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Continuous-time quantum walks on the threshold network model

Published online by Cambridge University Press:  08 November 2010

YUSUKE IDE  and
NORIO KONNO
YUSUKE IDE
Affiliation:
Department of Information Systems Creation, Faculty of Engineering, Kanagawa University, Kanagawa, Yokohama 221-8686, Japan. Email: ide@kanagawa-u.ac.jp
NORIO KONNO
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya, Yokohama 240-8501, Japan. Email: konno@ynu.ac.jp
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Abstract

It is well known that many real world networks have a power-law degree distribution (the scale-free property). However, there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyse the space–time behaviour of continuous-time quantum walks and random walks on the threshold network model, which is a reasonable candidate model having the scale-free property. We show that the quantum walker exhibits localisation at the starting point, although the random walker tends to spread uniformly.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Special Issue 6: Quantum Algorithms , December 2010 , pp. 1079 - 1090
Copyright
Copyright © Cambridge University Press 2010

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