AI 中文总结
本研究提出有限可逆模型的同步认证问题，通过共享表可行性公式和精确基准，证明联合拟合与单独拟合的严格分离，并给出重复电路视界与置信测试方法。
AI 中文摘要
一个有限可逆模型可以近似单个量子门，同时在其转换表和制备上下文中保留自由度。我们提出了同步认证问题，其中一台固定控制器和一条制备定律必须重现整个电路概率集合。对于指定的框架目录、精度图和校准约束，我们给出了一个精确的共享表可行性公式，并区分了固定表的证书与完整模型类的证书。一个四框架量子比特示例展示了单独拟合两个电路与联合拟合它们之间的严格分离。一个更大的精确基准使用464个框架和一种相位对称性，该对称性消除了制备先验依赖性。我们独立地重构了其允许图，并证明了一个尖锐的重复电路视界：一台控制器在192个块内保持概率误差在1/3以内，而每个允许的控制器在第193个块时违反该阈值。另一台控制器在相同容差内重现了所有8,190个长度至多十二的非空Hadamard相位词。我们还推导了有限窗口谱障碍和有限次置信测试，并通过一个可复现的采样实验加以说明。结论涉及所述有限可逆模型类；它们并未建立通用记忆界限或物理量子硬件的差异。
英文摘要
A finite reversible model can approximate individual quantum gates while retaining freedom in its transition tables and preparation contexts. We formulate the simultaneous certification problem in which one stationary controller and one preparation law must reproduce an entire collection of circuit probabilities. For a specified frame catalogue, accuracy graph and calibration constraints, we give an exact shared-table feasibility formulation and distinguish certificates for a fixed table from certificates for the complete model class. A four-frame qubit example exhibits a strict separation between fitting two circuits individually and fitting them jointly. A larger exact benchmark uses 464 frames and a phase symmetry that removes preparation-prior dependence. We independently reconstruct its admissible graph and certify a sharp repeated-circuit horizon: one controller stays within probability error 1/3 through 192 blocks, whereas every allowed controller violates that threshold by block 193. A separate controller reproduces all 8,190 nonempty Hadamard-phase words of length at most twelve within the same tolerance. We also derive a finite-window spectral obstruction and finite-shot confidence tests, illustrated by a reproducible sampling experiment. The conclusions concern the stated finite reversible model classes; they do not establish a universal memory bound or a discrepancy for physical quantum hardware.
Comments15 pages, 3 figures, includes exact computational certificates and a reproducible finite-shot simulation study
