐空间虚时演化，赋予架构物理意义。
- 在阻挫J1-J2海森堡模型上，参数更少但精度媲美或超越顶尖方法。
- 适合关注量子模拟可解释性与高效模型设计的研究者。
神经量子态（NQS）是变分蒙特卡罗框架中的强大变分族，但其架构常被视为黑箱。本文提出一种物理透明的框架，将NQS视为隐空间虚时演化的神经近似。该视角表明，标准Transformer基量子态（TQS）对应于依赖隐空间虚时的物理上无根据的有效哈密顿量。基于此，我们引入物理启发的Transformer量子态（PITQS），通过层间权重共享强制静态有效哈密顿量，并利用Trotter-Suzuki分解提升传播精度，而无需增加变分参数。在阻挫J1-J2海森堡模型上，我们的变分族实现与现有最优TQS相当或更优的精度，同时使用显著更少的变分参数。研究表明，将深度网络结构重新解读为隐空间冷却过程，可实现更具物理基础、系统化且紧凑的设计，从而弥合黑箱表达力与物理透明构造之间的鸿沟。
原文摘要 · Abstract (English)
Neural quantum states (NQS) are powerful ansätze in the variational Monte Carlo framework, yet their architectures are often treated as black boxes. We propose a physically transparent framework in which NQS are treated as neural approximations to latent imaginary-time evolution. This viewpoint suggests that standard Transformer-based NQS (TQS) architectures correspond to physically unmotivated effective Hamiltonians dependent on imaginary time in a latent space. Building on this interpretation, we introduce physics-inspired transformer quantum states (PITQS), which enforce a static effective Hamiltonian by sharing weights across layers and improve propagation accuracy via Trotter-Suzuki decompositions without increasing the number of variational parameters. For the frustrated $J_1$-$J_2$ Heisenberg model, our ansätze achieve accuracies comparable to or exceeding state-of-the-art TQS while using substantially fewer variational parameters. This study demonstrates that reinterpreting the deep network structure as a latent cooling process enables a more physically grounded, systematic, and compact design, thereby bridging the gap between black-box expressivity and physically transparent construction.
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