The characterization of errors in a quantum system is a fundamental step for two important goals. First, learning about specific sources of error is essential for optimizing experimental design and error correction methods. Second, verifying that the error is below some threshold value is required to meet the criteria of threshold theorems. We consider the case where errors are dominated by the generalized damping channel (encompassing the common intrinsic processes of amplitude damping and dephasing) but may also contain additional unknown error sources. We demonstrate the robustness of standard $T_1$ and $T_2$ estimation methods and provide expressions for the expected error in these estimates under the additional error sources. We then derive expressions that allow a comparison of the actual and expected results of fine-grained randomized benchmarking experiments based on the damping parameters. Given the results of this comparison, we provide bounds that allow robust estimation of the thresholds for fault-tolerance.

中文翻译：

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将T1和T2估计与随机基准进行组合并限制菱形距离

量子系统中的错误表征是实现两个重要目标的基本步骤。首先，了解错误的具体来源对于优化实验设计和错误纠正方法至关重要。其次，需要验证误差在某个阈值以下才能满足阈值定理的标准。我们考虑的情况是误差由广义阻尼通道（包含振幅阻尼和相移的常见内在过程）主导，但也可能包含其他未知误差源。我们展示了标准的稳健性${Ť}_{\mathrm{1个}}$ 和 ${Ť}_2$估计方法，并在其他误差源下提供这些估计中预期误差的表达式。然后，我们得出表达式，该表达式允许根据阻尼参数比较细粒度随机基准测试的实际结果和预期结果。给定此比较的结果，我们提供了允许可靠估计容错阈值的界限。