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van Mourik MW, Zapusek E, Hrmo P, Gerster L, Blatt R, Monz T, Schindler P, Reiter F. Experimental Realization of Nonunitary Multiqubit Operations. PHYSICAL REVIEW LETTERS 2024; 132:040602. [PMID: 38335353 DOI: 10.1103/physrevlett.132.040602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Accepted: 11/13/2023] [Indexed: 02/12/2024]
Abstract
We demonstrate a novel experimental tool set that enables irreversible multiqubit operations on a quantum platform. To exemplify our approach, we realize two elementary nonunitary operations: the or and nor gates. The electronic states of two trapped ^{40}Ca^{+} ions encode the logical information, and a cotrapped ^{88}Sr^{+} ion provides the irreversibility of the gate by a dissipation channel through sideband cooling. We measure 87% and 81% success rates for the or and nor gates, respectively. The presented methods are a stepping stone toward other nonunitary operations such as in quantum error correction and quantum machine learning.
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Affiliation(s)
- M W van Mourik
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020 Innsbruck, Austria
| | - E Zapusek
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - P Hrmo
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020 Innsbruck, Austria
| | - L Gerster
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020 Innsbruck, Austria
| | - R Blatt
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020 Innsbruck, Austria
| | - T Monz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020 Innsbruck, Austria
- AQT, Technikerstraße 17, 6020 Innsbruck, Austria
| | - P Schindler
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020 Innsbruck, Austria
| | - F Reiter
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
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2
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Singh VP, Weimer H. Driven-Dissipative Criticality within the Discrete Truncated Wigner Approximation. PHYSICAL REVIEW LETTERS 2022; 128:200602. [PMID: 35657854 DOI: 10.1103/physrevlett.128.200602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 04/14/2022] [Indexed: 06/15/2023]
Abstract
We present an approach to the numerical simulation of open quantum many-body systems based on the semiclassical framework of the discrete truncated Wigner approximation. We establish a quantum jump formalism to integrate the quantum master equation describing the dynamics of the system, which we find to be exact in both the noninteracting limit and the limit where the system is described by classical rate equations. We apply our method to simulation of the paradigmatic dissipative Ising model, where we are able to capture the critical fluctuations of the system beyond the level of mean-field theory.
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Affiliation(s)
- Vijay Pal Singh
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
- Zentrum für Optische Quantentechnologien and Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
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3
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Cole DC, Erickson SD, Zarantonello G, Horn KP, Hou PY, Wu JJ, Slichter DH, Reiter F, Koch CP, Leibfried D. Resource-Efficient Dissipative Entanglement of Two Trapped-Ion Qubits. PHYSICAL REVIEW LETTERS 2022; 128:080502. [PMID: 35275690 DOI: 10.1103/physrevlett.128.080502] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Accepted: 12/02/2021] [Indexed: 06/14/2023]
Abstract
We demonstrate a simplified method for dissipative generation of an entangled state of two trapped-ion qubits. Our implementation produces its target state faster and with higher fidelity than previous demonstrations of dissipative entanglement generation and eliminates the need for auxiliary ions. The entangled singlet state is generated in ∼7 ms with a fidelity of 0.949(4). The dominant source of infidelity is photon scattering. We discuss this error source and strategies for its mitigation.
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Affiliation(s)
- Daniel C Cole
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - Stephen D Erickson
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Giorgio Zarantonello
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Karl P Horn
- Theoretische Physik, Universität Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany
| | - Pan-Yu Hou
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Jenny J Wu
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Daniel H Slichter
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - Florentin Reiter
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Christiane P Koch
- Theoretische Physik, Universität Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Dietrich Leibfried
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
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Malinowski M, Zhang C, Negnevitsky V, Rojkov I, Reiter F, Nguyen TL, Stadler M, Kienzler D, Mehta KK, Home JP. Generation of a Maximally Entangled State Using Collective Optical Pumping. PHYSICAL REVIEW LETTERS 2022; 128:080503. [PMID: 35275689 DOI: 10.1103/physrevlett.128.080503] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Revised: 12/10/2021] [Accepted: 01/11/2022] [Indexed: 06/14/2023]
Abstract
We propose and implement a novel scheme for dissipatively pumping two qubits into a singlet Bell state. The method relies on a process of collective optical pumping to an excited level, to which all states apart from the singlet are coupled. We apply the method to deterministically entangle two trapped ^{40}Ca^{+} ions. Within 16 pumping cycles, an initially separable state is transformed into one with 83(1)% singlet fidelity, and states with initial fidelity of ⪆70% converge onto a fidelity of 93(1)%. We theoretically analyze the performance and error susceptibility of the scheme and find it to be insensitive to a large class of experimentally relevant noise sources.
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Affiliation(s)
- M Malinowski
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - C Zhang
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - V Negnevitsky
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - I Rojkov
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - F Reiter
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - T-L Nguyen
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - M Stadler
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - D Kienzler
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - K K Mehta
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - J P Home
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
- Quantum center, ETH Zürich, 8093 Zürich, Switzerland
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5
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Kwon H, Mukherjee R, Kim MS. Reversing Lindblad Dynamics via Continuous Petz Recovery Map. PHYSICAL REVIEW LETTERS 2022; 128:020403. [PMID: 35089760 DOI: 10.1103/physrevlett.128.020403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Revised: 11/26/2021] [Accepted: 12/14/2021] [Indexed: 06/14/2023]
Abstract
An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the Lindblad master equation. The reverse dynamics can be obtained by constructing the Petz recovery map in continuous time. By providing the exact form of the Hamiltonian and jump operators for the reverse dynamics, we explore the potential of utilizing the near-optimal recovery of the Petz map in controlling noisy quantum dynamics. While time-dependent dissipation engineering enables us to fully recover a single quantum trajectory, we also design a time-independent recovery protocol to protect encoded quantum information against decoherence. Our protocol can efficiently suppress only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.
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Affiliation(s)
- Hyukjoon Kwon
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Korea Institute for Advanced Study, Seoul 02455, South Korea
| | - Rick Mukherjee
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - M S Kim
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Korea Institute for Advanced Study, Seoul 02455, South Korea
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Zippilli S, Vitali D. Dissipative Engineering of Gaussian Entangled States in Harmonic Lattices with a Single-Site Squeezed Reservoir. PHYSICAL REVIEW LETTERS 2021; 126:020402. [PMID: 33512179 DOI: 10.1103/physrevlett.126.020402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 12/18/2020] [Indexed: 06/12/2023]
Abstract
We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models which could be relevant for quantum technology applications. We assume minimal resources, represented by systems described by particle-conserving quadratic Hamiltonians, with a single localized squeezed reservoir. We show that in this way it is possible to prepare, in the steady state, the wide class of pure states which can be generated by applying a generic passive Gaussian transformation on a set of equally squeezed modes. This includes nontrivial multipartite entangled states such as cluster states suitable for measurement-based quantum computation.
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Affiliation(s)
- Stefano Zippilli
- School of Science and Technology, Physics Division, University of Camerino, I-62032 Camerino (MC), Italy
| | - David Vitali
- School of Science and Technology, Physics Division, University of Camerino, I-62032 Camerino (MC), Italy
- INFN, Sezione di Perugia, I-06123 Perugia, Italy
- CNR-INO, L.go Enrico Fermi 6, I-50125 Firenze, Italy
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7
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Raghunandan M, Wolf F, Ospelkaus C, Schmidt PO, Weimer H. Initialization of quantum simulators by sympathetic cooling. SCIENCE ADVANCES 2020; 6:eaaw9268. [PMID: 32181335 PMCID: PMC7060053 DOI: 10.1126/sciadv.aaw9268] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/06/2019] [Accepted: 12/11/2019] [Indexed: 06/10/2023]
Abstract
Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.
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Affiliation(s)
- Meghana Raghunandan
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraβe 2, 30167 Hannover, Germany
| | - Fabian Wolf
- QUEST Institut, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - Christian Ospelkaus
- QUEST Institut, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
| | - Piet O. Schmidt
- QUEST Institut, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
| | - Hendrik Weimer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraβe 2, 30167 Hannover, Germany
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8
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Dynamical and thermodynamical approaches to open quantum systems. Sci Rep 2020; 10:2607. [PMID: 32054893 PMCID: PMC7018693 DOI: 10.1038/s41598-020-59241-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 01/08/2020] [Indexed: 12/02/2022] Open
Abstract
The non-Markovian dynamics of open quantum systems is studied from two different points of view. The first one coincides with the traditional tracing out of the environmental degrees of freedom, presented in classical textbooks on open quantum systems. The second one is an approximation of the exact density operator with the knowledge of only several dynamical variables in the spirit of non-equilibrium thermodynamics. The approximation is based on the principle of maximal entropy. We discuss the information and the Renyi entropies, which lead to different approximations. The time-convolutionless master equation governs the dynamics of both traditional and approximated reduced density operator with a particular projection operator. Considering the example of two interacting qubits in a thermal environment, we compare the traditional and thermodynamical approaches.
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9
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Behzadi N, Ektesabi A, Ahansaz B. Well-protected quantum state transfer in a dissipative spin chain. Sci Rep 2018; 8:7906. [PMID: 29784933 PMCID: PMC5962563 DOI: 10.1038/s41598-018-26220-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Accepted: 05/02/2018] [Indexed: 11/29/2022] Open
Abstract
In this work, a mechanism is investigated for improving the quantum state transfer efficiency in a spin chain, which is in contact with a dissipative structured reservoir. The efficiency of the method is based on the addition of similar non-interacting auxiliary chains into the reservoir. In this way, we obtain the exact solution for the master equation of the spin chain in the presence of dissipation. It is found out that entering more auxiliary chains into the reservoir causes, in general, the better improvement of the fidelity of state transfer along the mentioned chain. Furthermore, it is reveal that the protocol has better efficiency for a chain with longer length. Therefore, by this method, quantum state transfer along a linear chain with an arbitrary number of qubits, can be well-protected against the dissipative noises.
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Affiliation(s)
- Naghi Behzadi
- Research Institute for Fundamental Sciences, University of Tabriz, Tabriz, Iran.
| | - Abbas Ektesabi
- Physics Department, Azarbaijan Shahid Madani University, Tabriz, Iran
| | - Bahram Ahansaz
- Physics Department, Azarbaijan Shahid Madani University, Tabriz, Iran
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Li C, Song J, Xia Y, Ding W. Driving many distant atoms into high-fidelity steady state entanglement via Lyapunov control. OPTICS EXPRESS 2018; 26:951-962. [PMID: 29401983 DOI: 10.1364/oe.26.000951] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2017] [Accepted: 12/28/2017] [Indexed: 06/07/2023]
Abstract
Based on Lyapunov control theory in closed and open systems, we propose a scheme to generate W state of many distant atoms in the cavity-fiber-cavity system. In the closed system, the W state is generated successfully even when the coupling strength between the cavity and fiber is extremely weak. In the presence of atomic spontaneous emission or cavity and fiber decay, the photon-measurement and quantum feedback approaches are proposed to improve the fidelity, which enable efficient generation of high-fidelity W state in the case of large dissipation. Furthermore, the time-optimal Lyapunov control is investigated to shorten the evolution time and improve the fidelity in open systems.
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Reiter F, Sørensen AS, Zoller P, Muschik CA. Dissipative quantum error correction and application to quantum sensing with trapped ions. Nat Commun 2017; 8:1822. [PMID: 29180753 PMCID: PMC5704006 DOI: 10.1038/s41467-017-01895-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2017] [Accepted: 10/24/2017] [Indexed: 11/09/2022] Open
Abstract
Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error-correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin-flips or phase-flips. Our dissipative error correction scheme operates in a continuous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
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Affiliation(s)
- F Reiter
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria.
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020, Innsbruck, Austria.
- Harvard University, Department of Physics, Cambridge, MA, 02138, USA.
| | - A S Sørensen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen, Denmark
| | - P Zoller
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020, Innsbruck, Austria
| | - C A Muschik
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020, Innsbruck, Austria
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