{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T04:09:47Z","timestamp":1781582987118,"version":"3.54.5"},"reference-count":69,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T00:00:00Z","timestamp":1605571200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>As increasingly impressive quantum information processors are realized in laboratories around the world, robust and reliable characterization of these devices is now more urgent than ever. These diagnostics can take many forms, but one of the most popular categories is<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">tomography<\/mml:mtext><\/mml:mrow><\/mml:math>, where an underlying parameterized model is proposed for a device and inferred by experiments. Here, we introduce and implement efficient operational tomography, which uses experimental observables as these model parameters. This addresses a problem of ambiguity in representation that arises in current tomographic approaches (the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">gauge problem<\/mml:mtext><\/mml:mrow><\/mml:math>). Solving the gauge problem enables us to efficiently implement operational tomography in a Bayesian framework computationally, and hence gives us a natural way to include prior information and discuss uncertainty in fit parameters. We demonstrate this new tomography in a variety of different experimentally-relevant scenarios, including standard process tomography, Ramsey interferometry, randomized benchmarking, and gate set tomography.<\/jats:p>","DOI":"10.22331\/q-2020-11-17-364","type":"journal-article","created":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T18:11:36Z","timestamp":1605636696000},"page":"364","source":"Crossref","is-referenced-by-count":13,"title":["Operational, gauge-free quantum tomography"],"prefix":"10.22331","volume":"4","author":[{"given":"Olivia","family":"Di Matteo","sequence":"first","affiliation":[{"name":"TRIUMF, Vancouver, British Columbia, Canada V6T2A3"},{"name":"Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, Canada"},{"name":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John","family":"Gamble","sequence":"additional","affiliation":[{"name":"Microsoft Research, Quantum Architectures and Computation Group, Redmond, Washington 98052, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chris","family":"Granade","sequence":"additional","affiliation":[{"name":"Microsoft Research, Quantum Architectures and Computation Group, Redmond, Washington 98052, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kenneth","family":"Rudinger","sequence":"additional","affiliation":[{"name":"Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nathan","family":"Wiebe","sequence":"additional","affiliation":[{"name":"Microsoft Research, Quantum Architectures and Computation Group, Redmond, Washington 98052, USA"},{"name":"Department of Physics, University of Washington, Seattle, WA 98195, USA"},{"name":"Pacific Northwest National Laboratory, Richland, WA 99352, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2020,11,17]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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Blume-Kohout, ``Optimal, reliable estimation of quantum states,'' New J. Phys. 12, 043034 (2010).","DOI":"10.1088\/1367-2630\/12\/4\/043034"},{"key":"5","doi-asserted-by":"publisher","unstructured":"F. Husz\u00e1r and N. M. T. Houlsby, ``Adaptive Bayesian quantum tomography,'' Physical Review A 85, 052120 (2012).","DOI":"10.1103\/PhysRevA.85.052120"},{"key":"6","doi-asserted-by":"crossref","unstructured":"D. C. McKay, A. W. Cross, C. J. Wood, and J. M. Gambetta, ``Correlated randomized benchmarking,'' (2020), arXiv:2003.02354 [quant-ph].","DOI":"10.1103\/PhysRevLett.122.200502"},{"key":"7","doi-asserted-by":"publisher","unstructured":"M. Quadeer, M. Tomamichel, and C. Ferrie, ``Minimax quantum state estimation under bregman divergence,'' Quantum 3, 126 (2019).","DOI":"10.22331\/q-2019-03-04-126"},{"key":"8","doi-asserted-by":"publisher","unstructured":"P. Cerfontaine, R. Otten, and H. Bluhm, ``Self-consistent calibration of quantum gate sets,'' (2019), arXiv:1906.00950 [quant-ph] https:\/\/doi.org\/10.1103\/PhysRevApplied.13.044071.","DOI":"10.1103\/PhysRevApplied.13.044071"},{"key":"9","unstructured":"T. Guff, Y. R. Sanders, N. A. McMahon, and A. Gilchrist, ``Decision-making in quantum state discrimination,'' (2019), arXiv:1906.09737 [quant-ph]."},{"key":"10","doi-asserted-by":"crossref","unstructured":"L. J. Fiderer, J. Schuff, and D. Braun, ``Neural-network heuristics for adaptive bayesian quantum estimation,'' (2020), arXiv:2003.02183 [quant-ph].","DOI":"10.1103\/PRXQuantum.2.020303"},{"key":"11","doi-asserted-by":"publisher","unstructured":"J. M. Lukens, K. J. Law, A. Jasra, and P. Lougovski, ``A practical and efficient approach for bayesian quantum state estimation,'' (2020), arXiv:2002.10354 [quant-ph] https:\/\/doi.org\/10.1088\/1367-2630\/ab8efa.","DOI":"10.1088\/1367-2630\/ab8efa"},{"key":"12","doi-asserted-by":"publisher","unstructured":"J. B. 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Geller, ``Rigorous measurement error correction,'' (2020), arXiv:2002.01471 https:\/\/doi.org\/10.1088\/2058-9565\/ab9591 [quant-ph].","DOI":"10.1088\/2058-9565\/ab9591"},{"key":"22","doi-asserted-by":"publisher","unstructured":"L. Govia, G. Ribeill, D. Rist\u00e8, M. Ware, and H. Krovi, ``Bootstrapping quantum process tomography via a perturbative ansatz,'' Nature communications 11, 1 (2020).","DOI":"10.1038\/s41467-020-14873-1"},{"key":"23","doi-asserted-by":"publisher","unstructured":"S. S. Hong, A. T. Papageorge, P. Sivarajah, G. Crossman, N. Didier, A. M. Polloreno, E. A. Sete, S. W. Turkowski, M. P. da Silva, and B. R. Johnson, ``Demonstration of a parametrically activated entangling gate protected from flux noise,'' Physical Review A 101, 012302 (2020).","DOI":"10.1103\/PhysRevA.101.012302"},{"key":"24","doi-asserted-by":"publisher","unstructured":"A. Hughes, V. Sch\u00e4fer, K. Thirumalai, D. Nadlinger, S. Woodrow, D. Lucas, and C. 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Cory, ``Robust online Hamiltonian learning,'' New Journal of Physics 14, 103013 (2012).","DOI":"10.1088\/1367-2630\/14\/10\/103013"},{"key":"44","doi-asserted-by":"publisher","unstructured":"W. Bruzda, V. Cappellini, H.-J. Sommers, and K. \u017byczkowski, ``Random quantum operations,'' Physics Letters A 373, 320 (2009).","DOI":"10.1016\/j.physleta.2008.11.043"},{"key":"45","doi-asserted-by":"publisher","unstructured":"E. Magesan, J. M. Gambetta, and J. Emerson, ``Characterizing quantum gates via randomized benchmarking,'' Physical Review A 85 (2012).","DOI":"10.1103\/PhysRevA.85.042311"},{"key":"46","doi-asserted-by":"publisher","unstructured":"J. Emerson, R. Alicki, and K. \u017byczkowski, ``Scalable noise estimation with random unitary operators,'' J. Opt. B Quantum Semiclass. Opt. 7, S347 (2005).","DOI":"10.1088\/1464-4266\/7\/10\/021"},{"key":"47","doi-asserted-by":"publisher","unstructured":"J. Emerson, M. Silva, O. Moussa, C. Ryan, M. Laforest, J. Baugh, D. G. Cory, and R. 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