Abstract

We investigate randomized benchmarking in a general setting with quantum gates that form a representation, not necessarily an irreducible one, of a finite group. We derive an estimate for the average fidelity, to which experimental data may then be calibrated. The number of parameters that we need to fit is closely related to the structure of quantum channels that are covariant w.r.t. the representation at hand. Therefore, we also discuss how results on the structure of covariant channels can be used to improve randomized benchmarking protocols. Furthermore, we establish that randomized benchmarking can be achieved by the sole implementation of quantum gates that generate the group as well as one additional arbitrary group element if the quantum channel that describes the noise was close to a covariant channel. The efficiency of this protocol depends on mixing times of random walks on the group and we also briefly discuss how new results in this direction could improve our protocol.