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Practical and reliable error bars for quantum process tomography

Thinh, Le Phuc and Faist, Philippe and Helsen, Jonas and Elkouss, David and Wehner, Stephanie (2019) Practical and reliable error bars for quantum process tomography. Physical Review A, 99 (5). Art. No. 052311. ISSN 2469-9926. doi:10.1103/PhysRevA.99.052311.

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Current techniques in quantum process tomography typically return a single point estimate of an unknown process based on a finite albeit large amount of measurement data. Due to statistical fluctuations, however, other processes close to the point estimate can also produce the observed data with near certainty. Unless appropriate error bars can be constructed, the point estimate does not carry any sound operational interpretation. Here, we provide a solution to this problem by constructing a confidence region estimator for quantum processes. Our method enables reliable estimation of essentially any figure of merit for quantum processes on few qubits, including the diamond distance to a specific noise model, the entanglement fidelity, and the worst-case entanglement fidelity, by identifying error regions which contain the true state with high probability. We also provide a software package, QPtomographer, implementing our estimator for the diamond norm and the worst-case entanglement fidelity. We illustrate its usage and performance with several simulated examples. Our tools can be used to reliably certify the performance of, e.g., error correction codes, implementations of unitary gates, or more generally any noise process affecting a quantum system.

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Additional Information:© 2019 American Physical Society. Received 20 August 2018; revised manuscript received 4 February 2019; published 8 May 2019. L.P.T., J.H., D.E., and S.W. are supported by an ERC Starting Grant (S.W.), an NWO VIDI Grant (S.W.), and an NWO Zwaartekracht grant (Q.S.C.). P.F. acknowledges support from the Swiss National Science Foundation (SNSF) through the Early PostDoc. Mobility Fellowship No. P2EZP2_165239 hosted by the Institute for Quantum Information and Matter (IQIM) at Caltech, from the IQIM which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant No. PHY-1733907), and from the Department of Energy Award No. DE-SC0018407.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
European Research Council (ERC)UNSPECIFIED
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Swiss National Science Foundation (SNSF)P2EZP2_165239
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Department of Energy (DOE)DE-SC0018407
Issue or Number:5
Record Number:CaltechAUTHORS:20190208-123849148
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92797
Deposited By: Bonnie Leung
Deposited On:15 Feb 2019 21:10
Last Modified:16 Nov 2021 03:53

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