Quantum Google Algorithm: Construction and Application to Complex Networks

TL;DR

This paper reviews the Quantum PageRank algorithm's ability to analyze large complex networks, highlighting its advantages over classical methods in topology detection, stability, and importance distribution.

Contribution

It provides a comprehensive review of the Quantum PageRank algorithm's application to complex networks, emphasizing its improved stability and structural detection capabilities.

Findings

Unambiguously identifies network topology

Highlights secondary hubs effectively

Displays increased stability to damping parameter variations

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.