Scattering model for quantum random walks on a hypercube

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 1, 2005, Pages

  Kǒík, Jozef ^a   Bužek, Vladimír ^a,b  

^a INSTITUTE OF PHYSICS   (Slovakia)

^b MASARYK UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

HYPERCUBES; QUANTUM ALGORITHM; QUANTUM SYSTEMS; SCATTERING MODELS;

ALGORITHMS; GRAPH THEORY; HAMILTONIANS; MAPPING; MATHEMATICAL MODELS; PROBLEM SOLVING; QUANTUM THEORY;

SCATTERING;

EID: 18444390885     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.012306     Document Type: Article

References (20)

1. J. Kempe, Contemp. Phys. 44, 307 (2003).
2. N. Shenvi, J. Kempe, and K. B. Whaley, Phys. Rev. A 67, 052307 (2003).
3. A. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, in Proceedings of the 35th ACM Symposium on Theory of Computing (STOC'03) (ACM Press, New York, 2003), pp. 59-68.
4. We should note that there is nothing really random (in a classical sense) about quantum random walk: the quantum evolution is always unitary (deterministic), and the only randomness involved in the scheme is the random outcomes of the measurements.
5. Y. Aharonov, L. Davidovich, and N. Zagury, Phys. Rev. A 48, 1687 (1993).
6. A. M. Childs, E. Farhi, and S. Gutmann, Quantum Inf. Process. 1, 35 (2002).
7. J. Watrous, J. Comput. Syst. Sci. 62, 376 (2001).
8. M. Hillery, J. Bergou, and E. Feldman, Phys. Rev. A 68, 032314 (2003).
9. E. Feldman and M. Hillery, e-print quant-ph/0403066.
10. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC'01) (ACM Press, New York, 2001), pp. 50-59.
11. D. A. Meyer, J. Stat. Phys. 85, 551 (1996).
12. B. Schumacher and R. F. Werner, e-print quant-ph/0405174.
13. A. M. Childs and J. M. Eisenberg, e-print quant-ph/0311038;
14. see also A. Ambainis, e-print quant-ph/0311001.
15. V. Kendon, e-print quant-ph/0306140;
16. V. Kendon and B. Sanders, e-print quant-ph/0404043.
17. I. Jex, S. Stenholm, and A. Zeilinger, Opt. Commun. 117, 95 (1995).
18. C. Moore and A. Russel, e-print quant-ph/0104137.
19. A. Ambainis, e-print quant-ph/0403120.
20. M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).