Quantum walks, Ihara zeta functions and cospectrality in regular graphs

Quantum walks, Ihara zeta functions and cospectrality in regular graphs In this paper we explore an interesting relationship between discrete-time quantum walks and the Ihara zeta function of a graph. The paper commences by reviewing the related literature on the discrete-time quantum walks and the Ihara zeta function. Mathematical definitions of the two concepts are then provided, followed by analyzing the relationship between them. Based on this analysis we are able to account for why the Ihara zeta function can not distinguish cospectral regular graphs. This analysis suggests a means by which to develop zeta functions that have potential in distinguishing such structures. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum walks, Ihara zeta functions and cospectrality in regular graphs

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Publisher
Springer US
Copyright
Copyright © 2010 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-010-0205-y
Publisher site
See Article on Publisher Site

References

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