用注意力机制自动发现哈密顿量的对称性，提升物理模型理解效率。
Attention-based optimizer for symmetry finding
- 基于集合变换器与自注意力编码关联关系，搜索保罗矩阵对称性。
- 在伊辛与拓扑码模型中近乎确定地找到对称性，优于现有方法。
- 适用于物理系统对称性发现，适合量子计算与理论物理研究者。
对称性发现对于理解物理模型至关重要。本文提出一种优化框架，用于搜索哈密顿量的保罗对称性，融合机器学习与自动化对称性识别。该框架基于集合变换器架构，利用自注意力机制编码保罗字符串间的成对及高阶相关性，解码为候选对称性，并通过定制的交换关系目标函数进行优化，最终映射为输入哈密顿量的对称性。我们在随机保罗哈密顿量、周期性一维与二维横场伊辛模型以及拓扑码上测试该方法。结果显示，在物理哈密顿量（伊辛与拓扑码）上，该框架以近确定性概率成功，显著优于当前最优策略；对于随机保罗哈密顿量，我们估算出在固定设计规格下，实现高成功率所需并行启动次数与GPU数量。
原文摘要 · Abstract (English)
Finding symmetries is crucial for understanding physical models. In this work, we present an optimization framework that searches Pauli symmetries of Hamiltonians, merging the fields of machine learning with automated symmetry finding. Built on a Set-Transformer architecture, our framework uses self-attention to encode the pairwise and higher-order correlations among the Pauli-Strings. The relations are then decoded as a candidate, which is further optimized with a custom commutation-based objective, and mapped to a symmetry of the input Hamiltonian. We apply our method to random Pauli Hamiltonians, periodic one and two dimensional transverse-field Ising model and the Toric code. We show that for physical Hamiltonians (Ising and Toric), our framework succeeds with near-deterministic probability while providing substantial advantage compared to state-of-the-art strategies. For random Pauli Hamiltonians, we estimate the required computational resources, specifically the number of parallel starts and the number of GPUs, to find a symmetry with high success probability under fixed design specifications.
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