Accuracy versus run time in an adiabatic quantum search

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 5, 2010, Pages

  Rezakhani, A T ^a,b   Pimachev, A K ^a   Lidar, D A ^a,c  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^c NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADIABATIC QUANTUM SEARCH; ALGORITHMIC ERRORS; CONTINUOUS TIME; EVOLUTION PATHS; QUADRATIC SPEEDUP; QUANTUM ALGORITHMS; RUNTIMES;

QUANTUM THEORY;

ALGORITHMS;

EID: 78649603842     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.052305     Document Type: Article

References (68)

1. J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Science 284, 779 (1999).
2. E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, e-print arXiv:quant-ph/0001106.
3. E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292, 472 (2001).
4. D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, SIAM J. Comput. 37, 166 (2007).
5. R.Oliveira and B. Terhal, Quantum Inf. Comput. 8, 0900 (2008).
6. A. Mizel, D. A. Lidar, and M. Mitchell, Phys. Rev. Lett. 99, 070502 (2007).
7. S. P. Jordan, E. Farhi, and P. W. Shor, Phys. Rev. A 74, 052322 (2006).
8. D. A. Lidar, Phys. Rev. Lett. 100, 160506 (2008).
9. A. M. Childs, E. Farhi, and J. Preskill, Phys. Rev. A 65, 012322 (2001).
10. M. S. Sarandy and D. A. Lidar, Phys. Rev. Lett. 95, 250503 (2005).
11. M.H. S.Amin, P. J. Love, and C. J. S. Truncik, Phys. Rev. Lett. 100, 060503 (2008).
12. M. S. Sarandy and D. A. Lidar, Phys. Rev. A 71, 012331 (2005).
13. O. Oreshkov and J. Calsamiglia, Phys. Rev. Lett. 105, 050503 (2010).
14. R. Harris et al., Phys. Rev. B 82, 024511 (2010).
15. M. Born and V. A. Fock, Z. Phys. 51, 165 (1928).
16. T. Kato, J. Phys. Soc. Jpn. 5, 435 (1950).
17. A. Messiah, Quantum Mechanics (Dover Publications, New York, 1999).
18. S. Teufel, Adiabatic Perturbation Theory in Quantum Dynamics (Springer-Verlag, Berlin, 2003).
19. K.-P. Marzlin and B. C. Sanders, Phys. Rev. Lett. 93, 160408 (2004).
20. D. M. Tong, K. Singh, L. C. Kwek, and C. H. Oh, Phys. Rev. Lett. 95, 110407 (2005).
21. J. Du, L. Hu, Y.Wang, J.Wu,M. Zhao, and D. Suter, Phys. Rev. Lett. 101, 060403 (2008).
22. M. S. Sarandy, L.-A.Wu, and D. A. Lidar, Quant. Info. Proc. 3, 331 (2004).
23. M. H. S. Amin, Phys. Rev. Lett. 102, 220401 (2009).
24. J. E. Avron, R. Seiler, and L. G. Yaffe, Commun. Math. Phys. 110, 33 (1987).
25. J. E. Avron, R. Seiler, and L. G. Yaffe, Commun. Math. Phys. 156, 649 (1993).
26. G. Nenciu, Commun. Math. Phys. 152, 479 (1993).
27. A. Martinez, J. Math. Phys. 35, 3889 (1994).
28. G. A. Hagedorn and A. Joye, J. Math. Anal. Appl. 267, 235 (2002).
29. S. Jansen,M.-B. Ruskai, and R. Seiler, J. Math. Phys. 48, 102111 (2007).
30. M. J. O'Hara and D. P. O'Leary, Phys. Rev. A 77, 042319 (2008).
31. S. Boixo and R. D. Somma, Phys. Rev. A 81, 032308 (2010).
32. D. A. Lidar, A. T. Rezakhani, and A. Hamma, J. Math. Phys. 50, 102106 (2009).
33. L. K. Grover, Phys. Rev. Lett. 79, 325 (1997).
34. A. T. Rezakhani, W.-J. Kuo, A. Hamma, D. A. Lidar, and P. Zanardi, Phys. Rev. Lett. 103, 080502 (2009).
35. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
36. J. Roland and N. J. Cerf, Phys. Rev. A 65, 042308 (2002).
37. M. Andrecut and M. K. Ali, Int. J. Quantum Info. 2, 447 (2007).
38. C. Zalka, Phys. Rev. A 60, 2746 (1999).
39. L. K. Grover, Phys. Rev. Lett. 80, 4329 (1998).
40. M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, Fortschr. Phys. 46, 493 (1998).
41. L. K. Grover, Phys. Rev. Lett. 95, 150501 (2005).
42. E. Biham, O. Biham, D. Biron, M. Grassi, and D. A. Lidar, Phys. Rev. A 60, 2742 (1999).
43. E. Biham, O. Biham, D. Biron, M. Grassl, D. A. Lidar, and D. Shapira, Phys. Rev. A 63, 012310 (2000).
44. L. Accardi and R. Sabbadini, e-print arXiv:quant-ph/0012143.
45. I. L. Chuang, N. Gershenfeld, and M. Kubinec, Phys. Rev. Lett. 80, 3408 (1998).
46. J. A. Jones, M. Mosca, and R. H. Hansen, Nature 393, 344 (1998).
47. J. E. Ollerenshaw, D. A. Lidar, and L. E. Kay, Phys. Rev. Lett. 91, 217904 (2003).
48. D. Daems and S. Guérin, Phys. Rev. Lett. 99, 170503 (2007).
49. S. S. Ivanov, P. A. Ivanov, I. E. Linington, and N. V. Vitanov, Phys. Rev. A 81, 042328 (2010).
50. A. T. Rezakhani, D. F. Abasto, D. A. Lidar, and P. Zanardi, Phys. Rev. A 82, 012321 (2010).
51. D. Aharonov and A. Ta-Shma, SIAM J. Comput. 37, 47 (2007).
52. M. S. Siu, Phys. Rev. A 75, 062337 (2007).
53. L. M. Garrido and F. J. Sancho, Physica 28, 553 (1962).
54. J. I. Latorre and R. Orús, Phys. Rev. A 69, 062302 (2004).
55. G. Schaller, S. Mostame, and R. Schützhold, Phys. Rev. A 73, 062307 (2006).
56. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK, 1999).
57. R. Schützhold and G. Schaller, Phys. Rev. A 74, 060304(R) (2006).
58. G. Schaller, Phys. Rev. A 78, 032328 (2008).
59. M. H. S. Amin and V. Choi, Phys. Rev. A 80, 062326 (2009).
60. A. Galindo and P. Pascual, Quantum Mechanics I (Springer- Verlag, Berlin, 1990).
61. P. Pfeifer, Phys. Rev. Lett. 70, 3365 (1993).
62. V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 67, 052109 (2003).
63. L. B. Levitin and T. Toffoli, Phys. Rev. Lett. 103, 160502 (2009).
64. J. E. Avron, M. Fraas, G. M. Graf, and P. Grech, e-print arXiv:0912.4640.
65. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, San Diego, CA, 2001).
66. S. I. Hayek, Advanced Mathematical Methods in Science and Engineering (Marcel Dekker, New York, 2001).
67. M. Nakahara, Geometry, Topology and Physics (Institute of Physics, Bristol/Philadelphia, 2003).
68. I. M. Gel'fand and G. E. Shilov, Generalized Functions: Properties and Operations (Academic Press, New York, 1964), Vol. 1.