发表机构
University of the Basque Country UPV/EHU; EHU Quantum Center, University of the Basque Country UPV/EHU（巴斯克大学; 巴斯克大学 EHU 量子中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在简并极限下精确刻画了深强耦合量子拉比模型的Trotter化误差，发现轨迹几何重整化并可用复振幅无额外成本校正，为一般模型提供基准。
AI 中文摘要
在深强耦合区域对量子拉比模型进行数字量子模拟，激发了对 Trotter 化误差进行精确表征的需求，而此前仅通过定性界限得知。在此，我们在精确可解的简并极限中推导出这种表征，该表征对任意耦合强度均有效。一阶 Trotter 算子具有闭式表达式，表明生成的相空间轨迹精确地位于一个相对于精确轨迹被缩放并刚性旋转的圆上，而非仅仅是近似。这种几何重整化给出了态保真度的闭式形式，其结构与深强耦合区域中支配回响的物理存活概率在结构上相同：两者都是同一个几何问题——位移福克态的可区分性——应用于相空间中两对不同点。我们进一步表明，通过将 Trotter 步长耦合提升为复振幅，这种几何误差可以精确校正，且不增加电路成本。这些在精确可解的简并极限中获得的结果，为一般拉比模型中的 Trotter 化误差提供了基准。
英文摘要
Digital quantum simulation of the quantum Rabi model in the deep strong coupling regime motivates the need for an exact characterization of Trotterization errors, so far known only through qualitative bounds. Here we derive such a characterization in the exactly solvable degenerate limit, valid for arbitrary coupling strength. The first-order Trotter operator admits a closed expression, showing that the generated phase-space trajectory lies exactly on a circle that is rescaled and rigidly rotated with respect to the exact one, rather than merely approximating it. This geometric renormalization yields a closed form for the state fidelity, structurally identical to the physical survival probability governing revivals in the deep strong coupling regime: both are the same geometric question -- the distinguishability of a displaced Fock state -- applied to two different pairs of points in phase space. We further show that this geometric error is exactly correctable by promoting the Trotter-step coupling to a complex amplitude, at no additional circuit cost. These results, obtained in the exactly solvable degenerate limit, provide a benchmark for Trotterization errors in the general Rabi model.
Comments9 pages, 4 figures
