Randomized benchmarking for qudit Clifford gates

TL;DR

This paper extends randomized benchmarking techniques to qudit gates using unitary 2-designs, providing a new method for characterizing multi-qudit quantum operations with practical pseudocode implementation.

Contribution

The authors develop a novel qudit randomized benchmarking procedure that generalizes existing qubit methods and clarifies its unique aspects beyond multi-qubit cases.

Findings

Introduces a qudit URB protocol based on unitary 2-designs.

Shows qudit URB is not reducible to multi-qubit URB.

Provides pseudocode for practical implementation.

Abstract

We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single-and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications.