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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

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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.

Information

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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