  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.
