Characterizing graph symmetries through quantum Jensen-Shannon divergence

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

*Corresponding author for this work

Research output: Contribution to journalArticle

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
Number of pages9
JournalPhysical Review E
Volume88
Issue number3
DOIs
Publication statusPublished - 10 Sep 2013

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Quantum Walk
Divergence
divergence
Symmetry
symmetry
Graph in graph theory
Quantum Graphs
Vertex of a graph
wave functions
Wave Function
Assign
Experiment

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Rossi, Luca ; Torsello, Andrea ; Hancock, Edwin R. ; Wilson, Richard C. / Characterizing graph symmetries through quantum Jensen-Shannon divergence. In: Physical Review E. 2013 ; Vol. 88, No. 3.
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Characterizing graph symmetries through quantum Jensen-Shannon divergence. / Rossi, Luca; Torsello, Andrea; Hancock, Edwin R.; Wilson, Richard C.

In: Physical Review E, Vol. 88, No. 3, 032806, 10.09.2013.

Research output: Contribution to journalArticle

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