Experimental implementation of the quantum Baker's map

Physical Review Letters

Volumn 89, Issue 15, 2002, Pages

  Weinstein, Yaakov S ^a   Lloyd, Seth ^a   Emerson, Joseph ^a   Cory, David G ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CALCULATIONS; CHAOS THEORY; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; FOURIER TRANSFORMS; HAMILTONIANS; ITERATIVE METHODS; LYAPUNOV METHODS; NUCLEAR MAGNETIC RESONANCE; PERTURBATION TECHNIQUES;

QUANTUM BAKER MAP; QUANTUM CHAOTIC DYNAMICS; QUANTUM CHAOTIC MAP;

QUANTUM THEORY;

EID: 0037037867     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.89.157902     Document Type: Article

References (32)

1. A.J. Lichtenberg and M.A. Lieberman, Regular and Chaotic Dynamics (Springer-Verlag, Berlin, 1992).
2. M.V. Berry, Proc. R. Soc. London A 413, 183 (1987).
3. M.V. Berry, in New Trends in Nuclear Collective Dynamics, edited by Y. Abe, H. Horiuchi, and K. Matsuyanagi (Springer, Berlin, 1992), p. 183.
4. F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).
5. F. Haake, M. Kus, and R. Scharf, Z. Phys. B 65, 381, (1987).
6. A. Peres, in Quantum Chaos, Quantum Measurement, edited by H.A. Cerdeira, R. Ramaswamy, M.C. Gutzwiller, and G. Casati (World Scientific, Singapore, 1991).
7. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordecht, 1993).
8. R. Schack and C.M. Caves, Phys. Rev. Lett. 71, 525 (1993)
9. R. Schack, G. M. D'Ariano, and C.M. Caves, Phys. Rev. E 50, 972 (1994)
10. R. Schack and C.M. Caves, Phys. Rev. E 53, 3387 (1996)
11. R. Schack and C.M. Caves, Phys. Rev. E 53, 3257 (1996).
12. R.P. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
13. S. Lloyd, Science 273, 1073 (1996).
14. T.A. Brun and R. Schack, Phys. Rev. A 59, 2649 (1999).
15. R. Schack, Phys. Rev. A 57, 1634 (1998).
16. L.E. Ballentine and J.P. Zibin, Phys. Rev. A 54, 3813 (1996).
17. W.H. Zurek and J.P. Paz, Physica (Amsterdam) 83D, 300 (1995).
18. D.G. Cory, A.F. Fahmy, and T.F. Havel, Proc. Natl. Acad. Sci. U.S.A. 94, 1634 (1997).
19. N.A. Gershenfeld and I.L. Chuang, Science 275, 350 (1997).
20. We characterize liquid-state NMR as a quantum information processor to distinguish it from a quantum computer as defined by DiVincenzo [18]. Liquid-state NMR provides a test bed for simulating quantum dynamics on small Hilbert spaces. However, it is not scalable.
21. D.P. DiVincenzo, Fortschr. Phys. 48, 771 (2000).
22. N.L. Balazs and A. Voros, Ann. Phys. (N.Y.) 190, 1 (1989).
23. M. Saraceno, Ann. Phys. (N.Y.) 199, 37 (1990).
24. D. Coppersmith, IBM Research Report No. RC19642, 1994.
25. L. Viola, E.M. Fortunato, M.A. Pravia, E. Knill, R. Laflamme, and D.G. Cory, Science 293, 2059 (2001).
26. D.G. Cory, M.D. Price, W. Mass, E. Knill, R. Laflamme, W.H. Zurek, T.F. Havel, and S.S. Somaroo, Phys. Rev. Lett. 81, 2152 (1998).
27. B. Schumacher, Phys. Rev. A 54, 2614 (1996).
28. J. Emerson, Y.S. Weinstein, S. Lloyd, and D.G. Cory, quant-ph/0207099.
29. Y.S. Weinstein, M.A. Pravia, E.M. Fortunato, S. Lloyd, and D.G. Cory, Phys. Rev. Lett. 86, 1889 (2001).
30. E.M. Fortunato, M.A. Pravia, N. Boulant, G. Teklemariam, T.F. Havel, and D.G. Cory, J. Chem. Phys. 116, 7599 (2002).
31. G. Teklemariam, E.M. Fortunato, M.A. Pravia, T.F. Havel, and D.G. Cory, Phys. Rev. Lett. 86, 5845 (2001).
32. S.S. Somaroo, D.G. Cory, and T.F. Havel, Phys. Lett. A 240, 1 (1998).