Publication: Quantum Google in a complex network
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Nature Publishing Group
We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays 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, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks.
© 2013 All autors. The authors acknowledge the Centro de Supercomputación y Visualización de Madrid (CeSViMa) for CPU time on the Magerit2 cluster. This work has been supported by the Spanish MINECO grants and the European Regional Development Fund under projects FIS2012-33152, MTM2011-28800-C02-01, CAM research consortium QUITEMAD S2009-ESP-1594, European Commission PICC: FP7 2007-2013, Grant No. 249958 and UCM-BS grant GICC-910758.