Protecting coherence and entanglement by quantum feedback controls

IEEE Transactions on Automatic Control

Volumn 55, Issue 3, 2010, Pages 619-633

  Zhang, Jing ^a,b   Wu, Re Bing ^a,b   Li, Chun Wen ^a,b   Tarn, Tzyh Jong ^b,c  

^a TSINGHUA UNIVERSITY   (China)

^b TSINGHUA NATIONAL LABORATORY FOR INFORMATION SCIENCE AND TECHNOLOGY   (China)

^c WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Decoherence suppression; Entanglement protection; Quantum control; Quantum feedback control

Indexed keywords

COUPLING STRENGTHS; DECOHERENCE; DECOHERENCE EFFECTS; DECOHERENCE SUPPRESSION; DEPHASING; ENVIRONMENTAL DISTURBANCES; FEEDBACK CONTROL STRATEGIES; QUANTUM CONTROL; QUANTUM FEEDBACK CONTROL; QUANTUM STATE; QUANTUM SYSTEM; TWO-QUBIT; WEAK MEASUREMENTS;

DAMPING; FEEDBACK; FEEDBACK CONTROL; QUANTUM ELECTRONICS; QUANTUM OPTICS; STATE FEEDBACK;

QUANTUM ENTANGLEMENT;

EID: 77949425221     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2039238     Document Type: Article

References (79)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambrige, U.K.: Cambridge Univ. Press, 2000.
2. P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," in Proc. 35th Annu. Symp. Found. Comput. Sci., Santa Fe, NM, 1994, pp. 124-134.
3. L. K. Grover, "A fast quantum mechanics algorithm for database search," in Proc. 28th Annu. ACM Symp. Theory Computat., Philadelphia, PA, 1996, pp. 212-219.
4. D. D'Alessandro, Introduction to Quantum Control and Dynamics. Boca Raton, LA: Chapman & Hall, 2007.
5. G. M. Huang, T. J. Tarn, and J. W. Clark, "On the controllability of quantum-mechanical systems," J. Math. Phys., vol.24, pp. 2608-2618, 1983.
6. C. H. Lan, T. J. Tarn, Q. S. Chi, and J. Clark, "Analytic controllability of time-dependent quantum control systems," J. Math. Phys., vol.46, p. 052102, 2005.
7. N. Ganesan and T. J. Tarn, "Decoherence control in open quantum systems via classical feedback," Phys. Rev. A, vol.75, p. 032323, 2007.
8. N. Khaneja, R. Brockett, and S. J. Glaser, "Time optimal control in spin systems," Phys. Rev. A, vol.63, p. 032308, 2001.
9. N. Khaneja, S. J. Glaser, and R. Brokett, "Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer," Phys. Rev. A, vol.65, p. 032301, 2002.
10. M. R. James, "Risk-sensitive optimal control of quantum systems," Phys. Rev. A, vol.69, p. 032108, 2004.
11. M. R. James, H. I. Nurdin, and I. R. Petersen, "control of linear quantum stochastic systems," IEEE Trans. Autom. Control, vol.53, no.8, pp. 1787-1803, Sep. 2008.
12. F. Albertini and D. D'Alessandro, "Notions of controllability for bilinear multilevel quantum systems," IEEE Trans. Autom. Control, vol.48, no.8, pp. 1399-1403, Aug. 2003.
13. D. D'Alessandro and M. Dahleh, "Optimal control of two-level quantum systems," IEEE Trans. Autom. Control, vol.46, no.6, pp. 866-876, Jun. 2001.
14. R. Romano and D. D'Alessandro, "Incoherent control and entanglement for two-dimensional coupled systems," Phys. Rev. A, vol.73, p. 022323, 2006.
15. R. Romano and D. D'Alessandro, "Environment-mediated control of a quantum system," Phys. Rev. Lett., vol.97, p. 080402, 2006.
16. H. C. Fu, H. Dong, X. F. Liu, and C. P. Sun, "Indirect control with a quantum accessor: Coherent control of multilevel system via a qubit chain," Phys. Rev. A, vol.75, p. 052317, 2007.
17. S. Lloyd, "Almost any quantum logic gate is universal," Phys. Rev. Lett., vol.75, pp. 346-349, 1995.
18. S. G. Schirmer, H. Fu, and A. I. Solomon, "Complete controllability of quantum systems," Phys. Rev. A, vol.63, p. 063410, 2000.
19. R. B. Wu, T. J. Tarn, and C. W. Li, "Smooth controllability of infinite dimensional quantum mechanical systems," Phys. Rev. A, vol.73, p. 012719, 2006.
20. R. B. Wu, R. Chakrabarti, and H. Rabitz, "Optimal control theory for continuous-variable quantum gates," Phys. Rev. A, vol.77, p. 052303, 2008.
21. M. Mirrahimi and P. Rouchon, "Controllability of quantum harmonic oscillators," IEEE Trans. Autom. Control, vol.49, no.5, pp. 745-747, May 2004.
22. M. Mirrahimi and R. V. Handel, "Stabilizing feedback controls for quantum systems," SIAM J. Control Optim., vol.46, pp. 445-467, 2007.
23. N.Yamamoto, K. Tsumura, and S. Hara, "Feedback control of quantum entanglement in a two-spin system," Automatica, vol.43, pp. 981-992, 2007.
24. N. Yamamoto and L. Bouten, "Quantum risk-sensitive estimation and robustness," IEEE Trans. Autom. Control, vol.54, no.1, pp. 92-107, Jan. 2009.
25. D. Y. Dong, C. B. Zhang, H. Rabitz, A. Pechen, and T. J. Tarn, "Incoherent control of locally controllable quantum systems," J. Chem. Phys., vol.129, p. 154103, 2008.
26. S. Kuang and S. Cong, "Lyapunov control methods of closed quantum systems," Automatica, vol.44, pp. 98-108, 2008.
27. W. Cui, Z. R. Xi, and Y. Pan, "The entanglement dynamics of the bipartite quantum system: Toward entanglement sudden death," J. Phys. A: Math. Theor., vol.42, p. 025303, 2009.
28. P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A, vol.52, pp. R2493-R2496, 1995.
29. J. I. Cirac and T. Pellizzari, "Enforcing coherent evolution in dissipative quantum dynamics," Science, vol.273, pp. 1207-1210, 1996.
30. L. M. Duan and G. C. Guo, "Preserving coherence in quantum computation by pairing quantum bits," Phys. Rev. Lett., vol.79, pp. 1953-1956, 1997.
31. D. A. Lidar, I. L. Chuang, and K. B. Whaley, "Decoherence-free subspaces for quantum computation," Phys. Rev. Lett., vol.81, pp. 2594-2597, 1998.
32. L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, "Experimental realization of noiseless subsystems for quantum information processing," Science, vol.293, pp. 2059-2063, 2001.
33. F. Ticozzi and L. Viola, "Quantum Markovian subsystems: Invariance, attractivity and control," IEEE Trans. Autom. Control, vol.53, no.9, pp. 2048-2063, Oct. 2008.
34. L. Viola and S. Lloyd, "Dynamical suppression of decoherence in twostate quantum systems," Phys. Rev. A, vol.58, pp. 2733-2744, 1998.
35. D. A. Lidar and S. Schneider, "Stabilizing qubit coherence via trackingcontrol," Quant. Info. Comp., vol.5, pp. 350-363, 2005.
36. C. Altafini, "Controllability properties for finite dimensional quantum Markovian master equations," J. Math. Phys., vol.44, pp. 2357-2372, 2003.
37. C. Altafini, "Coherent control of open quantum dynamical systems," Phys. Rev. A, vol.70, p. 062321, 2004.
38. J. Zhang, R. B.Wu, C.W. Li, T. J. Tarn, and J. W.Wu, "Asymptotically noise decoupling for Markovian open quantum systems," Phys. Rev. A, vol.75, p. 022324, 2007.
39. A. G. Kofman and G. Kurizki, "Unified theory of dynamically suppressed qubit decoherence in thermal baths," Phys. Rev. Lett., vol.93, p. 130406, 2004.
40. G. Gordon, G. Kurizki, and A. G. Kofman, "Universal dynamical control of local decoherence for multipartite and multilevel systems," Opt. Commu., vol.264, pp. 398-406, 2006.
41. M. Zhang, H. Y. Dai, Z. R. Xi, H. W. Xie, and D. W. Hu, "Combating dephasing decoherence by periodically performing tracking control and projective measurement," Phys. Rev. A, vol.76, p. 042335, 2007.
42. J. Zhang, C. W. Li, R. B. Wu, T. J. Tarn, and X. S. Liu, "Maximal suppression of decoherence in Markovian quantum systems," J. Phys. A: Math. Gen., vol.38, pp. 6587-6601, 2005.
43. W. Cui, Z. R. Xi, and Y. Pan, "Optimal decoherence control in non- Markovian open dissipative quantum systems," Phys. Rev. A, vol.77, p. 032117, 2008.
44. H. Mabuchi and A. C. Doherty, "Cavity quantum electrodynamics: Coherence in context," Science, vol.298, pp. 1372-1377, 2002.
45. R. L. Cook, P. J. Martin, and J. M. Geremia, "Optical coherent state discrimination using a closed-loop quantum measurement," Nature, vol.446, pp. 774-777, 2007.
46. H. M.Wiseman, "Quantum theory of continuous feedback," Phys. Rev. A, vol.49, pp. 2133-2150, 1994.
47. R. van Handel, J. K. Stockton, and H. Mabuchi, "Feedback control of quantum state reduction," IEEE Trans. Autom. Control, vol.50, no.6, pp. 768-780, Jun. 2005.
48. A. C. Doherty and K. Jacobs, "Feedback control of quantum systems using continuous state estimation," Phys. Rev. A, vol.60, pp. 2700-2711, 1999.
49. K. Jacobs and A. P. Lund, "Feedback control of nonlinear quantum systems: A rule of thumb," Phys. Rev. Lett., vol.99, p. 020501, 2007.
50. L. Bouten, R. van Handel, and M. R. James, "An introduction to quantum filtering," SIAM J. Control Optim., vol.46, pp. 2199-2241, 2007.
51. N. Yamamoto, "Robust observer for uncertain linear quantum systems," Phys. Rev. A, vol.74, p. 032107, 2006.
52. J. E. Gough, "Construction of bilinear control Hamiltonians using the series product and quantum feedback," Phys. Rev. A, vol.78, p. 052311, 2008.
53. H. F. Hofmann, G. Mahler, and O. Hess, "Quantum control of atomic systems by homodyne detection and feedback," Phys. Rev. A, vol.57, pp. 4877-4888, 1998.
54. J. Wang and H. M. Wiseman, "Feedback-stabilization of an arbitrary pure state of a two-level atom," Phys. Rev. A, vol.64, p. 063810, 2001.
55. X. S. Liu, W. Z. Liu, R. B.Wu, and G. L. Long, "Control of state localization in a two-level quantum system," J. Opt. B: Quant. Semiclass. Opt., vol.7, pp. 66-69, 2005.
56. H. M. Wiseman, S. Mancini, and J. Wang, "Bayesian feedback versus Markovian feedback in a two-level atom," Phys. Rev. A, vol.66, p. 013807, 2002.
57. S. Mancini and H. M.Wiseman, "Optimal control of entanglement via quantum feedback," Phys. Rev. A, vol.75, p. 012330, 2007.
58. C. Hill and J. Ralph, "Weak measurement and control of entanglement generation," Phys. Rev. A, vol.77, p. 014305, 2008.
59. A. R. R. Carvalho and J. J. Hope, "Stabilizing entanglement by quantum-jump-based feedback," Phys. Rev. A, vol.76, p. 010301, 2007.
60. S. Mancini and J.Wang, "Towards feedback control of entanglement," Eur. Phys. J. D, vol.32, pp. 257-260, 2005.
61. C. Altafini, "Feedback control of spin systems," Quant. Info. Proc., vol.6, no.1, pp. 9-36, 2007.
62. C. Ahn, A. C. Doherty, and A. J. Landahl, "Continuous quantum error correction via quantum feedback control," Phys. Rev. A, vol.65, p. 042301, 2002.
63. Y. Aharonov, D. Z. Albert, and L. Vaidman, "How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100," Phys. Rev. Lett., vol.60, pp. 1351-1354, 1988.
64. K. Jacobs and D. A. Steck, "A straightforward introduction to continuous quantum measurement," Contemporary Phys., vol.47, no.5, pp. 279-303, 2006.
65. R. P. Puri, Mathematical Methods of Quantum Optics. New York: Springer Verlag, 2001.
66. G. Lindblad, "On the generators of quantum dynamical semigroups," Commun. Math. Phys., vol.48, pp. 119-130, 1976.
67. A. J. Scott and G. J. Milburn, "Quantum nonlinear dynamics of continuously measured systems," Phys. Rev. A, vol.63, p. 042101, 2001.
68. J. Gough and A. Sobolev, "Continuous measurement of canonical observables and limit stochastic Schrödinger equations," Phys. Rev. A, vol.69, p. 032107, 2004.
69. J. K. Stockton, R. van Handel, and H. Mabuchi, "Deterministic Dicke-state preparation with continuous measurement and control," Phys. Rev. A, vol.70, p. 022106, 2004.
70. K. Petersen, Ergodic Theory (Cambridge Studies in Advanced Mathematics). Cambridge, U.K.: Cambridge Univ. Press, 1990.
71. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, "Robust quantum parameter estimation: Coherent magnetometry with feedback," Phys. Rev. A, vol.69, p. 032109, 2004.
72. J. Zhang, Y. X. Liu, and F. Nori, "Cooling and squeezing the fluctuations of a nanomechanical beam by indirect quantum feedback control," Phys. Rev. A, vol.79, p. 052102, 2009.
73. J. Zhang, R. B. Wu, C. W. Li, and T. J. Tarn, "Using squeezed field to preserve two-atom entanglement against spontaneous emissions," J. Phys. A: Math. Theor., vol.42, p. 035304, 2009.
74. Y. Makhlin, G. Schön, and A. Shnirman, "Quantum-state engineering with Josephson-junction devices," Rev. Mod. Phys., vol.73, pp. 357-400, 2001.
75. J. Q. You and F. Nori, "Superconducting circuits and quantum information," Physics Today, vol.58, no.11, pp. 42-47, 2005.
76. J. Gambetta, A. Blais, M. Boissonneault, A. A. Houck, D. I. Schuster, and S. M. Girvin, "Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect," Phys. Rev. A, vol.77, p. 012112, 2008.
77. W. K. Wootters, "Entanglement of formation of an arbitrary state of two qubits," Phys. Rev. Lett., vol.80, pp. 2245-2248, 1998.
78. Y. X. Liu, L. F. Wei, J. S. Tsai, and F. Nori, "Controllable coupling between flux qubits," Phys. Rev. Lett., vol.96, p. 067003, 2006.
79. R. Alicki and K. Lendi, Quantum Dynamical Semigroup and Applications. New York: Springer Verlag, 1985.