General guarantees for randomized benchmarking with random quantum circuits

Speaker: Ingo Roth (Quantum research centre, Technology Innovation Institute, Abu Dhabi, UAE)

Title: General guarantees for randomized benchmarking with random quantum circuits

Time: Wednesday, 14.12.2022 at 14:30 CET

Location: room 203 at IFPAN

Zoom link: https://us06web.zoom.us/j/88571566818

Abstract

Randomized benchmarking protocols have become the prominent tool for assessing the quality of gates on digital quantum computing platforms. In `classical’ variants of randomized benchmarking multi-qubit gates are drawn uniformly from a finite group. The functioning of such schemes can be rigorous guaranteed under realistic assumptions. In contrast, experimentally attractive and practically more scalable randomized benchmarking schemes often directly perform random circuits or use other non-uniform probability measures. An important example for such a non-uniform protocol is linear cross-entropy benchmarking. The theoretical understanding of non-uniform randomized benchmarking is still an ongoing effort. We present a new extension of general theoretical guarantees for randomized benchmarking to non-uniform measures. Combined with results on random walks, our results identify experimental parameter regimes where one can guarantee non-uniform randomized benchmarking protocols to work reliably.  On the technical side, we develop a general perturbative description of noise in random circuits in terms of harmonic analysis that can also be used to analyze the noise-robustness of random circuit protocols beyond RB.

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