Markovianization through Dynamical Decoupling in Randomized Benchmarking

While a myriad of techniques for the characterization of quantum noise in the so-called Markovian, i.e., memoryless, regime have been developed to date, it is expected for temporal correlations and memory effects to become one of the major contributors to errors as quantum systems scale up in size and depth. We demonstrate the effectiveness of incorporating Dynamical Decoupling (DD) [1,2] and Randomized Benchmarking (RB) [3,4], two of the most user-friendly protocols known hitherto, to simultaneously consume temporal correlations, i.e., non-Markovianity, and predict average gate fidelities of effectively Markovianized noise.

We analytically predict a non-Markovian Average Sequence Fidelity (ASF) decay reducing to its Markovian counterpart, plus perturbative non-Markovian corrections, upon the application of suitable ideal DD pulses on a broad class of non-Markovian noise models. Furthermore, under finite-width DD pulses, we simulate and analyze the ASF for realistic noise sources, still obtaining an effective Markovianization of RB data in the fast and small-width DD sequence limit. Our results show a convenient and effective way of consuming non-Markovianity while benchmarking the error rates of the resulting Markovianized noise.

[1] G. D. Berk et. al., arXiv:2110.02613 [quant-ph] (2021).

[2] N. Ezzel et. al., arXiv:2207.03670 [quant-ph] (2022).

[3] J. Helsen et. al., PRX Quantum, 3, 020357 (2022).

[4] P. Figueroa-Romero, K. Modi & M.-H. Hsieh, arXiv:2202.11338 [quant-ph] (2022).