Control aspects of holonomic quantum computation

Journal of Mathematical Physics

Volumn 46, Issue 5, 2005, Pages

  Lucarelli, Dennis ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18844449373     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1888028     Document Type: Article

References (46)

1. Geometric Phases in Physics, edited by, A. Shapere, and, F. Wilczek, (World Scientific, Singapore, 1989).
2. A. Bloch, Nonholonomic Mechanics and Control (Springer-Verlag, New York, 2003).
3. P. S. Krishnaprasad, R. Yang, and W. P. Dayawansa, Proceedings of the 30th Conference on Decision and Control, 1991).
4. S. Kelly and R. Murray, J. Rob. Syst. 12, 417 (1995).
5. J. Radford and J. Burdick, Proceedings of the 1998 Conference on Mathematical Theory Network Systems, 1998.
6. J. P. Ostrowski and J. Burdick, Int. J. Robot. Res. 17, 683 (1998).
7. J. P. Ostrowski, Proceedings of the 14th IFAC World Congress, 1999.
8. R. Montogmery, Commun. Math. Phys. 128, 565 (1990).
9. R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics, and Applications (American Mathematical Society, Providence, RI, 2002).
10. W. Koon and J. Marsden, SIAM J. Control Optim. 35, 901 (1997).
11. P. Zanardi and M. Rasetti, Phys. Lett. A 264, 94 (1999).
12. J. Pachos and S. Chountasis, Phys. Rev. A 62, 052318 (2000).
13. J. Jones, Nature (London) 403, 869 (2000).
14. L. M. Duan, Science 292, 1695 (2001).
15. A. Recati, Phys. Rev. A 66, 032309 (2002).
16. J. Pachos, Phys. Rev. A 66, 063801 (2002).
17. P. Solinas, Phys. Rev. A 67, 062315 (2003).
18. L. Faoro, Phys. Rev. Lett. 90, 028301 (2003).
19. M. Choi, J. Phys.: Condens. Matter 15, 7823 (2003).
20. J. Pachos, P. Zanardi, and M. Rasetti, Phys. Rev. A 61, 010305 (2000).
21. J. Pachos and P. Zanardi, Int. J. Mod. Phys. B 15, 1257 (2001).
22. K. Fujii, J. Math. Phys. 41, 4406 (2000).
23. K. Fujii, Rep. Math. Phys. 48, 75 (2001).
24. K. Fujii, J. Appl. Math. 2, 371 (2002).
25. K. Fujii, arXiv.org/ quant-ph/0004102.
26. K. Fujii, arXiv.org/ quant-ph/0101102.
27. D. Lucarelli, J. Phys. A 35, 5107 (2002).
28. A. Niskanen, M. Nakahara, and M. Salomaa, Quantum Inf. Comput. 2, 560 (2002).
29. A. Niskanen, M. Nakahara, and M. Salomaa, Phys. Rev. A 67, 012319 (2003).
30. S. Tanimura, Phys. Lett. A 325, 199 (2004).
31. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
32. B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
33. Y. Aharanov and J. Anandan, Phys. Rev. Lett. 65, 1697 (1990).
34. F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984).
35. M. Nakahara, Geometry, Topology, and Physics (IOP, Bristol, 1990).
36. A. Bohm, The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics (Springer-Verlag, New York, 2003).
37. A. Bloch, Arch. Ration. Mech. Anal. 136, 21 (1996).
38. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995).
39. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (Wiley-Interscience, New York, 1969), Vol. 1.
40. R. Karp, F. Mansouri, and J. Rno, J. Math. Phys. 40, 6033 (1999).
41. N. E. Leonard and P. S. Krishnaprasad, IEEE Trans. Autom. Control 40, 1539 (1995).
42. D. D'Alessandro, Proceedings of the 2001 American Control Conference, 2001.
43. N. Khaneja and S. Glaser, Chem. Phys. 267, 11 (2001).
44. N. Khaneja, R. Brockett, and S. Glaser, Phys. Rev. A 63, 032308 (2001).
45. B. Kraus and J. Cirac, Phys. Rev. A 63, 062309 (2002).
46. M. S. Leifer, Phys. Rev. A 67, 012306 (2003).