Topological properties of reachable sets and the control of quantum bits

Systems and Control Letters

Volumn 41, Issue 3, 2000, Pages 213-221

  D'Alessandro, Domenico ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

Control of quantum mechanical systems; Nonlinear geometric control; Quantum computing; Reachable sets; Systems on lie groups

Indexed keywords

EID: 0001718151     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(00)00063-3     Document Type: Article

References (20)

1. J. Baillieul, Geometric methods for nonlinear optimal control problems, J. Optim. Theory Appl. 25 (4) (1978) 519-548.
2. R.W. Brockett, System theory on group manifolds and coset spaces, SIAM J. Control 10 (2) (1972) 265-284.
3. R. Carter, G. Segal, I. Mac Donald, Lectures on Lie Groups and Lie Algebras, London Mathematical Society, Student Texts, Vol. 32, Cambridge University Press, Cambridge, 1995.
4. C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics, Hermann and Wiley, Paris, 1977.
5. P.M. Cohn, Lie Groups, Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, Cambridge, 1965.
6. M.L. Curtis, Matrix Groups, Springer, New York, 1979.
7. D. D'Alessandro, M. Dahleh, Optimal control of two-level quantum systems, Technical Report, Department of Mechanical Engineering, University of California, Santa Barbara, 1999.
8. D. D'Alessandro, M. Dahleh, Optimal control of two-level quantum systems, in: Proceedings American Control Conference, Chicago, IL, June 2000.
9. D. Di Vincenzo, Quantum computation, Science 270 (5234) (1995) 255-261.
10. D. Di Vincenzo, Quantum gates and circuits, Proc. Roy. Soc. London A 454 (1998) 261-276.
11. V. Jurdjević, H.J. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972) 313-329.
12. H. Kunita, Supports of diffusion processes and controllability problems, in: K. Ito (Ed.), Proceedings of International Symposium on Stochastic Differential Equations, Wiley, New York, 1978, pp. 163-185.
13. E.B. Lee, L. Markus, Foundations of Optimal Control Theory, Wiley, New York, 1967.
14. F. Murnaghan, The Orthogonal and Symplectic Groups, Communications of the Dublin Institute for Advanced Studies, Series A, Theoretical Physics, No. 13, 1958.
15. J.F. Price, Lie Groups and Compact Groups, London Mathematical Society Lecture Note Series, Vol. 25, Cambridge University Press, Cambridge, 1977.
16. V. Ramakrishna, M.V. Salapaka, M. Dahleh, H. Rabitz, A. Peirce, Controllability of molecular systems, Phys. Rev. A 51 (2) (1995) 960-966.
17. K.N.S. Rao, Linear Algebra and Group Theory for Physicists, New Age International, New Delhi, India, 1996.
18. J.J. Sakurai, Modern Quantum Mechanics, Addison-Wesley, Reading, MA, 1994.
19. H.J. Sussmann, Lie brackets, real analyticity and geometric control, in: R.W. Brockett, R.S. Millman, H.J. Sussmann (Eds.), Differential Geometric Control Theory, Birkhauser, Boston, 1983, pp. 1-116.
20. W. Tung, Group Theory in Physics, World Scientific, Singapore, 1985.