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Onorati E, Werner AH, Eisert J. Randomized Benchmarking for Individual Quantum Gates. PHYSICAL REVIEW LETTERS 2019; 123:060501. [PMID: 31491181 DOI: 10.1103/physrevlett.123.060501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2019] [Indexed: 06/10/2023]
Abstract
Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized benchmarking allows for the relatively resource economical estimation of the average gate fidelity of quantum gates from the Clifford group, assuming identical noise levels for all gates, making use of suitable sequences of randomly chosen gates. In this work, we report significant progress on randomized benchmarking, by showing that it can be applied individually on a broad class of quantum gates outside the Clifford group, even for varying noise levels per quantum gate. This is possible at little overhead of quantum resources, but at the expense of a significant classical computational cost. At the heart of our analysis is a representation-theoretic framework which we bring into contact with classical estimation techniques based on bootstrapping and matrix pencils. We demonstrate the functioning of the scheme at hand of benchmarking tensor powers of T gates. Apart from its practical relevance, we expect this insight to be relevant as it highlights the role of assumptions made on unknown noise processes when characterizing quantum gates at high precision.
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Affiliation(s)
- E Onorati
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - A H Werner
- Department of Mathematical Sciences, University of Copenhagen, DK-2100 København, Denmark
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
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Gluza M, Kliesch M, Eisert J, Aolita L. Fidelity Witnesses for Fermionic Quantum Simulations. PHYSICAL REVIEW LETTERS 2018; 120:190501. [PMID: 29799258 DOI: 10.1103/physrevlett.120.190501] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Indexed: 06/08/2023]
Abstract
The experimental interest and developments in quantum spin-1/2 chains has increased uninterruptedly over the past decade. In many instances, the target quantum simulation belongs to the broader class of noninteracting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1/2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.
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Affiliation(s)
- M Gluza
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany
| | - M Kliesch
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Poland
- Institute for Theoretical Physics, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany
| | - L Aolita
- Instituto de Física, Universidade Federal do Rio de Janeiro, P.O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
- International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
- ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, UNESP-Universidade Estadual Paulista R. Dr. Bento T. Ferraz 271, Bl. II, São Paulo 01140-070, São Paulo, Brazil
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Riofrío CA, Gross D, Flammia ST, Monz T, Nigg D, Blatt R, Eisert J. Experimental quantum compressed sensing for a seven-qubit system. Nat Commun 2017; 8:15305. [PMID: 28513587 PMCID: PMC5442320 DOI: 10.1038/ncomms15305] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Accepted: 03/20/2017] [Indexed: 11/20/2022] Open
Abstract
Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies. The effort of quantum tomography—the reconstruction of states and processes of a quantum device—scales unfavourably: state-of-the-art systems can no longer be characterized. Quantum compressed sensing mitigates this problem by reconstructing states from incomplete data. Here we present an experimental implementation of compressed tomography of a seven-qubit system—a topological colour code prepared in a trapped ion architecture. We are in the highly incomplete—127 Pauli basis measurement settings—and highly noisy—100 repetitions each—regime. Originally, compressed sensing was advocated for states with few non-zero eigenvalues. We argue that low-rank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. The remaining eigenvectors behave consistently with a random-matrix model that carries no information about the true state. Quantum compressed sensing can provide a scalable way to characterize quantum states and devices, but has been so far limited to states with quickly decaying eigenvalues. Here the authors show that it can be appropriate even in the general case, demonstrating reconstruction the state of a seven-qubit system.
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Affiliation(s)
- C A Riofrío
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, D-14195 Berlin, Germany
| | - D Gross
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany.,Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales, Australia
| | - S T Flammia
- Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales, Australia
| | - T Monz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
| | - D Nigg
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
| | - R Blatt
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria.,Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21a, A-6020 Innsbruck, Austria
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, D-14195 Berlin, Germany
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Keil M, Amit O, Zhou S, Groswasser D, Japha Y, Folman R. Fifteen years of cold matter on the atom chip: promise, realizations, and prospects. JOURNAL OF MODERN OPTICS 2016; 63:1840-1885. [PMID: 27499585 PMCID: PMC4960518 DOI: 10.1080/09500340.2016.1178820] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2016] [Accepted: 03/22/2016] [Indexed: 05/30/2023]
Abstract
Here we review the field of atom chips in the context of Bose-Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and all the way to novel probing of surfaces and new forces. In addition, technological applications are also being intensively pursued. This review will describe these developments and more, including new ideas which have not yet been realized.
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Affiliation(s)
- Mark Keil
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Omer Amit
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Shuyu Zhou
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - David Groswasser
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Yonathan Japha
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Ron Folman
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
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