Quantum chaos in the spectrum of operators used in Shora's algorithm

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 3, 2006, Pages

  Maity, Krishnendu ^a   Lakshminarayan, Arul ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHAOS THEORY; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; RANDOM PROCESSES;

DESYMMETRIZATION; QUANTUM CHAOS; RANDOM MATRICES; TIME-REVERSAL SYMMETRY;

QUANTUM THEORY;

EID: 33748805991     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.035203     Document Type: Article

References (31)

1. M. V. Berry, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 413, 183 (1987).
2. Chaos and Quantum Physics, 1991 Les Houches Lectures II, edited by, M.-J. Giannoni, A. Voros, and, J. Zinn-Justin, (North-Holland, Amsterdam, 1991).
3. F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 1991).
4. B. Georgeot and D. L. Shepelyansky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.6366 62, 6366 (2000).
5. A. Lakshminarayan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64. 036207 64, 036207 (2001).
6. B. Georgeot and D. L. Shepelyansky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2890 86, 2890 (2001).
7. D. Braun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042317 65, 042317 (2002).
8. P. W. Shor, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539795293172 26, 1484 (1997);
9. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
10. Arul Lakshminarayan, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/37/ L01 38, L597 (2005).
11. N. L. Balazs and A. Voros, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(89)90259-5 190, 1 (1989).
12. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer, New York, 1992).
13. S. Nonnenmacher and M. Zworski, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/49/014 38, 10683 (2005).
14. M. Tracy Mark and A. J. Scott, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/39/314 35, 8341 (2002).
15. J. H. Hannay and M. V. Berry, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00106-2 1, 267 (1980);
16. J. P. Keating, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/4/2/006 4, 309 (1991).
17. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
18. L. K. M. Vandersypen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5452 85, 5452 (2000);
19. L. K. M. Vandersypen, Nature (London) NATUAS 0028-0836 10.1038/414883a 414, 883 (2001).
20. N. Meenakshisundaram and Arul Lakshminarayan, in Proceedings of the National Conference on Nonlinear Systems and Dynamics, edited by, M. Lakshmanan, and, R. Sahadevan, (Allied Publishers, Chennai, India, 2006).
21. J. P. Allouche and J. Shallit, Sequences and their Applications, Proceedings of the 1998 SETA Conference, edited by, C. Ding, T. Helleseth, and, H. Niederreiter, (Springer, Berlin, 1999);
22. Automatic Sequences: Theory, Applications and Generalizations (Cambridge University Press, Cambridge, England, 2003).
23. C. Godreche and J. M. Luck, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/23/16/024 23, 3769 (1999);
24. M. A. Zaks, A. S. Pikovsky, and J. Kurths, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/32/8/018 32, 1523 (1999).
25. N. Meenakshisundaram and Arul Lakshminarayan, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/36/006 39, 11205 (2006).
26. A. Schnirelman, Usp. Mat. Nauk UMANA5 0042-1316 29, 181 (1974).
27. M. L. Mehta, Random Matrices, 3rd ed. (Academic Press, New York, 1991).
28. A. Peres, in Quantum Chaos, edited by, H. A. Cerdeira, R. Ramaswamy, M. C. Gutzwiller, and, G. Casati, (World Scientific, Singapore, 1991).
29. R. Schack, G. M. D’Ariano, and C. M. Caves, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.972 50, 972 (1994);
30. R. Schack and C. M. Caves, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.3257 53, 3257 (1996).
31. N. Meenakshisundaram and Arul Lakshminarayan (unpublished).