Quantum Navigation and Ranking in Complex Networks

TL;DR

This paper introduces a quantum navigation method for ranking elements in complex networks, demonstrating faster convergence, resolution of degeneracies, and revealing new hierarchical features compared to classical algorithms.

Contribution

It presents a novel quantum algorithm for network ranking that improves convergence speed and resolves degeneracies in classical rankings.

Findings

Quantum navigation reduces the number of steps to reach stationarity.

Quantum coherence uncovers new hierarchical structures in networks.

The method is effective when implemented on real-world networks.

Abstract

Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.