Optimal control landscape for the generation of unitary transformations with constrained dynamics

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 6, 2010, Pages

  Hsieh, Michael ^a   Wu, Rebing ^c   Rabitz, Herschel ^d   Lidar, Daniel ^a,b  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b Tsinghua University ^*  (United States)

^c TSINGHUA UNIVERSITY   (China)

^d PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINED DYNAMICS; CONTROL PROBLEMS; CONTROL VARIABLE; DYNAMICAL SYMMETRY; LANDSCAPE ANALYSIS; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; OPTIMAL SOLUTIONS; OPTIMIZATION PROBLEMS; PHYSICAL SYSTEMS; QUANTUM CONTROL; QUANTUM-INFORMATION PROCESSING; UNITARY TRANSFORMATIONS;

CONTROL; CONTROL THEORY; DATA PROCESSING; DYNAMICAL SYSTEMS; QUANTUM OPTICS; QUANTUM THEORY; TOPOLOGY;

OPTIMIZATION;

EID: 77954182303     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.062352     Document Type: Article

References (64)

1. P. Brumer and M. Shapiro, Principles of Quantum Control of Molecular Processes (Wiley, Hoboken, NJ, 2003).
2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
3. S. Shi and H. Rabitz, Chem. Phys. CMPHC2 0301-0104 10.1016/0301-0104(89) 90011-6 139, 185 (1989).
4. G. Gordon, G. Kurizki, and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.010403 101, 010403 (2008);
5. C. Meier and M. Heitz, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1946737 123, 044504 (2005);
6. I. Serban, J. Werschnik, and E. K. U. Gross, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.053810 71, 053810 (2005);
7. M. Sukharev and T. Seideman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.093004 93, 093004 (2004);
8. C. M. Tesch and R. de Vivie-Riedle, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1818131 121, 12158 (2004);
9. E. Luc-Koenig, R. Kosloff, F. Masnou-Seeuws, and M. Vatasescu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.033414 70, 033414 (2004);
10. D. Babikov, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1791635 121, 7577 (2004);
11. B. Lan, I. Vrabel, and W. Jakubetz, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1812531 121, 10401 (2004);
12. J. P. Palao and R. Kosloff, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062308 68, 062308 (2003);
13. D. Geppert, A. Hoffman, and R. de Vivie-Riedle, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1603221 119, 5901 (2003);
14. T. Hornung, S. Gordienko, R. de Vivie-Riedle, and B. Verhaar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.043607 66, 043607 (2002);
15. J. P. Palao and R. Kosloff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.188301 89, 188301 (2002);
16. T. Mançal, U. Kleinekathofer, and V. May, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1481856 117, 636 (2002);
17. T. Hornung, M. Motzkus, and R. de Vivie-Riedle, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1378817 115, 3105 (2001);
18. Y. Ohtsuki, H. Kono, and Y. Fujimura, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.477593 109, 9318 (1998).
19. R. S. Judson and H. Rabitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.1500 68, 1500 (1992).
20. C. J. Bardeen, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(97) 01081-6 280, 151 (1997);
21. M. Bergt, T. Brixner, M. Strehle, and G. Gerber, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp992541k 103, 10381 (1999);
22. D. Meshulach and Y. Silberberg, Nature (London) NATUAS 0028-0836 10.1038/24329 396, 239 (1998);
23. A. Assion, Science SCIEAS 0036-8075 10.1126/science.282.5390.919 282, 919 (1998);
24. T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B: Lasers Opt. 71, 277 (2000);
25. T. Weinacht, J. White, and P. H. Bucksbaum, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp991977x 103, 10166 (1999);
26. R. Bartels, Nature (London) NATUAS 0028-0836 10.1038/35018029 406, 164 (2000);
27. C. Daniel, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(01)00315-9 267, 247 (2001);
28. T. Hornung, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(01)00254-3 267, 261 (2001);
29. J. Kunde, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.18.000872 18, 872 (2001);
30. T. Brixner, H. Damrauer, P. Niklaus, and G. Gerber, Nature (London) NATUAS 0028-0836 10.1038/35102037 414, 57 (2001);
31. R. J. Levis, G. M. Menkir, and H. Rabitz, Science SCIEAS 0036-8075 10.1126/science.1059133 292, 709 (2001);
32. M. Bergt, J. Organomet. Chem. JORCAI 0022-328X 10.1016/S0022-328X(02) 01821-1 661, 199 (2002);
33. T. Brixner, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340308233549 50, 539 (2003);
34. E. Hertz, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1524621 118, 595 (2003).
35. J. P. Palao and R. Kosloff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.188301 89, 188301 (2002).
36. C. M. Tesch and R. de Vivie-Riedle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.157901 89, 157901 (2002);
37. J. P. Palao and R. Kosloff, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062308 68, 062308 (2003);
38. D. Babikov, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1791635 121, 7577 (2004);
39. S. Suzuki, K. Mishima, and K. Yamashita, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/j.cplett.2005.05.090 410, 358 (2005);
40. Y. Ohtsuki, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/j.cplett.2005.01. 080 404, 126 (2005);
41. U. Troppmann and R. de Vivie-Riedle, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1881112 122, 154105 (2005).
42. H. Rabitz, M. Hsieh, and C. Rosenthal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.052337 72, 052337 (2005).
43. M. Hsieh and H. Rabitz, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.042306 77, 042306 (2008).
44. J. von Neumann, Tomsk Univ. Rev. 1, 286 (1937).
45. Differential and Combinatorial Topology, edited by, S. S. Cairns, (Princeton University Press, Princeton, 1965).
46. L. Geissinger, Lin. Multilin. Alg. LNMLAZ 0308-1087 10.1080/ 03081087808817212 5, 321 (1978).
47. M. Shayman (unpublished).
48. R. Brockett, Lin. Alg. Appl. LAAPAW 0024-3795 10.1016/0024-3795(89)90675- 7 122, 761 (1989)
49. K. Moore. M. Hsieh, and H. Rabitz, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2907740 128, 154117 (2008).
50. F. Dyson, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703773 3, 140 (1962).
51. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, UK, 1987).
52. N. E. Bonesteel, D. Stepanenko, and D. P. DiVincenzo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.207901 87, 207901 (2001).
53. D. Stepanenko, N. E. Bonesteel, D. P. DiVincenzo, G. Burkard, and D. Loss, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.68.115306 68, 115306 (2003).
54. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.915 58, 915 (1998).
55. A. Childs, E. Farhi, and S. Gutmann, Quant. Info. Proc. 1570-0755 10.1023/A:1019609420309 1, 35 (2002).
56. G. Giedke and J. Ignacio Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032316 66, 032316 (2002).
57. R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.37.3028 37, 3028 (1988).
58. Statistical Theories of Spectra: Fluctuations, edited by, C. E. Porter, (Academic, New York, 1965).
59. M. L. Mehta, Random Matrices (Academic, New York, 1991).
60. Algebraic K-Theory, edited by, G. Banaszak, W. Gajda, and, P. Krason, (American Mathematical Society, Providence, RI, 1996).
61. L. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains (American Mathematical Society, Providence, RI, 1963).
62. U. Helmke and J. Moore, Optimization and Dynamical Systems (Springer-Verlag, Berlin, 1994).
63. R. Horn and C. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, UK, 1985).
64. M. Demazure, Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems (Springer-Verlag, Berlin, 2000).