A framework for randomized benchmarking over compact groups

• Main Author: Kong, Linghang
• Format: Journal Article
• Language: English
• Published: 19-11-2021
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.2111.10357

Characterization of experimental systems is an essential step in developing
and improving quantum hardware. A collection of protocols known as Randomized
Benchmarking (RB) was developed in the past decade, which provides an efficient
way to measure error rates in quantum systems. In a recent paper
(arxiv:2010.07974), a general framework for RB was proposed, which encompassed
most of the known RB protocols and overcame the limitation on error models in
previous works. However, even this general framework has a restriction: it can
only be applied to a finite group of gates. This does not meet the need posed
by experiments, in particular the demand for benchmarking non-Clifford gates
and continuous gate sets on quantum devices. In this work we generalize the RB
framework to continuous groups of gates and show that as long as the noise
level is reasonably small, the output can be approximated as a linear
combination of matrix exponential decays. As an application, we numerically
study the fully randomized benchmarking protocol (i.e. RB with the entire
unitary group as the gate set) enabled by our proof. This provides a unified
way to estimate the gate fidelity for any quantum gate in an experiment.