Continuous-time quantum walks on trees in quantum probability theory

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 9, Issue 2, 2006, Pages 287-297

  Konno, Norio ^a  

^a YOKOHAMA NATIONAL UNIVERSITY   (Japan)

Author keywords

Limit theorem; Quantum walk; Tree

Indexed keywords

EID: 33745016978     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025706002354     Document Type: Article

References (23)

1. J. Kempe, Quantum random walks - An introductory overview, Contemp. Phys. 44 (2003) 307-327.
2. B. Tregenna, W. Flanagan, W. Maile and V. Kendon, Controlling discrete quantum walks: Coins and initial states, New J. Phys. 5 (2003) 83.
3. A. M. Childs, E. Farhi and S. Gutmann, An example of the difference between quantum and classical random walks, Quantum Infor. Proces, 1 (2002) 35-43.
4. A. Childs, E. Deotto, R. Cleve, E. Farhi, S. Gutmann and D. Spielman, Exponential algorithmic speedup by quantum walk, in Proc. 35th Annual ACM Sympo. on Theory of Computing (2003) 59-68.
5. H. Gerhardt and J. Watrous, Continuous-time quantum walks on the symmetric group, in Proc. 7th Workshop on Randomization and Approximation Techniques in Computer Science, Lecture Notes in Computer Science, Vol. 2764, eds. S. Arora et al. (Springer, 2003), pp. 290-301.
6. A. Ahmadi, R. Belk, C. Tamon and C. Wendler, On mixing in continuous-time quantum walks on some circulant graphs, Quantum Infor. Cornput. 3 (2003) 611-618.
7. W. Adamczak, K. Andrew, P. Hernberg and C. Tamon, A note on graphs resistant to quantum uniform mixing, quant-ph/0308073.
8. D. ben-Avraham, E. Bout and C. Tamon, One-dimensional continuous-time quantum walks, Quantum Infor. Proc. 3 (2004) 295-308.
9. 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.
10. N. Konno, Limit theorem for continuous-time quantum walk on the line, Phys. Rev. E 72 (2005) 026113.
11. A. D. Gottlieb, Convergence of continuous-time quantum walks on the line, Phys. Rev. E 72 (2005) 047102.
12. D. Solenov and L. Fedichkin, Continuous-time quantum walks on a cycle graph, quant-ph/0506096.
13. L. Fedichkin, D. Solenov and C. Tamon, Mixing and decoherence in continuous-time quantum walks on cycles, quant-ph/0509163.
14. M. A. Jafarizadeh and S. Salimi, Investigation of continuous-time quantum walk via spectral distribution associated with adjacency matrix, quant-ph/0510174.
15. O. Mülken, V. Bierbaum and A. Blumen, Coherent exciton transport in dendrimers and continuous-time quantum walks, cond-mat/0602040.
16. O. Mülken and A. Blumen, Quantum vs. classical percolability of graphs, quant-ph/0602120.
17. L. Accardi and M. Bożejko, Interacting Fock spaces and Gaussianization of probability measures, Inf. Dim. Anal. Quantum Probab. Rel. Topics 1 (1998) 663-670.
18. Y. Hashimoto, Quantum decomposition in discrete groups and interacting Fock spaces, Inf. Dim. Anal. Quantum Probab. Rel. Topics 4 (2001) 277-287.
19. N. Obata, Quantum probabilistic approach to spectral analysis of star graphs, Interdisciplinary Infor. Sci. 10 (2004) 41-52.
20. D. Igarashi and N. Obata, Asymptotic spectral analysis of growing graphs: Odd graphs and spidernets, to appear in Banach Center Publ.
21. N. Obata, Asymptotic spectral analysis of growing graphs: A quantum probabilistic approach, to appear in Proc. Jagna Workshop.
22. H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959) 336-354.
23. G. N. Watson, A Treatise, on the Theory of Bessel Functions, 2nd edn. (Cambridge Univ. Press, 1944).