  In this paper, we analyze the performance of randomized benchmarking
protocols on gate sets under a variety of realistic error models that include
systematic rotations, amplitude damping, leakage to higher levels, and 1/f
noise. We find that, in almost all cases, benchmarking provides better than a
factor-of-two estimate of average error rate, suggesting that randomized
benchmarking protocols are a valuable tool for verification and validation of
quantum operations. In addition, we derive new models for fidelity decay curves
under certain types of non-Markovian noise models such as 1/f and leakage
errors. We also show that, provided the standard error of the fidelity
measurements is small, only a small number of trials are required for high
confidence estimation of gate errors.
