Error statistics and scalability of quantum error mitigation formulas

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dc.contributor.authorQin, Dayueen
dc.contributor.authorChen, Yanzhuen
dc.contributor.authorLi, Yingen
dc.date.accessioned2023-08-31T17:03:34Zen
dc.date.available2023-08-31T17:03:34Zen
dc.date.issued2023-04en
dc.description.abstractQuantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(epsilon N) with the gate number N before mitigation and sublinearly O(epsilon'N-gamma) after mitigation, where gamma approximate to 0.5, epsilon is the error rate of a quantum gate, and epsilon' is a protocol-dependent factor. The root N scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.en
dc.description.notesAcknowledgementsThe authors thank Hang Ren for the discussions. We acknowledge the use of simulation toolkit QuESTlink55 for this work. We acknowledge the use of IBM Quantum services for this work. D.Y.Q. and Y.L. are supported by the National Natural Science Foundation of China (Grant Nos. 11875050 and 12088101) and NSAF (Grant No. U1930403). Y.C. acknowledges support from US Department of Energy (Award No. DE-SC0019318).Note.-When preparing the manuscript, we notice a recent preprint arXiv:2111.14907 that reports the global depolarising model as an effective model of noisy quantum circuits. This work studies the distribution of measurement outcomes in circuits with single-qubit noise channels. In comparison, our work studies expected-value computing using circuits with two-qubit noise channels as the dominant error source. We focus on properties of circuits with the same circuit frame, and we use the effective model in error mitigation. Our final result is on the bias scaling of error mitigation formulas.en
dc.description.sponsorshipNational Natural Science Foundation of China [11875050, 12088101]; NSAF [U1930403]; US Department of Energy [DE-SC0019318]en
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1038/s41534-023-00707-7en
dc.identifier.eissn2056-6387en
dc.identifier.issue1en
dc.identifier.other35en
dc.identifier.urihttp://hdl.handle.net/10919/116175en
dc.identifier.volume9en
dc.language.isoenen
dc.publisherNature Portfolioen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleError statistics and scalability of quantum error mitigation formulasen
dc.title.serialNpj Quantum Informationen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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