Decay Rates in Interleaved Benchmarking with Single-Qubit References

TL;DR

This paper provides a theoretical foundation for cross-entropy benchmarking with single-qubit references, revealing its accuracy and robustness for entangling gate characterization in quantum processors.

Contribution

It derives an analytical model for decay in single-qubit reference sequences and validates that XEB can reliably estimate multi-qubit gate fidelities without multi-qubit references.

Findings

XEB with single-qubit references matches IRB fidelity estimates

The additive error approximation often overestimates fidelities

Experimental validation on superconducting qubits confirms theoretical predictions

Abstract

Cross-entropy benchmarking (XEB) with single-qubit reference sequences is widely used to characterize multi-qubit gates in large-scale quantum processors, despite the lack of a rigorous theoretical justification. Here we show that the commonly employed additive single-qubit errors approximation underlying this approach breaks down and leads to a systematic overestimation of gate fidelities. We derive an analytical expression for the joint decay of simultaneous single-qubit reference sequences and introduce a refined expression for the interleaved gate fidelity estimation. Experiments on a superconducting quantum processor validate the theory and demonstrate that fidelities obtained using XEB with single-qubit references agree with those extracted from standard interleaved randomized benchmarking (IRB), while achieving higher precision due to reduced reference-sequence errors. Our results establish theoretical foundation for the single-qubit-based XEB and show that, with appropriate post-processing, it enables a reliable and robust approach for entangling gates benchmarking without the need for multi-qubit Clifford reference sequences.