Efficient Unitarity Randomized Benchmarking of Few-qubit Clifford Gates

TL;DR

This paper provides a new, efficient method for unitarity randomized benchmarking of small quantum systems, requiring significantly fewer data points for accurate coherence estimation under realistic noise conditions.

Contribution

It introduces a tight bound on data points needed for Clifford URB, improving efficiency and scalability, especially for small qubit systems with near-unitary noise.

Findings

Bound on data points scales favorably with confidence and noise parameters.

Few hundred data points suffice for single-qubit Clifford gate unitarity estimation.

Method reduces data requirements by orders of magnitude compared to previous bounds.

Abstract

Unitarity randomized benchmarking (URB) is an experimental procedure for estimating the coherence of implemented quantum gates independently of state preparation and measurement errors. These estimates of the coherence are measured by the unitarity. A central problem in this experiment is relating the number of data points to rigorous confidence intervals. In this work we provide a bound on the required number of data points for Clifford URB as a function of confidence and experimental parameters. This bound has favorable scaling in the regime of near-unitary noise and is asymptotically independent of the length of the gate sequences used. We also show that, in contrast to standard randomized benchmarking, a nontrivial number of data points is always required to overcome the randomness introduced by state preparation and measurement errors even in the limit of perfect gates. Our bound is sufficiently sharp to benchmark small-dimensional systems in realistic parameter regimes using a modest number of data points. For example, we show that the unitarity of single-qubit Clifford gates can be rigorously estimated using few hundred data points under the assumption of gate-independent noise. This is a reduction of orders of magnitude compared to previously known bounds.