Quantum Navigation and Ranking in Complex Networks

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.
This work has been partially supported by the Spanish DGICYT under projects FIS2009-13730-C02-02, FIS2009-13364-C02-01, CSD2007-046-Nanolight.es, MTM2009-13848, FIS2010-18639, FIS2011-25167 and EXPLORA FIS2011-14539-E; by the Generalitat de Catalunya and the Comunidad de Aragón through Project No. 2009SGR0838, FMI22/10; and by the J.S. McDonnell Foundation Research 344 Award. J.G.G is supported by MICINN through the Ramón y Cajal program.