High-fidelity fully randomized benchmarking and testing for time-dependent errors

Randomized benchmarking (RB) is a widely used strategy to assess the quality of quantum gates in a computational context. One topic of recent interest in RB has been the detection and interpretation of time-dependent errors. Here, we present the design, implementation, and analysis of single-qubit, fully randomized, Clifford RB experiments that are optimized for sensitivity to time-dependent errors. Full randomization requires that each random sequence is run only once, which crucially allows for hypothesis testing based on maximum-likelihood inference and also improves signal-to-noise of the experiment. For each RB experiment, we tested two hypotheses: 1. the success probability decays as a single exponential, and 2. the success probability decays as a mixture of exponentials. Such a mixture model can arise when the gate errors fluctuate randomly between experimental trials. As a demonstration, we implemented an RB experiment with intentionally-applied, trial-to-trial fluctuating errors, and then implemented it again with errors that grew systematically and identically during each trial. In both cases we find evidence against a single exponential decay, and only in the second case do we find evidence against a mixture of exponential decays. Finally, we report the results of an RB experiment with a maximum sequence length of 1e5 that achieves a step error of 1.60(05)e-6, comparable to the lowest previously-reported errors. In this experiment we find evidence against both hypotheses, which we interpret as an indication that errors late in a sequence are larger than errors earlier.