A general framework for randomized benchmarking

Randomized benchmarking (RB) has over the past decade become the gold standard for characterizing quantum gates, and a great many variations have been devised. In this work, we develop a comprehensive framework of RB, general enough to encompass almost all known RB protocols. This framework allows us to rigorously guarantee, under realistic conditions, that the output of a RB experiment is well-described by a linear combination of matrix exponential decays. We complement this with a detailed discussion of the RB fitting problem: we discuss modern signal processing techniques and their guarantees, give analytical sample complexity bounds, and numerically evaluate their performance. To reduce the resource demands of this fitting problem, we also provide scalable post-processing techniques to isolate exponential decays, improving the feasibility of a large set of RB protocols. These techniques generalize previously proposed methods such as character RB and linear-cross entropy benchmarking. Finally we discuss the relation between RB decay rates and the average fidelity in full generality. On the technical side, our work significantly extends the recently developed Fourier-theoretic perspective on RB and combines it with advanced perturbation theory and ideas from signal processing.