Continuous-time quantum walks on ultrametric spaces

International Journal of Quantum Information

Volumn 4, Issue 6, 2006, Pages 1023-1035

  Konno, Norio ^a  

^a YOKOHAMA NATIONAL UNIVERSITY   (Japan)

Author keywords

P adic integers; Quantum walks; Ultrametric space

Indexed keywords

PROBABILITY DISTRIBUTIONS; TREES (MATHEMATICS);

COMPLETE GRAPHS; CONTINUOUS-TIME QUANTUM WALKS; CYCLE GRAPHS; HIERARCHICAL STRUCTURES; QUANTUM SEARCH ALGORITHM; QUANTUM WALK; TIME-AVERAGED; ULTRAMETRIC SPACE;

CONTINUOUS TIME SYSTEMS;

EID: 33846148977     PISSN: 02197499     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219749906002389     Document Type: Article

References (25)

1. A. T. Ogielski and D. L. Stein, Dynamics on ultrametric spaces, Phys. Rev. Lett. 55 (1985) 1634-1637.
2. V. A. Avetisov, A. H. Bikulov and S. V. Kozyrev, Application of p-adic analysis to models of breaking of replica symmetry, J. Phys. A: Math. Gen. 32 (1999) 8785-8791.
3. G. Parisi and N. Sourlas, P-adic numbers and replica symmetry breaking, Eur. Phys. J. B 14 (2000) 535-542.
4. V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev and V. A. Osipov, p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes, J. Phys. A: Math. Gen. 35 177-189 (2002).
5. V. A. Avetisov, A. Kh. Bikulov and V. Al. Osipov, p-adic description of characteristic relaxation in complex systems, J. Phys. A: Math. Gen. 36 (2003) 7239-7246.
6. S. K. Nechaev and O. A. Vasilyev, On metric structure of ultrametric spaces, J. Phys. A: Math. Gen. 37 (2004) 3783-3803.
7. S. V. Kozyrev, V. Al. Osipov and V. A. Avetisov, Non degenerate ultrametric diffusion, cond-mat/0403440.
8. K. Lukierska-Walasek and K. Topolski, Random walk on p-adics in glassy systems, cond-mat/0505585.
9. A. M. Childs, E. Farhi and S. Gutmann, An example of the difference between quantum and classical random walks, Quant. Inf. Proc. 1 (2002) 35-43.
10. A. Childs, E. Deotto, R. Cleve, E. Farhi, S. Gutmann and D. Spielman, Exponential algorithmic speedup by quantum walk, Proc. 35th Ann. ACM Symp. Theory of Computing (2003), pp. 59-68.
11. A. Ahmadi, R. Belk, C. Tamon and C. Wendler, On mixing in continuous-time quantum walks on some circulant graphs, Quant. Inf. Comput. 3 (2003) 611-618.
12. W. Adamczak, K. Andrew, P. Hernberg and C. Tamon, A note on graphs resistant to quantum uniform mixing, quant-ph/0308073.
13. D. ben-Avraham, E. Bollt and C. Tamon, One-dimensional continuous-time quantum walks, Quant. Inf. Proc. 3 (2004) 295-308.
14. N. Inui, K. Kasahara, Y. Konishi and N. Konno, Evolution of continuous-time quantum random walks on circles, Fluctuation Noise Lett. 5 (2005) 73-83.
15. N. Konno, Limit theorem for continuous-time quantum walk on the line, Phys. Rev. E 72 (2005) 026113.
16. D. Solenov and L. Fedichkin, Continuous-time quantum walks on a cycle graph, quant-ph/0506096.
17. L. Fedichkin, D. Solenov and C. Tamon, Mixing and decoherence in continuous-time quantum walks on cycles, quant-ph/0509163.
18. M. A. Jafarizadeh and S. Salimi, Investigation of continuous-time quantum walk via spectral distribution associated with adjacency matrix, quant-ph/0510174.
19. J. Kempe, Quantum random walks - an introductory overview, Contemp. Phys. 44 (2003) 307-327.
20. B. Tregenna, W. Flanagan, W. Maile and V. Kendon, Controlling discrete quantum walks: Coins and initial states, New J. Phys. 5 83 (2003).
21. A. Yu. Khrennikov and M. Nilsson, P-adic Deterministic and Random Dynamics (Kluwer Academic Publishers, 2004).
22. D. J. Watts, P. S. Dodds and M. E. J. Newman, Identity and search in social networks, Science 296 (2002) 1302-1305.
23. P. S. Dodds, D. J. Watts and C. F. Sabel, Information exchange and the robustness of organizational networks, Proc. Natl. Acad. Sci. USA 100 (2003) 12516-12521.
24. D. J. Watts, R. Muhamad, D. C. Medina and P. S. Dodds, Multiscale, resurgent epidemics in a hierarchical metapopulation model, Proc. Natl. Acad. Sci. USA 102 (2005) 11157-11162.
25. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd edn. (Cambridge University Press, Cambridge, 1944).