Continuous-time quantum walks on the threshold network model

  • Authors:

  • Yusuke Ide;Norio Konno

  • Affiliations:

  • Department of information systems creation, faculty of engineering, kanagawa university, kanagawa, yokohama 221-8686, japan. email: ide@kanagawa-u.ac.jp;Department of applied mathematics, faculty of engineering, yokohama national university, hodogaya, yokohama 240-8501, japan. email: konno@ynu.ac.jp

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2010

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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.