Problem of equilibration and the computation of correlation functions on a quantum computer

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 2, 2000, Pages 22-

  Terhal, Barbara M ^a   DiVincenzo, David P ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84891680482     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.61.022301     Document Type: Article

References (52)

1. P. W. Shor, SIAM J. Computing 26, 1484 (1997).
2. A.Yu. Kitaev, e-print quant-ph/9511026;
3. A.Yu. KitaevRuss. Math. Surveys 52, 1191 (1999).
4. L. K. Grover, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing (ACM, New York, 1996), p. 212.
5. D. Deutsch, Proc. R. Soc. London, Ser. A 400, 97 (1985).
6. S. Lloyd, Science 273, 1073 (1996).
7. C. Zalka, Proc. R. Soc. London, Ser. A 454, 313 (1998);
8. S. Wiesner, e-print quant-ph/9603028;
9. B.M. Boghosian and W. Taylor, Physica D 120, 30 (1998).
10. J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods (Wiley, London, 1964).
11. Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, edited by M. Suzuki, Springer Series in Solid-State Sciences (Springer-Verlag, Berlin, 1986).
12. H. De Raedt and W. von der Linden, The Monte Carlo Method in Condensed Matter Physics, Topics in Applied Physics Vol. 71 (Springer-Verlag, Berlin, 1991).
13. M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
14. S. Doniach and E. H. Sondheimer, Green’s Functions for Solid State Physicists (Benjamin-Cummings, Reading, MA, 1974).
15. M. Jerrum and A. Sinclair, SIAM J. Comput. 22, 1087 (1993).
16. F. Barahona, J. Phys. A: Math. Gen. 15, 3241 (1982).
17. D. Lidar and O. Biham, Phys. Rev. E 56, 3661 (1997).
18. D.S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997).
19. D. P. DiVincenzo, in Mesoscopic Electron Transport, Vol. 345 of NATO Advanced Study Institute, Series E: Applied Sciences, edited by L. Sohn, L. Kouwenhoven, and G. Schoen (Kluwer, Dordrecht, 1997), p. 657;
20. D. P. DiVincenzoe-print cond-mat/9612126.
21. N. Gershenfeld and I.L. Chuang, Science 275, 350 (1997);
22. D. Cory, A. Fahmy, and T. Havel, Proc. Natl. Acad. Sci. USA 94, 1634 (1997).
23. D. Abrams and S. Lloyd, e-print quant-ph/9807070.
24. L. van Hove, Physica 23, 441 (1957).
25. E. Fick, G. Sauermann, and W. D. Brewer, Quantum Statistics of Dynamic Processes, Springer Series in Solid-State Sciences Vol. 86 (Springer-Verlag, Berlin, 1990);
26. M. Celio and D. Loss, Physica A 158, 769-783 (1989).
27. R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics (Springer-Verlag, Berlin, 1987).
28. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
29. E. B. Davies, Quantum Theory of Open Systems (Academic, New York, 1976).
30. E.B. Davies, Commun. Math. Phys. 39, 91 (1974).
31. E.B. Davies, Math. Ann. 219, 147 (1976).
32. R. Alicki, Rep. Math. Phys. 10, 249 (1976).
33. N. Dunford and J. T. Schwartz, Linear Operators (Interscience, New York, 1958), pt. I.
34. R. F. Werner (private communication).
35. A. Messiah, Quantum Mechanics (Wiley, London, 1976), Vol. II, Chap. XVI.
36. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, England, 1985).
37. Cf. M. Jerrum and A. Sinclair, in Approximation Algorithms for NP-hard Problems, edited by D. S. Hochbaum (PWS Publishing, Boston, 1996), pp. 482–520.
38. A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961);
39. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Clarendon Press, Oxford, 1987).
40. S. Richter and R.F. Werner, J. Stat. Phys. 82, 963 (1996).
41. D. Aharonov, A. Kitaev, and N. Nissan, in Proceedings of the 30th Annual ACM Symposium on Theory of Computation (ACM, New York, 1997), pp. 20–30.
42. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
43. R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, Proc. R. Soc. London, Ser. A 454, 339 (1998).
44. R. Jozsa, Proc. R. Soc. London, Ser. A 454, 323 (1998).
45. D.A. Lidar and H. Wang, Phys. Rev. E 59, 2429 (1999).
46. Cf. G. W. Stewart and Ji-guang Sun, Matrix Perturbation Theory, Computer Science and Scientific Computing (Academic, San Diego, 1990);
47. P.J. Schweitzer, J. Appl. Probab. 5, 401 (1968);
48. M. Haviv and L. van der Heyden, Adv. Appl. Probab. 16, 804 (1984).
49. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993).
50. W. Feller, An Introduction to Probability Theory and Its Application (Wiley, London, 1968), Vol. I.
51. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999).
52. K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A 58, 883 (1998).