Centrality measure based on continuous-time quantum walks and experimental realization
Josh Izaac, Xiang Zhan, Zhihao Bian, Kunkun Wang, Jian Li, Jingbo B. Wang, Peng Xue · Physical Review A · 2017
Network centrality has important implications well beyond its role in physical and information transport analysis; as such, various quantum-walk-based algorithms have been proposed for measuring network vertex centrality. In this work, we propose a continuous-time quantum walk algorithm for determining vertex centrality, and show that it generalizes to arbitrary graphs via a statistical analysis of randomly generated scale-free and Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi networks. As a proof of concept, the algorithm is detailed on a four-vertex star graph and physically implemented via linear optics, using spatial and polarization degrees of freedoms of single photons. This paper reports a successful physical demonstration of a quantum centrality algorithm.