Classical versus quantum errors in quantum computation of dynamical systems

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

Volumn 70, Issue 5 2, 2004, Pages

  Rossini, Davide ^a   Benenti, Giuliano ^a   Casati, Giulio ^a  

^a UNIVERSITY OF INSUBRIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHAOS THEORY; ERRORS; INTEGRATION; LYAPUNOV METHODS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

DYNAMICAL SYSTEMS; NATURAL PERTURBATIONS; QUANTUM ALGORITHMS; QUANTUM COMPUTATIONS;

QUANTUM THEORY;

EID: 41349107992     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.056216     Document Type: Article

References (48)

1. A. Peres, Phys. Rev. A 30, 1610 (1984).
2. R.A. Jalabert and H.M. Pastawski, Phys. Rev. Lett. 86, 2490 (2001).
3. F.M. Cucchietti, H.M. Pastawski, and D.A. Wisniacki, Phys. Rev. E 65, 045206(R) (2002).
4. Ph. Jacquod, P.G. Silvestrov, and C.W.J. Beenakker, Phys. Rev. E 64, 055203(R) (2001).
5. N.R. Cerruti and S. Tomsovic, Phys. Rev. Lett. 88, 054103 (2002).
6. V.V. Flambaum and F.M. Izrailev, Phys. Rev. E 64, 036220 (2001).
7. G. Benenti and G. Casati, Phys. Rev. E 65, 066205 (2002).
8. D.A. Wisniacki and D. Cohen, Phys. Rev. E 66, 046209 (2002).
9. T. Prosen, Phys. Rev. E 65, 036208 (2002); T. Prosen and M. Žnidarič, J. Phys. A 34, L681 (2001); 35, 1455 (2002).
10. T. Prosen, Phys. Rev. E 65, 036208 (2002); T. Prosen and M. Žnidarič, J. Phys. A 34, L681 (2001); 35, 1455 (2002).
11. T. Prosen, Phys. Rev. E 65, 036208 (2002); T. Prosen and M. Žnidarič, J. Phys. A 34, L681 (2001); 35, 1455 (2002).
12. Y.S. Weinstein, S. Lloyd, and C. Tsallis, Phys. Rev. Lett. 89, 214101 (2002).
13. W. Wang and B. Li, Phys. Rev. E 66, 056208 (2002).
14. Y. Adamov, I.V. Gornyi, and A.D. Mirlin, Phys. Rev. E 67, 056217 (2003).
15. F. Garcia-Mata, M. Saraceno, and M.E. Spina, Phys. Rev. Lett. 91, 064101 (2003).
16. J. Vaníǒek and E.J. Heller, Phys. Rev. E 68, 056208 (2003).
17. F.M. Cucchietti, D.A.R. Dalvit, J.P. Paz, and W.H. Zurek, Phys. Rev. Lett. 91, 210403 (2003).
18. M. Hiller, T. Kottos, D. Cohen, and T. Geisel, Phys. Rev. Lett. 92, 010402 (2004).
19. G. Veble and T. Prosen, Phys. Rev. Lett. 92, 034101 (2004).
20. W. Wang, G. Casati, and B. Li, Phys. Rev. E 69, 025201 (2004).
21. R. Schack, Phys. Rev. A 57, 1634 (1998).
22. B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett. 86, 2890 (2001).
23. G. Benenti, G. Casati, S. Montangero, and D.L. Shepelyansky, Phys. Rev. Lett. 87, 227901 (2001).
24. G. Benenti, G. Casati, S. Montangero, and D.L. Shepelyansky, Phys. Rev. A 67, 052312 (2003).
25. A.A. Pomeransky and D.L. Shepelyansky, Phys. Rev. A 69, 014302 (2004).
26. G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information (World Scientific, Singapore, 2004), Vol. 1.
27. Y.S. Weinstein, S. Lloyd, J. Emerson, and D.G. Cory, Phys. Rev. Lett. 89, 157902 (2002).
28. J. Emerson, Y.S. Weinstein, S. Lloyd, and D. Cory, Phys. Rev. Lett. 89, 284102 (2002).
29. D. Poulin, R. Blume-Kohout, R. Laflamme, and H. Ollivier, Phys. Rev. Lett. 92, 177906 (2004).
30. G. Casati, B.V. Chirikov, I. Guarneri, and D.L. Shepelyansky, Phys. Rev. Lett. 56, 2437 (1986).
31. I. Dana, N.W. Murray, and I.C. Percival, Phys. Rev. Lett. 62, 233 (1989).
32. F. Borgonovi, G. Casati, and B. Li, Phys. Rev. Lett. 77, 4744 (1996).
33. F. Borgonovi, Phys. Rev. Lett. 80, 4653 (1998).
34. G. Casati and T. Prosen, Phys. Rev. E 59, R2516 (1999).
35. A. Lakshminarayan and N. L. Balazs, Chaos, Solitons Fractals 5, 1169 (1995).
36. F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G.P.T. Lancaster, T. Deuschle, C. Becher, C.F. Roos, J. Eschner, and R. Blatt, Nature (London) 422, 408 (2003).
37. J.I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
38. C. Miquel, J.P. Paz, and W.H. Zurek, Phys. Rev. Lett. 78, 3971 (1997).
39. P.H. Song and D.L. Shepelyansky, Phys. Rev. Lett. 86, 2162 (2001).
40. D. Shapira, S. Mozes, and O. Biham, Phys. Rev. A 67, 042301 (2003).
41. S. Bettelli, Phys. Rev. A 69, 042310 (2004).
42. Strictly speaking, the coherent state (5) should be modified in order to take into account the periodic boundary conditions along θ and n, as explained in S.-J. Chang and K.-J. Shi, Phys. Rev. A 34, 7 (1986). However, this modification does not significantly affect the results discussed in this paper.
43. J.P. Paz, A.J. Roncaglia, and M. Saraceno, Phys. Rev. A 69, 032312 (2004).
44. S.A. Gardiner, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 79, 4790 (1997).
45. C. Miquel, J.P. Paz, M. Saraceno, E. Knill, R. Laflamme, and C. Negrevergne, Nature (London) 418, 59 (2002).
46. G. Benenti, G. Casati, and G. Veble, Phys. Rev. E 68, 036212 (2003).
47. q(x) = τ1 / N. This saturation value is given by the inverse of the size of the Hubert space and reflects the finiteness of the system.
48. We obtained a further confirmation of this statement by implementing the quantum algorithm without dynamical evolution - i.e., by putting T=0 and k=0 in Eq. (3). In such a situation, we found that the fidelity drops again exponentially and the ratio between the decay rates starting from a random or a Gaussian state is the same as in the quasi-integrable regime.