Non-Markovianity in Randomized Benchmarking

Joel J. Wallman, Steve Flammia, Marie Barnhill +1 more

Pedro Figueroa–Romero, Kavan Kishore Modi, Robert J. Harris +2 more

Estimating the features of noise is the first step in a chain of protocols that will someday lead to faulttolerant quantum computers.The randomized benchmarking (RB) protocol is designed with this exact mindset, estimating the average strength of noise in a quantum processor with relative ease in practice.However, RB, along with most other benchmarking and characterization methods, is limited in scope because it assumes that the noise is temporally uncorrelated (Markovian), which is increasingly evident not to be the case.Here, we combine the RB protocol with a recent framework describing non-Markovian quantum phenomena to derive a general analytical expression of the average sequence fidelity (ASF) for non-Markovian RB with the Clifford group.We show that one can identify non-Markovian features of the noise directly from the ASF through its deviations from the Markovian case, proposing a set of methods to collectively estimate these deviations, non-Markovian memory time scales, and diagnose (in)coherence of non-Markovian noise in a RB experiment.Finally, we demonstrate the efficacy of our proposal by means of several proof-of-principle examples.Our methods are directly implementable and pave the way for a better understanding of correlated noise in quantum processors.

Martin Kliesch

Shih-Xian Yang, Pedro Figueroa–Romero, Min-Hsiu Hsieh

The presence of correlations in noisy quantum circuits will be an inevitable side effect as quantum devices continue to grow in size and depth. Randomized Benchmarking (RB) is arguably the simplest method to initially assess the overall performance of a quantum device, as well as to pinpoint the presence of temporal-correlations, so-called non-Markovianity; however, when such presence is detected, it hitherto remains a challenge to operationally quantify its features. Here, we demonstrate a method exploiting the power of machine learning with matrix product operators to deduce the minimal average non-Markovianity displayed by the data of a RB experiment, arguing that this can be achieved for any suitable gate set, as well as tailored for most specific-purpose RB techniques.

Samyak Surti, Timothy J Proctor, Jordan Hines +1 more

Jordan Hines, Daniel Hothem, Marie Lu +12 more