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Garcia L, Bofill JM, Moreira IDPR, Albareda G. Highly Adiabatic Time-Optimal Quantum Driving at Low Energy Cost. PHYSICAL REVIEW LETTERS 2022; 129:180402. [PMID: 36374669 DOI: 10.1103/physrevlett.129.180402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2022] [Revised: 05/25/2022] [Accepted: 09/13/2022] [Indexed: 06/16/2023]
Abstract
Time-efficient control schemes for manipulating quantum systems are of great importance in quantum technologies, where environmental forces rapidly degrade the quality of pure states over time. In this Letter, we formulate an approach to time-optimal control that circumvents the boundary-value problem that plagues the quantum brachistochrone equation at the expense of relaxing the form of the control Hamiltonian. In this setting, a coupled system of equations, one for the control Hamiltonian and another one for the duration of the protocol, realizes an ansatz-free approach to quantum control theory. We show how driven systems, in the form of a Landau-Zener type Hamiltonian, can be efficiently maneuvered to speed up a given state transformation in a highly adiabatic manner and with a low energy cost.
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Affiliation(s)
- Lluc Garcia
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
| | - Josep Maria Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
| | - Ibério de P R Moreira
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Departament de Ciència de Materials i Química Física, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
| | - Guillermo Albareda
- Institute of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Ideaded, Carrer de la Tecnologia, 35, 08840 Viladecans, Barcelona, Spain
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
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Ozeri R, Langer C, Jost JD, DeMarco B, Ben-Kish A, Blakestad BR, Britton J, Chiaverini J, Itano WM, Hume DB, Leibfried D, Rosenband T, Schmidt PO, Wineland DJ. Hyperfine coherence in the presence of spontaneous photon scattering. PHYSICAL REVIEW LETTERS 2005; 95:030403. [PMID: 16090723 DOI: 10.1103/physrevlett.95.030403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2005] [Indexed: 05/03/2023]
Abstract
The coherence of a hyperfine-state superposition of a trapped 9Be+ ion in the presence of off-resonant light is studied experimentally. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. We observe coherence times that exceed the average scattering time of 19 photons which is determined from measured Stark shifts. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.
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Affiliation(s)
- R Ozeri
- NIST Boulder, Time and Frequency Division, Boulder, CO 80305, USA
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3
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Taneichi T, Kobayashi T. Enhanced entanglement of two atoms confined in a multi-mode optical cavity. Chem Phys Lett 2003. [DOI: 10.1016/s0009-2614(03)01330-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Han S, Yu Y, Chu X, Chu SI, Wang Z. Time-resolved measurement of dissipation-induced decoherence in a Josephson junction. Science 2001; 293:1457-9. [PMID: 11520978 DOI: 10.1126/science.1062266] [Citation(s) in RCA: 88] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
We determined the dissipation-induced decoherence time (DIDT) of a superconducting Josephson tunnel junction by time-resolved measurements of its escape dynamics. Double-exponential behavior of the time-dependent escape probability was observed, suggesting the occurrence of a two-level decay-tunneling process in which energy relaxation from the excited to the ground level significantly affects the escape dynamics of the system. The observation of temporal double-exponential dependence enables direct measurements of the DIDT, a property critical to the study of quantum dynamics and the realization of macroscopic quantum coherence and quantum computing. We found that the DIDT was tau(d) > 11 micros at T = 0.55 K, demonstrating good prospects for implementing quantum computing with Josephson devices.
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Affiliation(s)
- S Han
- Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA.
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5
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Peng X, Zhu X, Fang X, Feng M, Gao K, Yang X, Liu M. Preparation of pseudo-pure states by line-selective pulses in nuclear magnetic resonance. Chem Phys Lett 2001. [DOI: 10.1016/s0009-2614(01)00421-3] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Parker S, Plenio MB. Efficient factorization with a single pure qubit and logN mixed qubits. PHYSICAL REVIEW LETTERS 2000; 85:3049-3052. [PMID: 11006000 DOI: 10.1103/physrevlett.85.3049] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2000] [Indexed: 05/23/2023]
Abstract
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number N requires a pure initial state. Here we demonstrate that a single pure qubit, together with a collection of log 2N qubits in an arbitrary mixed state, is sufficient to implement Shor's factorization algorithm efficiently.
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Affiliation(s)
- S Parker
- Optics Section, The Blackett Laboratory, Imperial College, London SW7 2BW, England
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7
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Beige A, Braun D, Tregenna B, Knight PL. Quantum computing using dissipation to remain in a decoherence-free subspace. PHYSICAL REVIEW LETTERS 2000; 85:1762-1765. [PMID: 10970608 DOI: 10.1103/physrevlett.85.1762] [Citation(s) in RCA: 69] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/1999] [Revised: 04/10/2000] [Indexed: 05/23/2023]
Abstract
We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.
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Affiliation(s)
- A Beige
- Optics Section, Blackett Laboratory, Imperial College London, London SW7 2BZ, England
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8
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Jones JA, Mosca M. Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer. J Chem Phys 1998. [DOI: 10.1063/1.476739] [Citation(s) in RCA: 267] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chuang IL, Gershenfeld N, Kubinec MG, Leung DW. Bulk quantum computation with nuclear magnetic resonance: theory and experiment. Proc Math Phys Eng Sci 1998. [DOI: 10.1098/rspa.1998.0170] [Citation(s) in RCA: 240] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- I. L. Chuang
- Los Alamos National Laboratory, Theoretical Astrophysics T‐6, Mail Stop B288, Los Alamos, NM 87545, USA
| | - N. Gershenfeld
- Physics and Media Group, MIT Media Laboratory, 20 Ames Street, Cambridge, MA 02139, USA
| | - M. G. Kubinec
- College of Chemistry, D7 Latimer Hall, University of California Berkeley, Berkeley, CA 94720-1460, USA
| | - D. W. Leung
- ERATO Quantum Fluctuation Project, Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
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Wineland DJ, Monroe C, Meekhof DM, King BE, Leibfried D, Itano WM, Bergquist JC, Berkeland D, Bollinger JJ, Miller J. Quantum state manipulation of trapped atomic ions. Proc Math Phys Eng Sci 1998. [DOI: 10.1098/rspa.1998.0168] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- D. J. Wineland
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - C. Monroe
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. M. Meekhof
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - B. E. King
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. Leibfried
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - W. M. Itano
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. C. Bergquist
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. Berkeland
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. J. Bollinger
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. Miller
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
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12
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Plenio MB, Knight PL. Decoherence limits to quantum computation using trapped ions. Proc Math Phys Eng Sci 1997. [DOI: 10.1098/rspa.1997.0109] [Citation(s) in RCA: 76] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- M. B. Plenio
- Blackett Laboratory, Imperial College of Science, Technology and Medicine, London SW7 2BZ, UK
| | - P. L. Knight
- Blackett Laboratory, Imperial College of Science, Technology and Medicine, London SW7 2BZ, UK
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Moussa MH. Teleportation of a cavity-radiation-field state: An alternative scheme. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:4661-4669. [PMID: 9914030 DOI: 10.1103/physreva.54.4661] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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14
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Hughes RJ, James DF, Knill EH, Laflamme R, Petschek AG. Decoherence Bounds on Quantum Computation with Trapped Ions. PHYSICAL REVIEW LETTERS 1996; 77:3240-3243. [PMID: 10062169 DOI: 10.1103/physrevlett.77.3240] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Miquel C, Paz JP, Perazzo R. Factoring in a dissipative quantum computer. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:2605-2613. [PMID: 9913769 DOI: 10.1103/physreva.54.2605] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Barenco A, Ekert A, Suominen KA, Törmä P. Approximate quantum Fourier transform and decoherence. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:139-146. [PMID: 9913466 DOI: 10.1103/physreva.54.139] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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