Landscape for optimal control of quantum-mechanical unitary transformations

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 72, Issue 5, 2005, Pages

  Rabitz, Herschel ^a   Hsieh, Michael ^a   Rosenthal, Carey ^b  

^a PRINCETON UNIVERSITY   (United States)

^b DREXEL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROLLABLE QUANTUM SYSTEM; UNITARY TRANSFORMATIONS;

MATHEMATICAL TRANSFORMATIONS; OPTIMAL CONTROL SYSTEMS;

QUANTUM THEORY;

EID: 28844474543     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.72.052337     Document Type: Article

References (20)

1. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, Science SCIEAS 0036-8075 10.1126/science.288.5467.824 288, 824 (2000).
2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York 2000).
3. C. M. Tesch, L. Kurtz, R. de Vivie-Riedle, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(01)00748-5 342, 633 (2001);
4. J. Palao and R. Kosloff, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062308 68, 062308 (2003).
5. V. Ramakrishna, M. V. Salapaka, M. Dahleh, H. Rabitz, and A. Peirce, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.51.960 51, 960 (1995).
6. The assumption of full controllability is actually stronger than necessary in the analysis of the paper, as {C(t)} is only required to be linearly independent. Full controllability assures this prospect as well as the independence of all higher-order functional derivatives.
7. R. S. Judson and H. Rabitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.1500 68, 1500 (1992).
8. G. H. Golub and C. F. van Loan, Matrix Computations (Johns Hopkins University Press, Maryland, 1983).
9. The derivative with respect to Apq is understood to be taken separately with the actual variables ReApq and ImApq.
10. D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.023420 64, 023420 (2001);
11. B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.063412 63, 063412 (2001).
12. J. Palao, and R. Kosloff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.188301 89, 188301 (2002).
13. A. M. Weiner, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.1150614 71, 1929 (2000).
14. M. Oskin and F. Chong, and I. Chuang, IEEE Comp. 35, 79 (2002).
15. H. Rabitz, M. Hsieh, and C. Rosenthal, Science SCIEAS 0036-8075 10.1126/science.1093649 303, 1998 (2004).
16. The word kinematics is used here in the sense that Eq. 4 does not depend on the evolution with respect to any particular Hamiltonian.
17. T. Frankel in, Differential and Combinatorial Topology, edited by, S. S. Cairns, (Princeton University Press, Princeton 1965);
18. L. Geissinger, Lin. and Mult. Alg. 5, 321 (1978);
19. M. Shayman (unpublished).
20. K. Moore, M. Hsieh, and H. Rabitz (unpublished).