General methods to control right-invariant systems on compact Lie groups and multilevel quantum systems

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 39, 2009, Pages

  D'Alessandro, Domenico ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449631340     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/39/395301     Document Type: Article

References (33)

1. Albertini F and D'Alessandro D 2003 Notions of controllability for bilinear multilevel quantum systems IEEE Trans. Autom. Control 48 1399-403
2. Cassels J W S 1957 An introduction to diophantine approximation Cambridge Tracts in Mathematics and Mathematical Physics vol 35 (New York: Cambridge University Press)
3. Childs A M 2008 On the relationship between continuous and discrete-time quantum walk arXiv:0810.0312v2 [quant-ph]
4. D'Alessandro D 2009 Connection between continuous and discrete time quantum walks on d-dimensional lattices; extensions to general graphs arXiv:0902.3496 [quant-ph]
5. D'Alessandro D 2004 Optimal evaluation of generalized angles with applications to control Automatica 40 1997-2002
6. D'Alessandro D 2002 Uniform finite generation of compact Lie groups Syst. Control Lett. 47 87-90
7. D'Alessandro D 2003 Controllability of one spin and two interacting spins Math. Control Signals Syst. 16 1-25
8. D'Alessandro D 2008 Lie algebraic analysis and control of quantum dynamics arXiv.org/quant-ph:0803.1193
9. D'Alessandro D 2007 Introduction to Quantum Control and Dynamics (Boca Raton, FL: CRC Press)
10. Hildebrand F B 1987 Introduction to Numerical Analysis (Dover Books on Advanced Mathematics) 2nd edn (New York: Dover Publications)
11. Hilgert J, Hoffmann K H and Lawson J D 1989 Lie Groups, Convex Cones, and Semigroups (Oxford: Oxford University Press)
12. Horn R A and Johnson C R 1994 Topics in Matrix Analysis (Cambridge: Cambridge University Press)
13. Huang G M, Tarn T J and Clark J W 1983 On the controllability of quantum-mechanical systems J. Math. Phys. 24 2608-18
14. Jurdjević V and Sussmann H 1972 Control systems on Lie groups J. Diff. Eqns 12 313-29
15. Jurkat W, Kratz W and Peyerimhoff A 1979 On the best two-dimensional Dirichlet-approximations and their algorithmic calculation Math. Ann. 244 1-32
16. Just B 1992 Generalizing the continued fraction algorithm to arbitrary dimensions SIAM J. Comput. 21 909-26
17. Khaneja N, Brockett R and Glaser S J 2001 Time optimal control of spin systems Phys. Rev. A 63 032308
18. Knapp A 2002 Lie Groups: Beyond an Introduction 2nd edn (Boston, MA: Birkhauser)
19. Koch R and Lowenthal F 1975 Uniform finite generation of three-dimensional linear Lie groups Can. J. Math. 27 396-417
20. Moler C and Van Loan C 2003 Nineteen dubious ways to compute the exponential of a matrix, twentyfive years later SIAM Rev. 45 3-49
21. Moskowitz M and Sacksteder R 2003 The exponential map and differential equations on real Lie groups J. Lie Theory 13 291-306
22. Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
23. Polack T, Suchowski H and Tannor D J 2009 Uncontrollable quantum systems: a classification scheme based on Lie subalgebras Phys. Rev. A 79 053403
24. Rice S A and Zhao M 2000 Optical Control of Molecular Dynamics (New York: Wiley)
25. Rosen K H 2005 Elementary Number Theory and its Applications 5th edn (Reading, MA: Addison-Wesley)
26. Schirmer S G 2001 Quantum control using Lie group decompositions Proc. 40-th IEEE Conf. on Decision and Control (4-7 Dec.) vol 1 pp 298-303
27. Shapiro M and Brumer P 2003 Principles of the Quantum Control of Molecular Processes (Hoboken, NJ: Wiley)
28. Shen Z, Hsieh M and Rabitz H 2006 Quantum optimal control: Hessian analysis of the control landscape J. Chem. Phys. 124 204106
29. Stepanski M R 2007 Compact Lie Groups (Graduate Texts in Mathematics) (Berlin: Springer)
30. Wang X and Schirmer S 2009 Analysis of Lyapunov method for control of quantum states: generic case arXiv:0901.4515 [quant-ph]
31. Wang X and Schirmer S 2009 Analysis of Lyapunov method for control of quantum states: nongeneric case arXiv:0901.4522 [quant-ph]
32. Wood J 1973 Power conversion in electrical networks NASA Technical Report CR-120830
33. Wood J 1974 PhD Thesis Harvard University