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Quantum Information Processing

, Volume 10, Issue 3, pp 405–417 | Cite as

Quantum walks, Ihara zeta functions and cospectrality in regular graphs

  • Peng RenEmail author
  • Tatjana Aleksić
  • David Emms
  • Richard C. Wilson
  • Edwin R. Hancock
Article

Abstract

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.

Keywords

Quantum walks Ihara zeta functions Cospectrality 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Peng Ren
    • 1
    Email author
  • Tatjana Aleksić
    • 2
  • David Emms
    • 1
  • Richard C. Wilson
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceThe University of YorkYorkUK
  2. 2.Faculty of ScienceUniversity of KragujevacKragujevacSerbia

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