AI 中文总结
该研究针对受监控拓扑不变量的后选择瓶颈，用随机对称本征态、普通边界监控与离线扭曲解码器替代扭曲实验，重构SPT通量-电荷响应，可确定其拓扑类并验证形变。
AI 中文摘要
一类受监控拓扑不变量会比较具有相同随机记录的普通量子轨迹与对称扭曲量子轨迹，因此直接估计需要指数成本的匹配记录后选择。我们用具有已知电荷的均匀随机对称本征态、普通边界监控以及离线扭曲解码器替代扭曲量子实验，它们的关联产生了精确的有限时间响应恒等式，消除了这一实验采样瓶颈。当普通电荷变得尖锐且普通到通量的形变具有平凡的净读出特征流时，该响应收敛到对称保护拓扑（SPT）相的投影对易子；此时生成元对响应可确定其有限阿贝尔上同调类。旁观者区的交叉可能会闭合全局李雅普诺夫间隙，但不会改变该特征值响应。在受监控团簇电路中，解码器是精确的，在高斯极限下为多项式复杂度，而高斯衰减重构可处理相互作用记录；独立的联合区光谱学与效应态诊断验证了该拓扑形变。
英文摘要
A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.
