Interleaved Benchmarking with Single-Qubit References

arXiv:2603.05422v2 Announce Type: replace 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, identify when interleaved circuits generate sufficient randomization for the standard depolarizing approximation, and obtain 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 interleaved benchmarking protocols employing single-qubit reference sequences and show that, with appropriate post-processing, they provide a simple and accurate alternative to multi-qubit Clifford reference circuits.

Authors:Ilya A. Simakov, Arina V. Zotova, Tatyana A. Chudakova, Alena S. Kazmina, Artyom M. Polyanskiy, Nikolay N. Abramov, Mikhail A. Tarkhov, Alexander M. Mumlyakov, Igor V. Trofimov, Nikita Yu. Rudenko, Maxim V. Chichkov, Vladimir I. Chichkov, Grigoriy S. Mazhorin

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, identify when interleaved circuits generate sufficient randomization for the standard depolarizing approximation, and obtain 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 interleaved benchmarking protocols employing single-qubit reference sequences and show that, with appropriate post-processing, they provide a simple and accurate alternative to multi-qubit Clifford reference circuits.

arXiv:2603.05422 [quant-ph]

(or arXiv:2603.05422v2 [quant-ph] for this version)

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Interleaved Benchmarking with Single-Qubit References

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