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Feedback control of quantum system

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Abstract

Feedback is a significant strategy for the control of quantum system. Information acquisition is the greatest difficulty in quantum feedback applications. After discussing several basic methods for information acquisition, we review three kinds of quantum feedback control strategies: quantum feedback control with measurement, coherent quantum feedback, and quantum feedback control based on cloning and recognition. The first feedback strategy can effectively acquire information, but it destroys the coherence in feedback loop. On the contrary, coherent quantum feedback does not destroy the coherence, but the capability of information acquisition is limited. However, the third feedback scheme gives a compromise between information acquisition and measurement disturbance.

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References

  1. Shapiro M. and Brumer P., Principles of the quantum control of molecular processes. New Jersey: John Wiley & Sons, Inc., 2003

    Google Scholar 

  2. Rabitz H., de Vivie-Riedle R, Motzkus M, et al., Whither the future of controlling quantum phenomena? Science, 2000, 288: 824–828

    Article  ADS  Google Scholar 

  3. Dong Dao-yi and Chen Zong-hai, Applications of quantum control theory in chemistry. Progress in Chemistry, 2005, 17(4): 581–587 (in Chinese)

    Google Scholar 

  4. Chen Zong-hai, Dong Dao-yi, and Zhang Chen-bin, Quantum control: An introduction. Hefei: University of Science and Technology of China Press, 2005

    Google Scholar 

  5. Rice S. and Zhao M., Optical Control of Molecular Dynamics. New York: Wiley, 2000

    Google Scholar 

  6. Nielsen M. A. and Chuang I. L., Quantum computation and quantum information, Cambridge: Cambridge University Press, 2000

    MATH  Google Scholar 

  7. Solomon A. I. and Schrirmer S. G., Limitations in quantum control, Int. J. Mod. Phys. B, 2002, 16: 2107–2112

    Article  MATH  ADS  Google Scholar 

  8. Huang G. M., Tarn T. J., and Clark J. W., On the controllability of quantum-mechanical systems. J. Math. Phys., 1983, 24(11): 2608–2618

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Albertini F. and D’Alessandro D., Notions of controllability for bilinear multilevel quantum systems, IEEE Trans. Automat. Contr., 2003, 48(8): 1399–1403

    Article  MathSciNet  Google Scholar 

  10. Schirmer S. G., Fu H, and Solomon A. I., Complete controllability of quantum systems, Phys. Rev. A, 2001, 63: 063410

    Google Scholar 

  11. Zhang Chen-bin, Dong Dao-yi, and Chen Zong-hai, Control of non-controllable quantum system: A quantum control algorithm based on Grover iteration, J. Opt. B: Quantum Semiclass Opt., 2005, 7: S313–S317

    Article  MathSciNet  ADS  Google Scholar 

  12. Peirce A. P., Dahleh M., and Rabitz H., Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications, Phys. Rev. A, 1988, 37(12): 4950–4964

    Article  MathSciNet  ADS  Google Scholar 

  13. Rabitz H., Optimal control of quantum systems: Origins of inherent robustness to control field fluctuations, Phys. Rev. A, 2002, 66: 063405

    Google Scholar 

  14. Khaneja N., Brockett R., and Glaser S. J., Time optimal control in spin systems, Phys. Rev. A, 2001, 63: 032308

    Google Scholar 

  15. Warren W. S., Rabitz H., and Dahleh M., Coherent control of quantum dynamics: the dream is alive, Science, 1993, 259: 1581–1589

    MathSciNet  ADS  Google Scholar 

  16. Weinacht T. C. and Bucksbaum P. H., Using feedback for coherent control of quantum systems, J. Opt. B: Quantum Semiclass Opt., 2002, 4: R35–R52

    Article  ADS  Google Scholar 

  17. Rice S. A., Interfering for the good of a chemical reaction, Nature, 2001, 409: 422–426

    Article  ADS  Google Scholar 

  18. Dong Dao-yi and Chen Zong-hai, Progress of the research on quantum feedback control, Chinese Journal of Quantum Electronics, 2005, 22(6): 833–839 (in Chinese)

    Google Scholar 

  19. Haus H. A. and Yamamoto Y., Theory of feedback-generated states, Phys. Rev. A, 1986, 34(1): 270–292

    Article  ADS  Google Scholar 

  20. Wiseman H. M. and Milburn G. J., Quantum theory of optical feedback via homodyne detection, Phys. Rev. Lett., 1993, 70(5): 548–551

    Article  ADS  Google Scholar 

  21. Doherty A. C. and Jacobs K., Feedback control of quantum systems using continuous state estimation, Phys. Rev. A, 1999, 60: 2700–2711

    Article  ADS  Google Scholar 

  22. Giovannetti V., Tombesi P., and Vitali D., Non-Markovian quantum feedback from homodyne measurements: The effect of a nonzero feedback delay time, Phys. Rev. A, 1999, 60(2): 1549–1561

    Article  ADS  Google Scholar 

  23. Lloyd S., Coherent Quantum Feedback, Phys. Rev. A, 2000, 62: 022108

    Google Scholar 

  24. Dong Dao-yi, Zhang Chen-bin, Chen Zong-hai, and Chen Chun-lin, Information-technology approach to quantum feedback control, Int. J. Mod. Phys. B, 2006, 20: 1304–1316

    Article  ADS  MathSciNet  Google Scholar 

  25. Yamamoto Y., Imoto N., and Machida S., Amplitude squeezing in a semiconductor laser using quantum nondemolition measurements and negative feedback, Phys. Rev. A, 1986, 33(5): 3243–3261

    Article  ADS  Google Scholar 

  26. Dong Dao-yi, Chen Chun-lin, Chen Zong-hai, and Zhang Chen-bin, Estimation-based information acquisition in quantum feedback control. ICCSA06, 2006, Dynamics of Continuous, Discrete and Impulsive Systems (in press)

  27. Preskill J., Lecture Notes for Physics229: Quantum Information and Computation. California Institute of Technology, 1998. (http://www.theory.caltech.edu/people/preskill/ph229/)

  28. Braginsky V. B. and Khalili F. Y., Quantum nondemolition measurements: the route from toys to tools, Rev. Mod. Phys., 1996, 68: 1–11

    Article  MathSciNet  ADS  Google Scholar 

  29. Braginsky V. B., Vorontsov Y. I., and Thorne K. S., Quantum non-demolition measurements, Science, 1980, 209: 547–557

    ADS  Google Scholar 

  30. Tombesi P. and Vitali D., Physical realization of an environment with squeezed quantum fluctuations via quantum-nondemolition-mediated feedback and Phys. Rev. A, 1994, 50(5): 4253–4257

    Article  Google Scholar 

  31. Wiseman H. M. and Milburn G. J., Squeezing via feedback, Phys. Rev. A, 1994, 49(2): 1350–1366

    Article  ADS  Google Scholar 

  32. Wang J. and Wiseman H. M., Feedback-stabilization of an arbitrary pure state of a two-level atom, Phys. Rev. A, 2001, 64: 063810

    Google Scholar 

  33. Reiner J. E., Wiseman H. M., and Mabuchi H., Quantum jumps between dressed states: A proposed cavity-QED test using feedback, Phys. Rev. A, 2003, 67: 042106

    Google Scholar 

  34. Wiseman H. M., Mancini S., and Wang J., Bayesian feedback versus Markovian feedback in a two-level atom, Phys. Rev. A, 2002, 66: 013807

    Google Scholar 

  35. Doherty A. C., Habib S., Jacobs K., et al., Quantum feedback control and classical control theory, Phys. Rev. A, 2000, 62: 012105

    Google Scholar 

  36. Doherty A. C., Habib S., and Jungman G., Information, Disturbance, and Hamiltonian Quantum Feedback Control, Phys. Rev. A, 2001, 63: 062306

    Google Scholar 

  37. Korotkov A. N., Selective quantum evolution of a qubit state due to continuous measurement, Phys. Rev. B, 2001, 63: 115403

    Google Scholar 

  38. Ruskov R. and Korotkov A. N., Quantum feedback control of a solid-state qubit. Phys. Rev. B, 2002, 66: 041401R

    Google Scholar 

  39. Wang J., Wiseman H. M. and Milburn G. J., Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment, Chem. Phys., 2001, 268: 221–235

    Article  Google Scholar 

  40. Nelson R. J., Weinstein Y., Cory D., et al., Experimental demonstration of fully coherent quantum feedback, Phys. Rev. Lett., 2000, 85: 3045–3048

    Article  ADS  Google Scholar 

  41. Dong Dao-yi, Zhang Chen-bin, and Chen Zong-hai, Quantum feedback control using quantum cloning and state recognition, In: Proceedings of the 16th IFAC World Congress, Prague, 2005, July 4–8: 1965

  42. Wootters W. K. and Zurek W. H., A single quantum cannot be cloned. Nature, 1982, 299: 802–803

    Article  ADS  Google Scholar 

  43. Scarani V., Iblisdir S., Gisin N., et al., Quantum cloning, Rev. Mod. Phys., 2005, 77(4): 1225–1256

    Article  MathSciNet  ADS  Google Scholar 

  44. Duan L. M. and Guo G. C., Probabilistic cloning and identification of linearly independent quantum states, Phys. Rev. Lett., 1998, 80(22): 4999–5002

    Article  ADS  Google Scholar 

  45. Bužek V. and Hillery M., Quantum copying: Beyond the no-cloning theorem, Phys. Rev. A, 1996, 54(3): 1844–1852

    Article  MathSciNet  ADS  Google Scholar 

  46. Gisin N. and Massar S., Optimal quantum cloning machines, Phys. Rev. Lett., 1997, 79(11): 2153–2156

    Article  ADS  Google Scholar 

  47. Dong Dao-yi, Chen Zong-hai, and Jiang Sheng-xiang, Pattern recognition of quantum information based on pattern-distance, Journal of Systems Engineering and Electronics, 2005, 16(4): 917–923

    Google Scholar 

  48. Dong Dao-yi and Chen Zong-hai, Clustering recognition of quantum states based on quantum module distance, Acta Sinica Quantum Optica, 2003, 9: 144–148

    Google Scholar 

  49. Fuchs C. A. and van de Graaf J., Cryptographic distinguishability measures for quantum-mechanical states, IEEE Trans, Information Theory, 1999, 45(4): 1216–1227

    Article  MATH  Google Scholar 

  50. Jacobs K., How to project qubits faster using quantum feedback, Phys. Rev. A, 2003, 67: 030301R

    Google Scholar 

  51. Handel R. van, Stockton J. K., and Mabuchi H., Feedback control of quantum state reduction, IEEE Trans. Automat. Contr., 2005, 50: 768–780

    Article  Google Scholar 

  52. Morrow N. V., Dutta S. K., and Raithel G., Feedback control of atomic motion in an optical lattice, Phys. Rev. Lett., 2002, 88: 093303

    Google Scholar 

  53. Handel R. van, Stockton J. K., and Mabuchi H., Modelling and feedback control design for quantum state preparation, J. Opt. B: Quantum Semiclass Opt., 2005, 7: S179–S197

    Article  Google Scholar 

  54. Geremia J. M., Stockton J. K., and Mabuchi H., Real-time quantum feedback control of atomic spin-squeezing, Science, 2004, 304(5668): 270–273

    Article  ADS  Google Scholar 

  55. Gough J., Belavkin V. P., and Smolyanov O. G., Hamilton-Jacobi-Bellman equations for quantum optimal feedback control, J. Opt. B: Quantum Semiclass Opt., 2005, 7: S237–S244

    Article  MathSciNet  ADS  Google Scholar 

  56. Combes J. and Jacobs K., Rapid state reduction of quantum systems using feedback control, Phys. Rev. Lett., 2006, 96: 010504

    Google Scholar 

  57. Dong Dao-yi, Chen Chun-lin, Zhang Chen-bin, and Chen Zong-hai. Quantum robot: structure, algorithms and applications, Robotica, in press (DOI: 10.1017/S0263574705002596)

  58. Dong Dao-yi, Chen Chun-lin, Chen Zong-hai, and Zhang Chen-bin, Quantum mechanics helps in learning for more intelligent robots, Chin. Phys. Lett., 2006, 23(7): 1691–1694

    Article  ADS  Google Scholar 

  59. Dong Dao-yi, Chen Chun-lin, and Chen Zong-hai, Quantum reinforcement learning, ICNC2005, Lecture Notes in Computer Science, 2005, 3611: 686–689

    Article  Google Scholar 

  60. Dong Dao-yi, Chen Chun-lin, Zhang Chen-bin, and Chen Zong-hai, An autonomous mobile robot based on quantum algorithm, CIS05, Lecture Notes in Artificial Intelligence, 2005, 3801: 393–398

    Google Scholar 

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Correspondence to Chen Zong-hai.

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Dong, Dy., Chen, Zh., Zhang, Cb. et al. Feedback control of quantum system. Front. Phys. China 1, 256–262 (2006). https://doi.org/10.1007/s11467-006-0032-x

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  • DOI: https://doi.org/10.1007/s11467-006-0032-x

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