Eur. Phys. J. Plus (2014) 129: 150
https://doi.org/10.1140/epjp/i2014-14150-y

Regular Article

Quantum Google algorithm

Construction and application to complex networks

¹ Departamento de Física Teórica I, Universidad Complutense, 28040, Madrid, Spain
² Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain

^* e-mail: gpaparo@ucm.es

Received: 30 April 2014
Accepted: 10 June 2014
Published online: 22 July 2014

Abstract

We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks. The algorithm has been shown to identify unambiguously the underlying topology of the network and to be capable of clearly highlighting the structure of secondary hubs of networks. Furthermore, it can resolve the degeneracy in importance of the low-lying part of the list of rankings. Examples of applications include real-world instances from the WWW, which typically display a scale-free network structure and models of hierarchical networks. The quantum algorithm has been shown to display an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance among the nodes, as compared to the classical algorithm.