发表机构
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种物理感知的排序Transformer，直接为海森堡哈密顿量学习Trotter排序，无需候选枚举或模拟，在多种几何形状上泛化至更大系统，并达到接近模拟退火参考的保真度。
AI 中文摘要
Trotter化通过顺序应用哈密顿量项来近似量子时间演化。由于非对易项会引入依赖于排序的误差，选择最优项排序是一个在阶乘搜索空间上的组合问题。先前的方法依赖于固定启发式或预定义结构化排序中的选择，这两种方法在做出选择之前都需要模拟候选方案。对于一维和二维海森堡型哈密顿量，我们转而使用物理感知的排序Transformer直接学习排序，该Transformer为每个哈密顿量项分配一个标量分数，并通过对这些分数进行排序来预测排序。物理结构通过对易子偏置注意力和反对易加权排序损失引入，模型在模拟退火（SA）参考排序上进行训练。我们分别为一阶和二阶Trotter化训练了单独的模型，每个模型都在长达14个量子比特的链和长达12个量子比特的格子上联合训练，并在16-20个量子比特的未见链以及16和20个量子比特的格子上进行评估。预测排序通过相对于SA参考的模拟保真度的中位数差距进行评估。在一阶，模型在链上达到低于10^-4的合并差距，在16和20个量子比特的三角格上分别为0.0144和0.0088，在矩形格上分别为0.0948和0.0823；在二阶，差距分别为0.0114、0.0364和0.0244，以及0.1348和0.1239。预测在一阶链实例的34%和二阶链实例的8%上超过了SA参考，并且即使两个序列不同，也能匹配其保真度，因为对易项可以在不改变Trotter酉的情况下重新排列。学习到的模型在所有三种几何形状上都能泛化到更大的系统，在链和三角格上表现最佳，并且无需候选枚举、模拟退火或保真度评估即可在一次前向传播中产生排序。
英文摘要
Trotterization approximates quantum time evolution by sequentially applying Hamiltonian terms. Because noncommuting terms introduce ordering-dependent errors, selecting an optimal term ordering is a combinatorial problem over a factorial search space. Prior approaches rely on fixed heuristics or on selection among predefined structured orderings, both of which require simulating candidates before choosing among them. For 1D and 2D Heisenberg-style Hamiltonians, we instead learn the ordering directly with a physics-aware ranking transformer that assigns a scalar score to each Hamiltonian term and predicts an ordering by sorting these scores. Physical structure enters through commutator-biased attention and an anticommutation-weighted ranking loss, and the models are trained on simulated-annealing (SA) reference orderings. We train separate models for first- and second-order Trotterization, each jointly on chains up to 14 qubits and lattices up to 12 qubits, and evaluate them on unseen chains with 16-20 qubits and lattices with 16 and 20 qubits. Predicted orderings are evaluated by the median gap in simulation fidelity to the SA reference. At first order, the model reaches a pooled gap below 10^-4 on chains, 0.0144 and 0.0088 on triangular lattices, and 0.0948 and 0.0823 on rectangular lattices at 16 and 20 qubits; at second order, the gaps are 0.0114, 0.0364 and 0.0244, and 0.1348 and 0.1239. The prediction exceeds the SA reference on 34% of first-order and 8% of second-order chain instances and can match its fidelity even when the two sequences differ because commuting terms may be rearranged without changing the Trotter unitary. The learned models generalize to larger systems across all three geometries, performing best on chains and triangular lattices, and produce an ordering in one forward pass without candidate enumeration, simulated annealing, or fidelity evaluation.
Comments8 pages, 4 figures. Accepted at 2026 IEEE 2nd International Conference on Quantum Artificial Intelligence (QAI)
