Quantum random walks: An introductory overview

Contemporary Physics

Volumn 44, Issue 4, 2003, Pages 307-327

  Kempe, Julia ^a,b  

^a CNRS   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0043092395     PISSN: 00107514     EISSN: None     Source Type: Journal    
DOI: 10.1080/00107151031000110776     Document Type: Review

References (52)

1. Nielsen, M. A., and Chuang, I. L., 2000, Quantum Computation and Quantum Information (Cambridge: Cambridge University Press).
2. Hughes, R. J., Alde, D. M., Dyer, P., Luther, G. G., Morgan, G. L., and Schauer, M., 1995, Contemp. Phys., 36, 149.
3. Gisin, N., Ribordy, G. G., Tittel, W., and Zbinden, H., 2002, Rev. Mod. Phys., 74, 145.
4. Shor, P. W., 1994, in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, edited by S. Goldwasser (Los Alamitos, CA: IEEE Computer Society), pp. 124-134 (final version in [52]).
5. Aharonov, Y., Davidovich, L., and Zagury, N., 1993, Phys. Rev. A, 48, 1687.
6. Feynman, R. P., and Hibbs, A. R., 1965, Quantum Mechanics and Path Integrals, International Series in Pure and Applied Physics (New York: McGraw-Hill).
7. Meyer, D., 1996, J. Stat. Phys., 85, 551.
8. Meyer, D., 1996, Phys. Lett. A, 223, 337.
9. Watrous, J., 2000, unpublished.
10. Watrous, J., 2001, J. Comput. Syst. Sci., 62, 376.
11. Aharonov, D., Ambainis, A., Kempe, J., and Vazirani, U., 2001, Proceedings of the 33th STOC (New York, NY: ACM), pp. 50 - 59.
12. Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., and Watrous, J., 2001, Proceedings of the 33th STOC (New York, NY: ACM), pp. 60 - 69.
13. Harmin, D. A., 1997, Phys. Rev. A, 56, 232.
14. Bouwmeester, D., Marzoli, I., Karman, G. P., Sohleich, W., and Woerdman, J. P., 1999, Phys. Rev. A, 61, 013410-1.
15. Nayak, A., and Vishwanath, A., 2000, DIMACS Technical Report 2000 - 43 and Los Alamos preprint archive, quant-ph/0010117.
16. Bach, E., Coppersmith, S., Goldschen, M., Joynt, R., and Watrous, J., 2002, lanl-archive quant-ph/0207008.
17. Moore, C., and Russell, A., 2002, Proceedins of RANDOM 2002, edited by J. D. P. Rolim and S. Vadhan (Cambridge, MA: Springer), pp. 164 - 178.
18. Kempe, J., 2002, lanl-arXiv quant-ph/0205083.
19. Mackay, T. D., Bartlett, S. D., Stephenson, L. T., and Sanders, B. C., 2002. J. Phys. A: Math. Gen., 35, 2745.
20. Yamasaki, T., Kobayashi, H., and Imai, H., 2002, Unconventional Models of Computation, Third International Conference, UMC 2002, Kobe, Japan, 15-19 October, Vol. 2509, Lecture Notes in Computer Science, edited by C. Calude, M. J. Dinneen, and F. Peper (Berlin: Springer), pp. 315- 330.
21. Tamon, C., 2002, lanl-arXiv quant-ph/0209106.
22. Shenvi, N., Kempe, J., and Whaley, K. B., 2003, Phys. Rev. A, to appear.
23. Grover, L., 1996, Proceedings of the 28th STOC (Philadelphia, Pennsylvania: ACM Press), pp. 212 - 219.
24. Farhi, E., and Gutmann, S., 1998, Phys. Rev. A, 58, 915.
25. Childs, A., Farhi, E., and Gutmann, S., 2002, Quantum Information Processing, 1, 35; lanl-report quant-ph/0103020.
26. Aldous, D., and Fill, J., Reversible markov chains and random walks on graphs, preprint available at http://stat-www.berkeley.edu/users/ aldous/book.html.
27. Childs, A. M., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., and Spielman, D. A., 2002, lanl-report quant-ph/0209131.
28. Preskill, J., 2002, private communication.
29. Shenvi, N., and Kempe, J., 2002, unpublished.
30. Papadimitriou, C., 1994, Computational Complexity (Reading, MA: Addison Wesley).
31. Motwani, R., and Raghavan, P., 1995, Randomized Algorithms (Cambridge: Cambridge University Press).
32. Sinclair, A., 1993, Algorithms for Random Generation and Counting, a Markov Chain Approach (Boston, MA: Birkhauser Press).
33. Dyer, M., Frieze, A., and Kannan, R., 1991, J. ACM, 38, 1.
34. Jerrum, M., Sinclair, A., and Vigoda, E., 2001, Proceedings of the 33th STOC (New York, NY: ACM), pp. 712 - 721.
35. Schöning, U., 1999, 40th Annual Symposium on Foundations of Computer Science (New York, NY: IEEE), pp. 17 - 19.
36. Feller, W., 1968, An Introduction to Probability Theory and its Applications (New York: John Wiley).
37. Lovasz, L., and Winkler, P., 1998, Microsurveys in Discrete Probability, Vol. 41, DIMACS Series on Disc. Mathematics and Theoretical Computer Science, edited by D. Aldous and J. Propp (Providence, RI: AMS), pp. 85 - 134.
38. Bennett, Ch., 1973, IBM J. Res. Develop., 17, 5225.
39. Aharonov, D., 2002, unpublished.
40. Aharonov, D., and Ta-Shma, A., 2003, Proceedings of the 35th STOC (New York, NY: ACM) to appear.
41. Bernstein, E., and Vazirani, U., 1997, SIAM J. Comput., 26, 1411.
42. Travaglione, B. C., and Milburn, G. J., 2002, Phys. Rev. A, 65, 032310.
43. Sanders, B. C., Bartlett, S. D., Tregenna, B., and Knight, P. L., 2002, arXive eprint quant-ph/0207028.
44. Dür, W., Raussendorf, R., Kendon, V. M., and Briegel, H. J., 2002, Phys. Rev. A, 66, 052319.
45. Sasura, M., and Buzek, V., 2002, J. mod. Optics, 49, 1593.
46. Wineland, D. J., Monroe, C., Itano, W. M., Leibfield, D., King, B. E., and Meekof, D. M., 1998, J. Res. Natl. Inst. Stand. Technol., 103, 256.
47. Scully, M. O., and Zubairy, M. S., 1997, Quantum Optics (New York: Cambridge University Press).
48. Kendon, V., and Tregenna, B., 2002, lanl-arXive quant-ph/0209005.
49. Brun, T. A., Carteret, H. A., and Ambainis, A., 2002, lanl preprint quant-ph/0208195.
50. Brun, T. A., Carteret, H. A., and Ambainis, A., 2002, lanl preprint quant-ph/0210180.
51. Brun, T. A., Carteret, H. A., and Ambainis, A., 2002, lanl preprint quant-ph/0210161.
52. Shor, P. W., 1997, SIAM J. Comput., 26, 1484.