Randomized benchmarking in the presence of time-correlated dephasing noise

Randomized benchmarking (RB) has emerged as a popular and easy-to-implement experimental technique for gauging the quality of gate operations in quantum computing devices. A typical randomized procedure identifies exponential decay fidelity sequence gates increases length, rate is used to estimate gate. Our current theory RB, based on assumption time-independent or static noise gates, predicts an fidelity. Observed deviations from standard are usually attributed some amount time correlations noise, though precise mechanisms deviation have yet be fully explored. In this paper, we examine question time-correlated noise---specifically dephasing exact solvability---and elucidate circumstances which can expected, well point out situations where prevails despite presence correlations.