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CRC Press eBooks

Applications of Quantum Walks in Node Discovery

Fei Yan, Liang Wen, Fangyan Dong

Published Nov 24, 2025• 0 citations
Publisher

Abstract

This chapter explores the applications of discrete-time quantum walks in node mining, covering algorithms such as the quantum PageRank, the parameterized coin quantum walk, and the three-degree decay Grover walk. It also examines the applications of continuous-time quantum walks in this domain, including adaptations of the Google PageRank algorithm for open quantum systems, the quantum Jensen-Shannon divergence algorithm, and an information propagation model based on quantum walks.

DOI
10.1201/9781003683902-5

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This chapter explores the applications of discrete-time quantum walks in node mining, covering algorithms such as the quantum PageRank, the parameterized coin quantum walk, and the three-degree decay Grover walk. It also examines the applications of continuous-time quantum walks in this domain, including adaptations of the Google PageRank algorithm for open quantum systems, the quantum Jensen-Shannon divergence algorithm, and an information propagation model based on quantum walks.
This book explores the intersection of quantum computing and network science. It bridges the theoretical foundations of quantum walk algorithms with their applications in the structural exploration and representation learning of complex networks. Quantum walks, a technology that is pivotal to universal quantum computational models, examines the movement of particles on a graph composed of nodes and links. Quantum superposition enables these particles to traverse these graphs more quickly, while measurement-induced collapse introduces fluctuations, making the identification of critical nodes challenging yet intriguing. At its core, the book explores how quantum walk algorithms can transform the structural and representational analysis of complex networks. It begins by introducing the fundamental concepts of quantum computing and quantum walks, including generalized definitions and the properties of low-dimensional quantum walks. Then, it discusses the implementation of discrete- and continuous-time quantum walks for mining network nodes, links, and subgraphs, as well as their use in network representation learning and graph neural networks. The book will serve as a valuable reference for researchers, students, and educators interested in quantum walks, complex networks, quantum mechanics, and information engineering.
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, Erdős-Rényi random network, Watts-Strogatz network, spatial network, Zachary Karate club network, GNC, GN, GNR networks, Barabási and Albert network, etc. In addition, we study the convergence of the quantum PageRank process and its dependency on the damping factor α. We observe that this quantum PageRank procedure is faster than many other proposals reported in the literature.
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entangle-ment as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete-time quantum walks.