메뉴 건너뛰기




Volumn 3, Issue 1, 2003, Pages 15-37

Simulation of quantum dynamics with quantum optical systems

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; DYNAMICS; HAMILTONIANS; IONS; OPTICAL LATTICES; QUANTUM THEORY;

EID: 0038542062     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (160)

References (48)
  • 1
    • 0002433737 scopus 로고
    • R. P. Feynman, Opt. News 11, 11 (1985): Found. Phys. 16 507 (1986); Int. J. Theor. Phys. 21, 467 (1982).
    • (1985) Opt. News , vol.11 , pp. 11
    • Feynman, R.P.1
  • 2
    • 5344230456 scopus 로고
    • R. P. Feynman, Opt. News 11, 11 (1985): Found. Phys. 16 507 (1986); Int. J. Theor. Phys. 21, 467 (1982).
    • (1986) Found. Phys. , vol.16 , pp. 507
  • 3
    • 51249180339 scopus 로고
    • R. P. Feynman, Opt. News 11, 11 (1985): Found. Phys. 16 507 (1986); Int. J. Theor. Phys. 21, 467 (1982).
    • (1982) Int. J. Theor. Phys. , vol.21 , pp. 467
  • 4
    • 0141559680 scopus 로고    scopus 로고
    • proceedings of Royal Society Discussion Meeting "Quantum Computation: Theory and Experiment", november
    • A. Ekert and R. Jozsa, Phil. Trans. Roy. Soc, London 1998, proceedings of Royal Society Discussion Meeting "Quantum Computation: Theory and Experiment", november 1997.
    • (1997) Phil. Trans. Roy. Soc, London 1998
    • Ekert, A.1    Jozsa, R.2
  • 5
    • 0000211877 scopus 로고
    • J. Hubbard, Proc. Roy. Soc. A 276, 238 (1963); J. Kanamori, Prog. Theor. Phys. 30, 275 (1963); M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).
    • (1963) Proc. Roy. Soc. A , vol.276 , pp. 238
    • Hubbard, J.1
  • 6
    • 0000541030 scopus 로고
    • J. Hubbard, Proc. Roy. Soc. A 276, 238 (1963); J. Kanamori, Prog. Theor. Phys. 30, 275 (1963); M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).
    • (1963) Prog. Theor. Phys. , vol.30 , pp. 275
    • Kanamori, J.1
  • 7
    • 33744619385 scopus 로고
    • J. Hubbard, Proc. Roy. Soc. A 276, 238 (1963); J. Kanamori, Prog. Theor. Phys. 30, 275 (1963); M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).
    • (1963) Phys. Rev. Lett. , vol.10 , pp. 159
    • Gutzwiller, M.C.1
  • 9
    • 0029838223 scopus 로고    scopus 로고
    • Universal quantum simulators
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • (1996) Science , vol.273 , pp. 1073-1078
    • Lloyd, S.1
  • 10
    • 0031222446 scopus 로고    scopus 로고
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 2586
    • Abrams, D.S.1    Lloyd, S.2
  • 11
    • 0029838223 scopus 로고    scopus 로고
    • quant-ph/9603028
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • Wiesner, S.1
  • 12
    • 0031222328 scopus 로고    scopus 로고
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • (1997) Phys. Rev. E , vol.56 , pp. 3661
    • Lidar, D.A.1    Biham, O.2
  • 13
    • 0032162402 scopus 로고    scopus 로고
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • (1998) Physica D , vol.120 , pp. 30
    • Boghosian, B.M.1    Taylor, W.2
  • 14
    • 1542405949 scopus 로고    scopus 로고
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • (1998) Proc. Roy. Soc. London A , vol.454 , pp. 313
    • Zalka, C.1
  • 15
    • 0029838223 scopus 로고    scopus 로고
    • quant-ph/0003137
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • Bravyi, S.B.1    Kitaev, A.Y.2
  • 16
    • 0035435494 scopus 로고    scopus 로고
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • (2001) Phys. Rev. A , vol.64 , pp. 22319
    • Ortiz, G.1    Gubernatis, J.E.2    Knill, E.3    Laflamme, R.4
  • 17
    • 0029838223 scopus 로고    scopus 로고
    • quant-ph/0108146
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • Somma, R.1    Ortiz, G.2    Gubernatis, J.E.3    Knill, E.4    Laflamme, R.5
  • 18
    • 0029838223 scopus 로고    scopus 로고
    • quant-ph/0108110
    • S. Lloyd, Universal quantum simulators. Science 273, 1073-1078 (1996); D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997); S. Wiesner, quant-ph/9603028; D.A. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997): B. M. Boghosian and W. Taylor, Physica D 120, 30 (1998); C. Zalka, Proc. Roy. Soc. London A 454, 313 (1998); S. B. Bravyi and A. Y. Kitaev, quant-ph/0003137; G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, Phys. Rev. A 64, 22319 (2001); R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill and R. Laflamme, quant-ph/0108146; L.-A. Wu, M.S. Byrd and D.A. Lidar, quant-ph/0108110 (to appear in Phys. Rev. Lett.).
    • Phys. Rev. Lett.
    • Wu, L.-A.1    Byrd, M.S.2    Lidar, D.A.3
  • 25
    • 0141782998 scopus 로고    scopus 로고
    • note
    • Any valid scheme for universal quantum computation can be used, in principle, to simulate quantum systems, and the schemes for a UQS presented in this paper are nothing but particular realizations of a quantum computer. In practice, however, experimental limitations drastically interfere with the ideal performance of any of these devices. Imperfect manipulations and finite decoherent times introduce errors at a rate far above the estimated threshold for achieving fault-tolerant controlled quantum evolutions. In this situation, a quantum computer that operates by, say, performing CNOT gates and one-qubit rotations is notoriously less succesful at tracing the dynamics of an array of interacting qubits than a device especially designed for this purpose.
  • 26
    • 0141448113 scopus 로고    scopus 로고
    • note
    • By a short gate we mean one that does not differ much from the identity operator.
  • 29
    • 0141559681 scopus 로고    scopus 로고
    • quant-ph/0106077
    • J. L. Dodd, M. A. Nielsen, M. J. Bremner, and R. T. Thew, quant-ph/0106064; P.Wocjan, D. Janzing and Th. Beth, quant-ph/0106077.
    • Wocjan, P.1    Janzing, D.2    Beth, Th.3
  • 32
    • 0141448109 scopus 로고    scopus 로고
    • note
    • Multi-qubit systems with n-body interactions, n > 2, d-level systems with d > 2 and more exotic systems such as fermions can also be simulated using our schemes. In this cases we encounter, however, that the time required to perform the simulation does no longer grow linearly in the simulated time, but according to some higher order polynomial.
  • 33
    • 0141782997 scopus 로고    scopus 로고
    • note
    • Through the paper we use the convention ℏ = 1.
  • 34
    • 0141448107 scopus 로고    scopus 로고
    • note
    • By symmetrizing the evolution according to the spectral method for dynamical evolution, see numerical recipes, one can easily reduce the control complexity x to scale as √T′/ε instead of T′/ε.
  • 35
    • 0141671126 scopus 로고    scopus 로고
    • note
    • For simplicity, we describe only a ID optical lattice. For 2D [3D] lattices, one uses four (six) interfering laser beams, one pair for each dimension.
  • 39
    • 0141448108 scopus 로고    scopus 로고
    • unpublished
    • I. Bloch et al., unpublished.
    • Bloch, I.1
  • 40
    • 4243241882 scopus 로고    scopus 로고
    • Elliptical ion traps and trap arrays for quantum computation
    • R. G. DeVoe, Elliptical ion traps and trap arrays for quantum computation. Phys. Rev. A 58, 910-914 (1998).
    • (1998) Phys. Rev. A , vol.58 , pp. 910-914
    • DeVoe, R.G.1
  • 41
    • 4244043498 scopus 로고
    • Quantum computations with cold trapped ions
    • J. I. Cirac and P. Zoller. Quantum computations with cold trapped ions, Phys. Rev. Lett. 74, 4091-4099 (1995); J. F. Poyatos, J. I. Cirac and P. Zoller, ibid 81, 1322-1325 (1998).
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 4091-4099
    • Cirac, J.I.1    Zoller, P.2
  • 42
    • 0000001257 scopus 로고    scopus 로고
    • J. I. Cirac and P. Zoller. Quantum computations with cold trapped ions, Phys. Rev. Lett. 74, 4091-4099 (1995); J. F. Poyatos, J. I. Cirac and P. Zoller, ibid 81, 1322-1325 (1998).
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 1322-1325
    • Poyatos, J.F.1    Cirac, J.I.2    Zoller, P.3
  • 43
  • 45
    • 0141448106 scopus 로고    scopus 로고
    • private communication
    • M. A. Calzadilla, private communication.
    • Calzadilla, M.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.