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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 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. On the technical side, we develop a general perturbative description of noise in random circuits in terms of harmonic analysis that can also be used to analyze the noise-robustness of random circuit protocols beyond RB.

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Markus Heinrich, Uni Düsseldorf
Seminarraum Pohligstr.
Contact: David Gross