🤖 AI Summary
This work addresses the vertex ranking problem in graphs by proposing a novel quantum PageRank algorithm based on discrete-time open quantum walks (DT-OQWs). The method introduces the Weyl operator as a Kraus operator to construct the DT-OQW model, integrating quantum Markovian dynamics with a tunable damping factor α. This design enables faster convergence and enhanced robustness in vertex ranking. The algorithm is universally applicable to arbitrary directed or undirected complex networks. Extensive evaluation on benchmark real-world and synthetic networks—including Barabási–Albert (BA), Watts–Strogatz (WS), and the Karate Club network—demonstrates that the proposed approach achieves significantly faster convergence than existing quantum PageRank variants, while exhibiting superior stability and controllability with respect to the damping parameter α. This work establishes a new paradigm for quantum-based network analysis.
📝 Abstract
This article presents a new quantum PageRank algorithm on graphs using discrete-time open quantum walks. Google's PageRank is a widely used algorithm for ranking the web pages on the World Wide Web in classical computation. From a broader perspective, it is also a fundamental measure for quantifying the importance of vertices in a network. Similarly, the new quantum PageRank also serves to quantify the significance of a network's vertices. In this work, we extend the concept of discrete-time open quantum walk on arbitrary directed and undirected graphs by utilizing the Weyl operators as Kraus operators. This new model of quantum walk is useful for building up the quantum PageRank algorithm, discussed in this article. We compare the classical PageRank and the newly defined quantum PageRank for different types of complex networks, such as the scale-free network, ErdH{o}s-R'enyi random network, Watts-Strogatz network, spatial network, Zachary Karate club network, GNC, GN, GNR networks, Barab'asi and Albert network, etc. In addition, we study the convergence of the quantum PageRank process and its dependency on the damping factor $alpha$. We observe that this quantum PageRank procedure is faster than many other proposals reported in the literature.