Characterizing graph symmetries through quantum Jensen-Shannon divergence

Luca Rossi, Andrea Torsello, Edwin R. Hancock, Richard C. Wilson

Research output: Journal article publicationJournal articleAcademic researchpeer-review

32 Citations (Scopus)

Abstract

In this paper we investigate the connection between quantum walks and graph symmetries. We begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse. To achieve this, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the quantum Jensen-Shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries. Hence, we assign to each pair of nodes of the graph a value of the divergence, and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph.

Original languageEnglish
Article number032806
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume88
Issue number3
DOIs
Publication statusPublished - 10 Sep 2013
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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