What randomized benchmarking actually measures

Understand

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect.

• In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric $r$.
• For Clifford gates with arbitrary small errors described by process matrices, $r$ was believed to reliably correspond to the mean, over all Cliffords, of the average gate infidelity (AGI) between the imperfect gates and their ideal counterparts.
• We show that this quantity is not a well-defined property of a physical gateset.