Quantum walks and the size of the graph

A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix quantum walk model, the number of edges is bounded below by a...

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Bibliographic Details
Published in:Discrete mathematics 2019-10, Vol.342 (10), p.2765-2769
Main Author: Coutinho, Gabriel
Format: Article
Language:English
Subjects:
Quantum walk
Spectral bounds
State transfer
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Summary:A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix quantum walk model, the number of edges is bounded below by a cubic function on the eccentricity of a periodic vertex. This gives some idea on the shape of a graph that would admit periodicity or perfect state transfer. We also raise some extremal type of questions in the end that could lead to future research.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2018.04.011