Evolution of continuous-time quantum random walks on circles

Fluctuation and Noise Letters

Volumn 5, Issue 1, 2005, Pages

  Inui, Norio ^a   Kasahara, Koichiro ^b   Konishi, Yoshinao ^a   Konno, Norio ^b  

^a UNIVERSITY OF HYOGO   (Japan)

^b YOKOHAMA NATIONAL UNIVERSITY   (Japan)

Author keywords

Circle; Quantum walk; Temporal fluctuation

Indexed keywords

EID: 17644389848     PISSN: 02194775     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219477505002410     Document Type: Article

References (18)

1. E. Farhi and S. Gutmann, Quantum computation and decision trees, Phys. Rev. A 58 (1998) 915-928.
2. A. Childs, E. Deotto, R. Cleve, E. Farhi, S. Gutmann and D. Spielman, Exponential algorithmic speedup by quantum walk, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing (2003) 59-68.
3. C. Moore and A. Russell, Quantum walks on the hypercubes (2001) quant-ph/0104137.
4. A. Ahmadi, R. Belk, C. Tamon and C. Wendler, On mixing in continuous-time quantum walks on some circulant graphs, Quantum Information and Computation 3 (2003) 611-618.
5. W. Adamczak, K. Andrew, P. Hernberg and C. Tamon, A note on graphs resistant to quantum uniform mixing (2003) quant-ph/0308073.
6. H. Gerhardt and J. Watrous, Continuous-time quantum walks on the symmetric group (2003) quant-ph/0305182, to appear at RANDOM'03.
7. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath and J. Watrous, One-dimensional quantum walks, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (2001) 37-49.
8. D. Aharonov, A. Ambainis, J. Kempe and U. V. Vazirani, Quantum walks on graphs, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (2001) 50-59.
9. N. Konno, Quantum random walks in one dimension, Quantum Information Processing 1 (2002) 345-354.
10. G. Grimmett, S. Janson and P. F. Scudo, Weak limits for quantum random walks, Phys. Rev. E 69 (2003) 026119.
11. J. Kempe, Quantum random walks - an introductory overview, Contemporary Physics 44 (2003) 307-327.
12. B. Tregenna, W. Flanagan, W. Maile and V. Kendon, Controlling discrete quantum walks: coins and initial states, New Journal of Physics 5 (2003) 83.
13. M. Bednarska, A. Grudka, P. Kurzyński, T. Luczak and A. Wójcik, Quantum walks on cycles, Phys. Lett. A 317 (2003) 21-25.
14. A. Romanelli, A. C. Sicardi Schifino, R. Siri, G. Abal, A. Auyuanet and R. Donangelo, Quantum random walk on the line as a Markovian process, Physica A 338 (2003) 395-405.
15. N. Inui, Y. Konishi, N. Konno and T. Soshi, Fluctuations of quantum random walks on circles (2003) quant-ph/0309204.
16. G. E. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press (1999).
17. R. B. Schinazi, Classical and Spatial Stochastic Processes, Birkhäuser (1999).
18. D. Aldous and J. A. Fill, Reversible Markov Chains and Random Walks on Graphs, available at http://stat-www.berkeley.edu/users/aldous/RWG.