  In its many variants, randomized benchmarking (RB) is a broadly used
technique for assessing the quality of gate implementations on quantum
computers. A detailed theoretical understanding and general guarantees exist
for the functioning and interpretation of RB protocols if the gates under
scrutiny are drawn uniformly at random from a compact group. In contrast, many
practically attractive and scalable RB protocols implement random quantum
circuits with local gates randomly drawn from some gate-set. Despite their
abundance in practice, for those non-uniform RB protocols, general guarantees
for gates from arbitrary compact groups under experimentally plausible
assumptions are missing. In this work, we derive such guarantees for a large
class of RB protocols for random circuits that we refer to as filtered RB.
Prominent examples include linear cross-entropy benchmarking, character
benchmarking, Pauli-noise tomography and variants of simultaneous RB. Building
upon recent results for random circuits, we show that many relevant filtered RB
schemes can be realized with random quantum circuits in linear depth, and we
provide explicit small constants for common instances. We further derive
general sample complexity bounds for filtered RB. We show filtered RB to be
sample-efficient for several relevant groups, including protocols addressing
higher-order cross-talk. Our theory for non-uniform filtered RB is, in
principle, flexible enough to design new protocols for non-universal and analog
quantum simulators.
