Hitting time for the continuous quantum walk

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 2, 2008, Pages

  Varbanov, Martin ^a   Krovi, Hari ^b   Brun, Todd A ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b NEC LABORATORIES AMERICA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME SYSTEMS; NUMERICAL ANALYSIS; POISSON DISTRIBUTION; QUANTUM EFFICIENCY;

CONTINUOUS QUANTUM; CONTINUOUS-TIME QUANTUM WALKS; DISCRETE-TIME; EXPLICIT FORMULAS; HITTING TIME; HITTING TIMES; POISSON PROCESSES; QUANTUM ZENO EFFECT; RANDOM WALKS;

RANDOM PROCESSES;

EID: 49749141943     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.022324     Document Type: Article

References (42)

1. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.915 58, 915 (1998).
2. R. Motwani and P. Raghavan, Randomized Algorithms (Cambridge University Press, Cambridge, 1995), p. 476.
3. A. Ambainis, in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (IEEE Computer Society, Washington, DC, 2004).
4. H. Buhrman and R. Spalek, in Proceedings of the 17th ACM-SIAM SODA (ACM, Miami, FL, 2006), p. 880.
5. F. Magniez, M. Santha, and M. Szegedy, in Proceedings of the 16th ACM-SIAM SODA (ACM, Vancouver, 2005), p. 1109.
6. F. F. Magniez and A. Nayak, Lect. Notes Comput. Sci. LNCSD9 0302-9743 1770, 1312 (2005).
7. E. Farhi, J. Goldstone, and S. Gutmann, e-print arXiv:quant-ph/0702144v2.
8. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, Proceedings of the 35th ACM symposium on theory of computing, 2003 (Assoc for Comp. Machinery, New York, 2001), p. 59.
9. A. M. Childs, E. Farhi, and S. Gutmann, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A:1019609420309 1, 35 (2002).
10. A. Nayak and A. Vishwanath, e-print arXiv: quant-ph/0010117.
11. E. Bach, S. Coppersmith, M. Goldschen, R. Joynt, and J. Watrous, J. Comput. Syst. Sci. JCSSBM 0022-0000 10.1016/j.jcss.2004.03.005 69, 562 (2004).
12. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.130602 91, 130602 (2003).
13. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.032304 67, 032304 (2003).
14. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052317 67, 052317 (2003).
15. D. Aharanov, A. Ambainis, J. Kempe, and U. Vazirani, Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001) (Assoc. for Comp. Machinery, New York, 2001), pp. 50-59.
16. B. Tregenna, W. Flanagan, R. Maile, and V. Kendon, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/383 5, 83 (2003).
17. N. Shenvi, J. Kempe, and K. Birgitta Whaley, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052307 67, 052307 (2003).
18. C. Moore and A. Russell, Proceedings of 6th International workshop on randomization and approximation techniques in computer sciences (RANDOM 2002), of Lect. Notes Comput. Sci., edited by, J. D. P. Rolim, and, S. P. Vadhan, (Springer, London, 2002), p. 164.
19. J. Kempe, in Proceedings of 7th International Workshop on Randomization and Approximation Techniques in Computer Sciences (RANDOM 2003), edited by, S. Arora, K. Jansen, J. D. P. Rolim, and, A. Sahai, (Springer, Berlin, 2003), p. 354.
20. H. Krovi and T. A. Brun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.032341 73, 032341 (2006).
21. H. Krovi and T. A. Brun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.042334 74, 042334 (2006).
22. V. Kendon, Int. J. Quantum Inf. ZZZZZZ 0219-7499 4, 791 (2006).
23. A. Ambainis, Int. J. Quantum Inf. ZZZZZZ 0219-7499 1, 507 (2003).
24. A. Montanaro, Quantum Inf. Comput. QICUAW 1533-7146 7, 1 (2007).
25. V. Kendon, Math. Struct. Comp. Sci. MCSCEA 0960-1295 17, 1169 (2006).
26. J. Kempe, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107151031000110776 44, 307 (2003).
27. B. Misra and E. C. G. Sudarshan, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.523304 18, 756 (1977).
28. V. Kendon and B. C. Sanders, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022307 71, 022307 (2005).
29. P. C. Richter, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/3/072 9, 72 (2007).
30. P. C. Richter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.042306 76, 042306 (2007).
31. A. M. Childs and J. Goldstone, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.022314 70, 022314 (2004).
32. M. Guţǎ, L. Bouten, and H. Maassen, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/9/010 37, 3189 (2004).
33. A. Guichardet, Symmetric Hilbert Spaces and Related Topics, Lect. Notes Math. Vol. 261 (Springer, New York, 1972).
34. T. Yamasaki, H. Kobayashi, and H. Imai, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012302 68, 012302 (2003).
35. Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60.1351 60, 1351 (1988).
36. T. A. Brun, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1475328 70, 719 (2002).
37. M. Hillery, J. Bergou, and E. Feldman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032314 68, 032314 (2003).
38. A. P. Hines and P. C. E. Stamp, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.062321 75, 062321 (2007).
39. S. Lloyd, Science SCIEAS 0036-8075 10.1126/science.274.5290.1073 273, 1073 (1996).
40. F. R. Gantmakher, The Theory of Matrices (Chelsea, New York, 1959), Vols. I, II.
41. S. K. Godunov, Modern Aspects of Linear Algebra (American Mathematical Society, Providence, RI, 1998).
42. H. Krovi and T. A. Brun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.062332 75, 062332 (2007).