Real Randomized Benchmarking

TL;DR

This paper introduces real randomized benchmarking, a protocol that separately estimates the real and complex parts of quantum error rates, providing more detailed error characterization with similar resource costs as standard methods.

Contribution

It defines a new benchmarking protocol using the real Clifford group, enabling detailed error analysis for real encodings and fault-tolerant gates without full Clifford group implementation.

Findings

Enables separate estimation of real and complex error rates.

Uses the real Clifford group as an orthogonal 2-design for benchmarking.

Applicable to quantum computations on rebits and real encodings.

Abstract

Randomized benchmarking provides a tool for obtaining precise quantitative estimates of the average error rate of a physical quantum channel. Here we define real randomized benchmarking, which enables a separate determination of the average error rate in the real and complex parts of the channel. This provides more fine-grained information about average error rates with approximately the same cost as the standard protocol. The protocol requires only averaging over the real Clifford group, a subgroup of the full complex Clifford group, and makes use of the fact that it forms an orthogonal 2-design. It therefore allows benchmarking of fault-tolerant gates for an encoding which does not contain the full Clifford group transversally. Furthermore, our results are especially useful when considering quantum computations on rebits (or real encodings of complex computations), in which case the real Clifford group now plays the role of the complex Clifford group when studying stabilizer circuits.