  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.
