Forward Discrete‐Time Quantum Walk for Efficiently Identifying Critical Nodes of Complex Networks
Zhengyi Wang, Feng Gao, Yuan Xu, Xiao-Hui Wang, Jingyang Fang · Advanced Quantum Technologies · 2025
Abstract Critical node identification is the precondition for exploring complex networks, which is a graph‐based optimal search problem in principle. Classical methods, hindered by limited parallel processing capabilities, often grapple with high computational demands and inefficiency. Recent studies have leveraged quantum walk (QW) to tackle such challenges. However, existing QW‐based approaches are constrained by graph structures and prone to recurrent traversal issues. Being different, a novel forward discrete‐time quantum walk (F‐DTQW) method is proposed, which can traverse without redundant visits by prohibiting reverse and lateral propagations. The proposed method significantly enhances the efficiency of critical node identification and is applicable to arbitrary complex networks. The proposed method is validated on typical complex networks such as small‐world, scale‐free, and directed networks, and calculates the transition probability of nodes, corresponding to the centrality measurement index of transition connectivity (TC), which expands from the betweenness centrality (BC) index. The time complexity of F‐DTQW is also analyzed, which is reduced from O ( N 3 ) to O ( N 2 ) compared to the classical method.