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Recovering Quantum Gates from Few Average Gate Fidelities

Roth, I. and Kueng, R. and Kimmel, S. and Liu, Y.-K. and Gross, D. and Eisert, J. and Kliesch, M. (2018) Recovering Quantum Gates from Few Average Gate Fidelities. Physical Review Letters, 121 (17). Art. No. 170502. ISSN 0031-9007. doi:10.1103/physrevlett.121.170502.

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Characterizing quantum processes is a key task in the development of quantum technologies, especially at the noisy intermediate scale of today’s devices. One method for characterizing processes is randomized benchmarking, which is robust against state preparation and measurement errors and can be used to benchmark Clifford gates. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. In this Letter, we show that the favorable features of both approaches can be combined. For characterizing multiqubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured with respect to random Clifford unitaries. Moreover, for general unital quantum channels, we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity—a figure of merit characterizing the coherence of a process.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Gross, D.0000-0001-8888-3028
Kliesch, M.0000-0002-8009-0549
Additional Information:© 2018 American Physical Society. Received 5 May 2018; published 24 October 2018. We thank Steven T. Flammia, Christian Krumnow, Robin Harper, and Michaeł Horodecki for inspiring discussions and helpful comments. R. K. is particularly grateful for a “peaceful disagreement” (we borrow this term from Ref. [88]) with Mateus Araújo that ultimately led to our current understanding of the relation between Clifford gates and tight frames. We used code from Refs. [89–91] to run our simulations. The work of I. R., R. K., and J. E. was funded by analog quantum simulators (AQuS), DFG (Grants No. SPP1798 CoSIP, No. EI 519/9-1, No. EI 519/7-1, and No. EI 519/14-1), the ERC (TAQ), and the Templeton Foundation. The project leading to this application has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant agreement No. 817482 (PASQUANS). “Parts of Y. K. L.’s work were carried out in the context of the MURI project ‘Optimal Measurements for Scalable Quantum Technologies’ funded by the Air Force Office of Scientific Research. Contributions to this work by NIST, an agency of the U.S. Government, are not subject to U.S. copyright. Any mention of commercial products does not indicate endorsement by NIST. D. G.’s work has been supported by the Excellence Initiative of the German Federal and State Governments (ZUK 81), the ARO under Contract No. W911NF-14-1-0098 (Quantum Characterization, Verification, and Validation), Universities Australia and DAAD’s Joint Research Co-operation Scheme (using funds provided by the German Federal Ministry of Education and Research), and the DFG (SPP1798 CoSIP, Project No. B01 of CRC 183). The work of M. K. was funded by the National Science Centre, Poland within the project Polonez (Project No. 2015/19/P/ST2/03001), which has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant No. 665778.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SPP1798
Deutsche Forschungsgemeinschaft (DFG)EI 519/9-1
Deutsche Forschungsgemeinschaft (DFG)EI 519/7-1
Deutsche Forschungsgemeinschaft (DFG)EI 519/14-1
European Research Council (ERC)817482
John Templeton FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)ZUK 81
Army Research Office (ARO)W911NF-14-1-0098
Universities AustraliaUNSPECIFIED
Deutscher Akademischer Austauschdienst (DAAD)UNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)CRC 183
National Science Centre (Poland)2015/19/P/ST2/03001
Marie Curie Fellowship665778
Issue or Number:17
Record Number:CaltechAUTHORS:20181025-104453537
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90413
Deposited By: Tony Diaz
Deposited On:25 Oct 2018 18:11
Last Modified:16 Nov 2021 03:32

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