Control of quantum systems despite feedback delay

IEEE Transactions on Automatic Control

Volumn 54, Issue 4, 2009, Pages 876-881

  Kashima, Kenji ^a   Yamamoto, Naoki ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b KEIO UNIVERSITY   (Japan)

Author keywords

Delay systems; Filtering; Quantum control; Spin systems; Sum of squares

Indexed keywords

DELAY SYSTEMS; FILTERING; QUANTUM CONTROL; SPIN SYSTEMS; SUM OF SQUARES;

FEEDBACK; QUANTUM ELECTRONICS; QUANTUM OPTICS; SPIN DYNAMICS; STABILITY CRITERIA; STOCHASTIC SYSTEMS;

DELAY CONTROL SYSTEMS;

EID: 67349233545     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.2010969     Document Type: Article

References (37)

1. J. J. Sakurai, Modern Quantum Mechanics (Revised Ed.). Boston, MA: Addison Wesley, 1994.
2. V. P. Belavkin, "Quantum filtering of Markov signals with white quantum noise," Radiotechnika i Electronika, vol. 25, pp. 1445-1453, 1980.
3. V. P. Belavkin, "Quantum stochastic calculus and quantum nonlinear filtering," J. Multivariate Anal., vol. 42, pp. 171-201, 1992.
4. V. P. Belavkin, "Quantum continual measurements and a posteriori collapse on CCR," Commun. Math. Phys., vol. 146, pp. 611-635, 1992.
5. L. Bouten, R. Van Handel, and M. R. James, "An introduction to quantum filtering," SIAM J. Control Optim., vol. 46, pp. 2199-2241, 2007.
6. L. Bouten, S. C. Edwards, and V. B. Belavkin, "Bellman equations for optimal feedback control of qubit states," J. Phys. B, Mol. Opt. Phys., vol. 38, pp. 151-160, 2005.
7. A. C. Doherty and K. Jacobs, "Feedback control of quantum systems using continuous state-estimation," Phys. Rev. A, vol. 60, p. 2700, 1999.
8. R. van Handel, J. K. Stockton, and H. Mabuchi, "Feedback control of quantum state reduction," IEEE Trans. Automat. Control, vol. 50, no. 6, pp. 768-780, Jun. 2005.
9. M. R. James, "A quantum Langevin formulation of risk-sensitive optimal control," J. Opt. B: Quantum Semiclass. Opt., vol. 7, p. 198, 2005.
10. M. Mirrahimi and R. van Handel, "Stabilizing feedback controls for quantum systems," SIAM J. Control Optim., vol. 46, pp. 445-467, 2007.
11. L. Thomsen, S. Mancini, and H. M. Wiseman, "Continuous quantum nondemolition feedback and unconditional atomic spin squeezing," J. Phys. B, vol. 35, p. 4937, 2002.
12. H. M. Wiseman, "Quantum theory of continuous feedback," Phys. Rev. A, vol. 49, p. 2133, 1993.
13. N. Yamamoto, K. Tsumura, and S. Hara, "Feedback control of quantum entanglement in a two-spin system," Automatica, vol. 43, pp. 981-992, 2007.
14. 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.
15. C. Ahn, H. M. Wiseman, and G. J. Milburn, "Quantum error correction for continuously detected errors," Phys. Rev. A, vol. 67, p. 052310, 2003.
16. R. L. Hudson and K. R. Parthasarathy, "Quantum Ito's formula and stochastic evolution," Commun. Math. Phys., vol. 93, p. 301, 1984.
17. J. Stockton, M. Armen, and H. Mabuchi, "Programmable logic devices in experimental quantum optics," J. Opt. Soc. Am. B, vol. 19, pp. 3019-3027, 2002.
18. D. A. Steck, K. Jacobs, H. Mabuchi, S. Habib, and T. Bhattacharya, "Feedback cooling of atomic motion in cavity QED," Phys. Rev. A, vol. 74, p. 012322, 2006.
19. X. Mao, "Exponential stability of stochastic delay interval systems with Markovian switching," IEEE Trans. Automat. Control, vol. 47, no. 10, pp. 1604-1612, Oct. 2002.
20. S. A. Mohammed, "Stochastic differential systems with memory: Theory, examples and applications," in Stochastic Analysis and Related Topics, VI (Geilo, 1996). Boston, MA: Birkhäuser, 1998, pp. 1-77.
21. D. Yue and Q.-L. Han, "Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching," IEEE Trans. Automat. Control, vol. 50, no. 2, pp. 217-222, Feb. 2005.
22. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information Cambridge, U.K.: Cambridge University Press, 2000.
23. C. Gardiner and P. Zoller, Quantum Noise, 3rd ed. New York: Springer, 2004.
24. J. K. Stockton, "Continuous Quantum Measurement of Cold Alkali-Atom Spins," Ph.D. dissertation, California Institute of Technology, Pasadena, 2006.
25. 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.
26. F. Ticozzi and L. Viola, "Quantum Markovian subsystems: Invariance, attractivity, and control," IEEE Trans. Automat. Control, vol. 53, no. 9, pp. 2048-2063, Oct. 2008.
27. C. Altafini and F. Ticozzi, Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics arXiv:qUant-ph/0510222 2005.
28. L. Bouten and R. Van Handel, On the Separation Principle of Quantum Control, in Quantum Stochastics and Information: Statistics, Filtering and Control, V.P. Belavkin and M. Guta, Eds. Singapore:WOrld Scientific, 2008.
29. S. L. Adler, D. C. Brody, T. A. Brun, and L. P. Hughston, "Martin-gale models for quantum state reduction," J. Phys. A, vol. 34, pp. 8795-8820, 2001.
30. G. Chesi, A. Tesi, A. Vicino, and R. Genesio, "On convexification of some minimum distance problems," in Proc. 5th. Eur. Control Conf. 1999, [CD ROM].
31. B. Tibken, "Estimation of the domain of attraction for polynomial systems via LMI's," in Proc. 39th. IEEE Conf. Decision Control, 2000, pp. 3860-3864.
32. P. A. Parillo, "Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization," Ph.D. dissertation, California Institute of Technology, Pasadena, 2000.
33. P. A. Parillo, "Semidefinite programming relaxations for semialgebraic problems," Math. Program., ser. B, vol. 96, pp. 293-320, 2003.
34. S. Prajna, A. Papachristodoulou, and P. A. Parrilo, SOSTOOLS Ver 2.02: Sum of Squares Optimization Toolbox for MATLAB 2004.
35. J. Sturm and SeDuMi Version 1.1 2006.
36. K. Kashima and K. Nishio, "Global stabilization of two-dimensional quantum spin systems despite estimation delay," in Proc. 46th. IEEE CDC, 2007, pp. 6352-6357.
37. H. J. Kushner, "On the stability of processes defined by stochastic difference-differential equations," J. Differential Equations, vol. 4, pp. 424-443, 1968.