受物理启发的变换器量子态 via 隐含虚时间演化
Physics-inspired transformer quantum states via latent imaginary-time evolution
AI总结：
本文提出受物理启发的变换器量子态（PITQS），通过共享权重和Trotter-Suzuki分解提高精度，以更物理化的视角设计量子态近似方法。
摘要：
神经量子态（NQS）是变分蒙特卡洛框架中的强大近似方法，但其架构往往被视为黑箱。我们提出了一种物理上透明的框架，其中NQS被视为对隐含虚时间演化的神经近似。这一观点表明，标准的基于变换器的NQS（TQS）架构对应于在潜空间中依赖于虚时间的物理上不合理的有效哈密顿量。基于这一解释，我们引入了受物理启发的变换器量子态（PITQS），通过在层之间共享权重来强制静态有效哈密顿量，并通过 Trotter-Suzuki 分解提高传播精度，而无需增加变分参数的数量。对于受挫的J₁-J₂ Heisenberg模型，我们的近似方法在使用显著较少的变分参数的情况下，其准确性与或超过最先进的TQS相当。本研究证明了将深度网络结构重新解释为隐含冷却过程能够实现更物理上严谨、系统性和紧凑的设计，从而弥合黑箱表达力和物理上透明构造之间的差距。
英文摘要：
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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