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

TL;DR

This paper integrates $T_1$ and $T_2$ error estimation with randomized benchmarking to robustly characterize quantum errors, especially damping-related errors, and to bound the diamond distance for fault-tolerance verification.

Contribution

It introduces methods to combine $T_1$ and $T_2$ estimates with randomized benchmarking and derives bounds for the diamond distance, enhancing error characterization in quantum systems.

Findings

Standard $T_1$ and $T_2$ estimation methods are robust against additional errors.

Expressions for expected errors in $T_1$ and $T_2$ estimates are provided.

Bounds for fault-tolerance thresholds based on damping parameters are derived.

Abstract

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.