Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The main confounding factor in rigorously analyzing data from RB protocols is an unknown and noise-dependent distribution of survival probabilities over random sequences. We propose a hierarchical Bayesian method where these survival distributions are modeled as nonparametric Dirichlet process mixtures. Our method infers parameters of interest without additional assumptions about the underlying physical noise process. We show with numerical examples that our method works robustly for both standard and highly pathological error models. Our method also works reliably at low noise levels and with little data because we avoid the asymptotic assumptions of commonly used methods such as least-squares fitting. For example, our method produces a narrow and consistent posterior for the average gate fidelity from ten random sequences per sequence length in the standard RB protocol.
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