Parameters of integral circulant graphs and periodic quantum dynamics

Nitin Saxena*, Simone Severini, Igor Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticle

70 Citations (Scopus)

Abstract

The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system whose hamiltonian is identical to the adjacency matrix of a circulant graph is periodic if and only if all eigenvalues of the graph are integers (that is, the graph is integral). Motivated by this observation, we focus on relevant properties of integral circulant graphs. Specifically, we bound the number of vertices of integral circulant graphs in terms of their degree, characterize bipartiteness and give exact bounds for their diameter. Additionally, we prove that circulant graphs with odd order do not allow perfect state transfer.

Original languageEnglish
Pages (from-to)417-430
Number of pages14
JournalInternational Journal of Quantum Information
Volume5
Issue number3
DOIs
Publication statusPublished - Jun 2007

Keywords

  • Circulant graphs
  • Integral graphs
  • Perfect state transfer
  • Periodic dynamics

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