Quantum walks with infinite hitting times

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 4, 2006, Pages

  Krovi, Hari ^a   Brun, Todd A ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; QUANTUM THEORY; TIME MEASUREMENT;

HITTING TIMES; QUANTUM WALKS; RANDOM WALK THEORY;

GRAPH THEORY;

EID: 33750443251     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.042334     Document Type: Article

References (29)

1. R. Motwani and P. Raghavan, Randomized Algorithms (Cambridge University Press, Cambridge, 1995).
2. P. W. Shor, in Proceedings of the 35th Annual Symposium on the Theory of Computer Science edited by, S. Goldwasser, (IEEE Computer Society Press, Los Alamitos, CA, 1994), p. 124.
3. A. Ambainis, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539702402780 34, 1324 (2005).
4. N. Shenvi, J. Kempe, and K. Birgitta Whaley, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052307 67, 052307 (2003).
5. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, and D. A. Spielman, in Proceedings of the 35th ACM Symposium on Theory of Computing (STOC 2003) (Association for Computer Machinery, New York, 2003), pp. 59-68.
6. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.915 58, 915 (1998).
7. A. M. Childs, E. Farhi, and S. Gutmann, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A:1019609420309 1, 35 (2002).
8. A. Nayak and A. Vishwanath, quant-ph/0010117.
9. E. Bach, S. Coppersmith, M. Goldschen, R. Joynt, and J. Watrous, J. Comput. Syst. Sci. JCSSBM 0022-0000 69, 562 (2004).
10. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.130602 91, 130602 (2003).
11. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.032304 67, 032304 (2003).
12. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052317 67, 052317 (2003).
13. C. Moore and A. Russell, in Proceedings of the 6th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM 2002), edited by, J. D. P. Rolim, and, S. Vadhan, (Springer, Berlin, 2002), pp. 164-178.
14. J. Kempe, in Proceedings of 7th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM 2003), edited by, S. Arora, K. Jansen, J. D. P. Rolim, and, A. Sahai, (Springer, Berlin, 2003), pp. 354-369.
15. H. Krovi and T. A. Brun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.032341 73, 032341 (2006).
16. A. Ambainis, Int. J. Quantum Inf. ZZZZZZ 0219-7499 1, 507 (2003).
17. V. Kendon, quant-ph/0306140.
18. A. Montanaro, quant-ph/0504116.
19. D. Aharanov, A. Ambaini J. Kempe, and U. Vazirani, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001) (Association for Computer Machinery, New York, 2001), pp. 50-59.
20. J. Kempe, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107151031000110776 44, 307 (2003).
21. V. Kendon, quant-ph/0606016.
22. H. Gerhardt and J. Watrous, in Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM 2003), edited by, S. Arora, K. Jansen, J. D. P. Rolim, and, A. Sahai, (Springer, Berlin, 2003), pp. 290-301.
23. F. W. Strauch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.030301 74, 030301 (R) (2006).
24. A. Ambainis, J. Kempe, and A. Rivosh, in Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms (SODA 2005) (SIAM, Philadelphia, 2005), pp. 1099-1108.
25. J. L. Gross and T. W. Tucker, Topological Graph Theory (Wiley, New York, 1987).
26. W. E. Roth, Bull. Am. Math. Soc. BAMOAD 0002-9904 40, 461 (1934).
27. S. Sternberg, Group Theory and Physics (Cambridge University Press, Cambridge, 1994).
28. J.-P. Serre, Linear Representations of Finite Groups (Springer-Verlag, New York, 1977).
29. J. P. Keating, N. Linden, J. C. F. Matthews, and A. Winter, quant-ph/0606205.