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Decoherence control for high-temperature reservoirs

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Abstract

We investigate the decoherence control coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum computation. Especially, we find that deriving optimal control using the Pontryagin maximum principle, the decoherence can be suppressed even in high-temperature reservoirs. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under ω c ≪ ω 0 condition, here ω 0 is the characteristic frequency of the quantum system of interest, and ω c the cut-off frequency of Ohmic reservoir. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compared the non-Markovian optimal decoherence control with the Markovian one and find that with non-Markovian the engineered artificial reservoirs are better than the Markovian approximate in controlling the decoherence of open, dissipative quantum systems.

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References

  1. Breuer H P, Petruccione F. The Theory of Open Quantum Systems. Oxford: Oxford University Press, 2002

    MATH  Google Scholar 

  2. Zhang J, Li C W, Wu R B, et al. Maximal suppression of decoherence in Markovian quantum systems. Journal of Physics A: Mathematical and General, 2005, 38(6587): 6587–6601

    Article  MATH  MathSciNet  Google Scholar 

  3. Lloyd S, Slotine J J E. Analog quantum error correction. Physical Review Letters, 1998, 80(18): 4088–4091

    Article  Google Scholar 

  4. Zanardi P, Rasetti M. Noiseless quantum codes. Physical Review Letters, 1997, 70(17): 3306–3309

    Article  Google Scholar 

  5. Chuang I L, Yamamoto Y. Simple quantum computer. Physical Review A, 1995, 52(5): 3489–3496

    Article  Google Scholar 

  6. Alicki R, Horodecki M, Horodecki R, et al. Dynamical description of quantum computing: Generic nonlocality of quantum noise. Physical Review A, 2002, 65(6): 062101–062111

    Article  MathSciNet  Google Scholar 

  7. Zanardi P. Stabilizing quantum information. Physical Review A, 2001, 63(1): 012301–012304

    Article  MathSciNet  Google Scholar 

  8. Neumann J Von. Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press, 1955

    MATH  Google Scholar 

  9. Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000

    MATH  Google Scholar 

  10. Mensky M B. Quantum Menseurements and Decoherence: Models and Phenomenology. Dordrecht: Kluwer Academic Publishers, 2000

    Google Scholar 

  11. Shor P W. Scheme for reducing decoherence in quantum computer memory. Physical Review A, 1995, 52(4): R2493–R2496

    Article  Google Scholar 

  12. Viola L, Lloyd S. Dynamical suppression of decoherence in two-state quantum systems. Physical Review A, 1998, 58(4): 2733–2744

    Article  MathSciNet  Google Scholar 

  13. Elattari B, Gurvitz S A. Effect of measurement on the decay rate of a quantum system. Physical Review Letters, 2000, 84(10): 2047–2051

    Article  Google Scholar 

  14. Altafini C. Controllability properties for finite dimensional quantum Markovian master equations. Journal of Mathematical Physics, 2003, 44: 2357–2372

    Article  MATH  MathSciNet  Google Scholar 

  15. Rabitz H, ViVie-Riedle R, Motzkus M, et al. Whither the future of controlling quantum phenomena? Science, 2000, 288(5467): 824–828

    Article  Google Scholar 

  16. Levis R J, Menkir G M, Rabitz H. Engineering Carbon Nanotubes and Nanotube Circuits Using Electrical Breakdown. Science, 2001, 292(5517): 706–709

    Article  Google Scholar 

  17. Rabitz H. Shaped laser pulses as reagents. Science, 2003, 299(5606): 525–527

    Article  Google Scholar 

  18. Krotov V F. Global Methods in Optimal Control Theory. New York: Marcel Dekker INC, 1996

    MATH  Google Scholar 

  19. Jirari H, PÖtz W. Quantum optimal control theory and dynamic coupling in the spin-boson model. Physical Review A, 2006, 74: 022306–022324

    Article  Google Scholar 

  20. Sugny D, Kontz C, Jauslin H R. Time-optimal control of a two-level dissipative quantum system. Physical Review A, 2007, 76: 023419–023430

    Article  Google Scholar 

  21. Weiss U. Quantum Dissipative System. Singapore: World Scientific Publishing, 1993

    Google Scholar 

  22. Gardiner C W, Zoller P. Quantum Noise (2nd Edition). New York: Springer-Verlag, 2000

    MATH  Google Scholar 

  23. Zurek W H. Decoherence, einselection, and the quantum origins of the classical. Review of Modern Physics, 2003, 75(3): 715–775

    Article  MathSciNet  Google Scholar 

  24. Garraway B M. Nonperturbative decay of an atomic system in a cavity. Physical Review A, 1997, 55(3): 2290–2303

    Article  Google Scholar 

  25. Zhang J, Wu R B, Li C W, et al. Asymptotically noise decoupling for Markovian open quantum systems. Physical Review A, 2007, 75: 22324–022335

    Article  Google Scholar 

  26. Tiersch M, Schützhold R. Non-Markovian decoherence in the adiabatic quantum search algorithm. Physical Review A, 2007, 75: 062313–062318

    Article  Google Scholar 

  27. Blum K. Density Matrix Theory and Applications. New York: Plenum Press, 1981

    Google Scholar 

  28. Thorwart M, Hartmann L, Goychuk I, et al. Controlling decoherence of a two-level-atom in a lossy cavity. Journal of Modern Optics, 2000, 47: 2905–2917

    Google Scholar 

  29. Scully M O, Zubairy M S. Quantum Optics. Cambridge: Cambridge University Press, 1997

    Google Scholar 

  30. Meystre P. Atom Optics. New York: Springer-Verlag, 2001

    Google Scholar 

  31. Anastopoulos C, Hu B L. Two-level atom-field interaction: Exact master equations for non-Markovian dynamics, decoherence, and relaxation. Physical Review A, 2000, 62(3): 033821–033834

    Article  Google Scholar 

  32. Shresta S, Anastopoulos C, Dragulescu A, et al. Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence, and entanglement. Physical Review A, 2005, 71: 022109–022119

    Article  Google Scholar 

  33. Maniscalco S, Olivares S, Paris M G A. Entanglement oscillations in non-Markovian quantum channels. Physical Review A, 2007, 75: 062119–062124

    Article  Google Scholar 

  34. Maniscalco S, Piilo J, Petruccione F, et al. Lindblad-and non-Lindblad-type dynamics of a quantum Brownian particle. Physical Review A, 2004, 70: 032113–032126

    Article  MathSciNet  Google Scholar 

  35. Myatt C J, King B E, Turchette Q A, et al. Decoherence of quantum superpositions through coupling to engineered reservoirs. Nature(London), 2000, 403: 267–273

    Google Scholar 

  36. Turchette Q A, Myatt C J, King B E, et al. Decoherence and decay of motional quantum states of a trapped atom coupled to engineered reservoirs. Physical Review A, 2000, 62: 053807–053829

    Article  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Institute of System Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wei Cui, Zairong Xi & Yu Pan

Authors
  1. Wei Cui
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  2. Zairong Xi
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  3. Yu Pan
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Correspondence to Zairong Xi.

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Cui, W., Xi, Z. & Pan, Y. Decoherence control for high-temperature reservoirs. Front. Comput. Sci. China 2, 129–137 (2008). https://doi.org/10.1007/s11704-008-0015-x

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  • DOI: https://doi.org/10.1007/s11704-008-0015-x

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