Connecting the discrete- and continuous-time quantum walks

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 3, 2006, Pages

  Strauch, Frederick W ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ATOMIC PHYSICS; PROBLEM SOLVING; RANDOM PROCESSES; THEOREM PROVING;

CONTINUOUS-TIME QUANTUM WALKS; DISCRETE-TIME QUANTUM WALKS; QUANTUM ALGORITHMS;

QUANTUM THEORY;

EID: 33748480690     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.030301     Document Type: Article

References (29)

1. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.915 58, 915 (1998).
2. A. M. Childs, in Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (ACM Press, New York, 2003), p. 59.
3. A. M. Childs, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A: 1019609420309 1, 35 (2002).
4. Y. Aharonov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.48.1687 48, 1687 (1993).
5. D. A. Meyer, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02199356 85, 551 (1996).
6. T. A. Brun, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91. 130602 91, 130602 (2003).
7. D. K. Wójcik and J. R. Dorfman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.230602 90, 230602 (2003).
8. P. Ribeiro, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93. 190503 93, 190503 (2004);
9. A. Wójcik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 93.180601 93, 180601 (2004).
10. P. L. Knight, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.020301 68, 020301 (R) (2003).
11. P. Blanchard and M.-O. Hongler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.120601 92, 120601 (2004).
12. F. W. Strauch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.054302 73, 054302 (2006).
13. A. Patel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032347 71, 032347 (2005).
14. A. Romanelli, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.02.061 338, 395 (2004).
15. N. Konno, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A:1023413713008 1, 345 (2002);
16. N. Konno, J. Math. Soc. Jpn. NISUBC 0025-5645 57, 1179 (2005);
17. G. Grimmett, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.026119 69, 026119 (2004);
18. N. Konno, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.026113 72, 026113 (2005);
19. A. D. Gottlieb, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.047102 72, 047102 (2005).
20. S. S. Schweber, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.58. 449 58, 449 (1986);
21. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
22. J. L. Richardson, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(91)90240-L 63, 84 (1991).
23. B. M. Boghosian and W. Taylor IV, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(98)00042-6 120, 30 (1998).
24. G. H. Weiss, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)00805-1 311, 381 (2002).
25. S. Godoy and F. Espinosa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.3381 52, 3381 (1995).
26. N. Konno, e-print quant-ph/0310191.
27. B. Gaveau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.419 53, 419 (1984).
28. I. Bialynicki-Birula, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.49. 6920 49, 6920 (1994).
29. A. Ambainis, in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SIAM Press, Philadelphia, 2005), p. 1099.