发表机构
University of Georgia; GyriQAI, Inc.; University of Tennessee at Chattanooga; Augusta University; Oak Ridge National Laboratory（佐治亚大学; GyriQAI公司; 田纳西大学查塔努加分校; 奥古斯塔大学; 橡树岭国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究相干量子比特噪声中相干过旋转故障的估计难题，该故障难以通过常规方法估计。提出用对数测量设计解决，证明其可行性，通过模拟验证，还观察到在IBM Heron硬件上的偏差差距，为量子处理器校准提供新方法。
AI 中文摘要
校准量子处理器意味着估计误差参数，而估计理论通常假设难以估计的参数是微弱的：其信号微弱但存在，因此更多的重复或更丰富的模型将恢复它。对于一种主要的硬件故障，这个假设不成立。相干过旋转是一种小的系统门校准错误。通过设备返回的最便宜的数据——一个固定基直方图——来测量，它不是微弱的而是不存在的：一阶情况下它使分布不变，与补偿随机误差无法区分，就像两个数无法从它们的和中分离出来一样。对于在规范输入上具有已知支持的对易单比特和两比特横向过旋转，直方图的费希尔信息在零角度处沿故障方向是奇异的，其克拉美 - 罗界是无穷大的，并且没有有限方差、局部无偏估计器可以恢复它。在一般非零角度下，简并部分解除；超过四个比特时完全解除，留下条件限制而非不存在作为障碍。解决方案是更丰富的测量，而不是更丰富的模型：一组固定的、对数级小的额外设置使每个这样的故障可见。仅可见性是不够的。采样成本由条件限制而非覆盖范围决定，通过一个下限，其完整族的封闭形式在比特数上呈指数级小。我们证明了不可能性和解决方案，在精确模拟中都得到了证实，表明条件限制预测了数百种设计中的恢复误差，并在IBM Heron硬件上观察到3 - 5倍的偏差差距作为一致性检查。非对易故障和未知支持仍然是未解决的问题。
英文摘要
Calibrating a quantum processor means estimating gate-error parameters from data, and a hard-to-estimate parameter is usually assumed to leave a weak signature more repetitions will resolve. Coherent over-rotations break that premise. For commuting single- and two-qubit transverse over-rotations with known support on a computational-basis input, the passive histogram is exactly invariant under a sign group acting on the coherent angles, of order $2^{n+1}$ for the complete family with $n\ge2$, so no estimator resolves the signs uniformly at any sample size. A calibration correction applied with the wrong sign doubles the rotation error it should remove. At zero angle the obstruction turns continuous, with a Fisher information singular along every coherent direction and an infinite Cramér-Rao bound. At generic angles the continuous defect clears for $5\le n\le8$, the range we compute, while the sign degeneracy persists. Covering the support removes both, and a design resolves the signed angles uniformly exactly when it covers. On $|η_R|<π/2$, $0\le p_R<1/2$ coverage is constructive, returning each angle in closed form from a ratio of two measured expectations without knowing the rates. A twirl-free code of $\lceil\log_2(n+1)\rceil$ added product-Pauli settings covers, and for the complete family none uses fewer. Conditioning then sets the Cramér-Rao cost, and we give its floor explicitly. Exact computation matches the theory, the passive fit stays at chance on the signs at every budget while the closed-form inverse recovers them, and angle magnitudes on two IBM Heron processors follow the conditioning ordering.
