Exploring Complex Networks with 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.

Fei Yan is a professor at the School of Computer Science and Technology, Changchun University of Science and Technology, China. He holds a Ph.D. in Engineering from the Tokyo Institute of Technology, Japan. His research interests include quantum information processing, complex networks, and image processing.

Wen Liang is an associate professor at the School of Information Science and Engineering, Shenyang Ligong University, China. He holds a Ph.D. in Engineering from the Changchun University of Science and Technology, China. His research interests include complex networks and quantum walks.

Fangyan Dong is a professor at the Faculty of Mechanical Engineering and Mechanics, Ningbo University, China. She holds a Ph.D. in Engineering from the Tokyo Institute of Technology, Japan. Her research interests include computational intelligence, fuzzy systems, and quantum computing.