Efficient algorithms for the laboratory discovery of optimal quantum controls

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 70, Issue 1 2, 2004, Pages

  Turinici, Gabriel ^a,b   Le Bris, Claude ^a,b   Rabitz, Herschel ^c  

^a INRIA ROCQUENCOURT   (France)

^b UNIVERSITÉ PARIS EST   (France)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; GENETIC ALGORITHMS; LARGE SCALE SYSTEMS; LASER PULSES; LASER THEORY; MONTE CARLO METHODS; OPTIMIZATION; OSCILLATIONS; QUANTUM INTERFERENCE PHENOMENA; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE;

COST FUNCTIONS; NOISE LEVELS; OPTIMIZATION ALGORITHMS; QUANTUM CONTROLS;

QUANTUM THEORY;

EID: 42749104212     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.016704     Document Type: Article

References (46)

1. S. Shi, A. Woody, and H. Rabitz, J. Chem. Phys. 88, 6870 (1988).
2. M. Shapiro and P. Brumer, Acc. Chem. Res. 22, 407 (1989).
3. H. Rabitz, G. Turinici, and E. Brown, in Computational Chemistry, edited by C. Le Bris, Special Volume of Handbook of Numerical Analysis, Vol. X, edited by P. G. Ciarlet (Elsevier Science, New York, 2003), pp. 833-887.
4. S. Rice and M. Zhao, Optical Control of Quantum. Dynamics (Wiley, New York, 2000).
5. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, Science 282, 919 (1998).
6. R. J. Levis, G. Menkir, and H. Rabitz, Science 292, 709 (2001).
7. T. Weinacht, J. Ahn, and P. Bucksbaum, Nature (London) 397, 233 (1999).
8. C. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, Chem. Phys. Lett. 280, 151 (1997).
9. C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, J. Am. Chem. Soc. 120, 13023 (1998).
10. T. Hornung, R. Meier, and M. Motzkus, Chem. Phys. Lett. 326, 445 (2000).
11. J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, Appl. Phys. Lett. 77, 924 (2000).
12. R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
13. A generally accepted view is that G As are efficient only when the stochastic operators have been adapted to the particular problem under study. It is thus surprising that GAs perform very well in this case generally without any tuning of the stochastic operators.
14. There exist situations when the derivatives are so expensive, either to determine or to implement, that one prefers to avoid them.
15. T. G. Kolda, R. M. Lewis, and V. Torczon, SIAM Rev. 45(3), 385 (2003).
16. Since the function evaluations are so cheap, one may ask why not use them to determine first derivatives through finite difference schemes. To some extent, the strategies we suggest reflect this remark, but only in a loose way. Indeed, calculating gradients often is not attractive in the optimization of highly nonconvex functionals such as the ones expected to exist in general quantum control problems.
17. Inversion of quantum control data is one circumstance in which reducing the number of experiments is of interest. The inversion operations can be far more time consuming than the experiments, and a premium would be placed on the efficiency of the inversion algorithm. In this case the control field would be chosen to reduce the uncertainty in the extracted Hamiltonian information [18,19].
18. J. M. Geremia and H. Rabitz, Phys. Rev. Lett. 89, 263902 (2002).
19. J. M. Geremia and H. Rabitz, J. Chem. Phys. 118, 5369 (2003).
20. R. M. Lewis and V. Torczon, SIAM J. Optim. 12, 1075 (2002).
21. P. D. Hough, T. G. Kolda, and V. J. Torczon, SIAM J. Sci. Comput. (USA) 23, 134 (2001).
22. R. M. Lewis and V. Torczon, SIAM J. Optim. 10, 917 (2000).
23. R. M. Lewis and V. Torczon, SIAM J. Optim. 9, 1082 (1999).
24. V. Torczon, SIAM J. Optim. 7, 1 (1997).
25. E. Anderson and M. Ferris, SIAM J. Optim. 11, 837 (2001).
26. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++, 2nd ed. (Cambridge University Press, Cambridge, 2002).
27. C. Léonard, F. Le Quéré, P. Rosmus, C. Puzzarini, and M. de Lara Castells, Phys. Chem. Chem. Phys. 2, 1117 (2000).
28. C. Léonard, G. Chambaud, P. Rosmus, S. Carter, and N. Handy, Phys. Chem. Chem. Phys. 3, 503 (2001).
29. R. R. Barton and J. S. J. Ivey, Manage. Sci. 42, 954 (1996). Following the notations of the paper, the modified simplex algorithm we used corresponds to the variants labeled "S9" and "RS."
30. D. G. Humphrey and J. R. Wilson, INFORMS J. Comput. 12, 272 (2000).
31. Y. C. Ho, R. S. Sreenivas, and P. Vakjli, Discrete Event Dyn. Syst. 2, 61 (1992); URL: http://citeseer.nj.nec.com/ho96ordinal.html
32. Y.-C. Ho and M. Larson, Discrete Event Dyn. Syst. 5, 281 (1995); URL: http://citeseer.nj.nec.com/ho95ordinal.html
33. M. Deng and Y.-C. Ho, Automatica J. IFAC 35, 331 (1999).
34. Y.-C. Ho, Inform. Sci. 113, 169 (1999).
35. This approach is based on the fact that the estimation of the relative ordering between two noisy values converges much more rapidly than the estimation of their difference. This remark is exploited by looking for ordinal rather than cardinal optimization, i.e., concentrating on finding good designs - relative to all possible designs - rather than on accurately estimating (by optimizing directly) the performance value of these designs. The solution obtained will therefore score conveniently in terms of percentile rank among all designs, but its precise performance with respect to the global optimum value is not known in advance.
36. D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, MA, 1989).
37. M. Keijzer, J. Merelo, G. G. Romero, and M. Schoenauer, Evolving Objects: A General Purpose Evolutionary Computation Library, Proceedings of the 5th International Conference on Artificial Evolution, 29-31 October 2001, Université de Bourgogne, France; URL: http://eodev.sourceforge.net
38. A. Torn and A. Zilinskas, Global Optimization, Lecture Notes in Computer Science, Vol. 350 (Springer, Berlin, 1989).
39. B. Li, G. Turinici, V. Ramakhrishna, and H. Rabitz, J. Phys. Chem. B 106, 8125 (2002).
40. H. Rabitz, Phys. Rev. A 66, 063405 (2002).
41. J. M. Geremia, W. Zhu, and H. Rabitz, J. Chem. Phys. 113, 10841 (2000).
42. We also used the modified simplex algorithm on signal averaged surfaces, and we confirmed that it does converge to good quality solutions.
43. H. Rabitz, M. Hsieh, and C. Rosental, Science 303, 1998 (2004).
44. G. Tóth, A. Lörincz, and H. Rabitz, J. Chem. Phys. 101, 3715 (1994).
45. P. Gross, D. Neuhauser, and H. Rabitz, J. Chem. Phys. 98, 4557 (1993).
46. M. Q. Phan and H. Rabitz, J. Chem. Phys. 110, 34 (1999).