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The characterization of errors in a quantum system is a fundamental step fortwo important goals. First, learning about specific sources of error isessential for optimizing experimental design and error correction methods.Second, verifying that the error is below some threshold value is required tomeet the criteria of threshold theorems. We consider the case where errors aredominated by the generalized damping channel (encompassing the common intrinsicprocesses of amplitude damping and dephasing) but may also contain additionalunknown error sources. We demonstrate the robustness of standard $T_1$ and$T_2$ estimation methods and provide expressions for the expected error inthese estimates under the additional error sources. We then derive expressionsthat allow a comparison of the actual and expected results of fine-grainedrandomized benchmarking experiments based on the damping parameters. Given theresults of this comparison, we provide bounds that allow robust estimation ofthe thresholds for fault-tolerance.

Combining $T_1$ and $T_2$ estimation with randomized benchmarking and bounding the diamond distance