Characterizing Universal Gate Sets via Dihedral Benchmarking

TL;DR

This paper introduces a practical protocol for robustly characterizing error rates of non-Clifford gates, including small-angle rotations, by generalizing randomized benchmarking to dihedral groups, aiding universal quantum gate assessment.

Contribution

It presents a novel dihedral benchmarking protocol that relaxes the unitary 2-design requirement, allowing efficient, error-independent characterization of universal quantum gate sets.

Findings

Enables direct benchmarking of the T gate in realistic error models

Generalizes randomized benchmarking to dihedral groups

Provides a method for error characterization independent of state-preparation and measurement errors

Abstract

We describe a practical experimental protocol for robustly characterizing the error rates of non-Clifford gates associated with dihedral groups, including gates in SU(2) associated with arbitrarily small angle rotations. Our dihedral benchmarking protocol is a generalization of randomized benchmarking that relaxes the usual unitary 2-design condition. Combining this protocol with existing randomized benchmarking schemes enables an efficient means of characterizing universal gate sets for quantum information processing in a way that is independent of state-preparation and measurement errors. In particular, our protocol enables direct benchmarking of the $T$ gate (sometime called $\pi/8$-gate) even for the gate-dependent error model that is expected in leading approaches to fault-tolerant quantum computation.