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CRC Press eBooks

Applications of Quantum Walks in Link Mining

Fei Yan, Wen Liang, Fangyan Dong

Published Nov 24, 2025• 0 citations
Publisher

Abstract

This chapter explores the applications of quantum walks in identifying and predicting critical links in complex networks. It covers the Hadamard walk algorithm for mining critical links in static networks and its applications in dynamic unmanned aerial vehicle (UAV) networks, the continuous-time quantum walk algorithm for link prediction, and the simplified quantum walk algorithm for predicting missing links in complex networks.

DOI
10.1201/9781003683902-6

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This chapter delineates potential research areas and challenges within the application domains of quantum walks and complex networks. These aspects entail the optimization of quantum walk computations on large-scale complex networks, the application of quantum walks across diverse types of complex networks, the exploration of quantitative relationships between quantum walk measurement outcomes and the statistical characteristics of complex networks, quantum walk algorithms for mining combined individuals within complex networks, and the requirement for a “dual-track” approach in the design of quantum walk algorithms on complex networks.

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This chapter explores the applications of quantum walks in identifying and predicting critical links in complex networks. It covers the Hadamard walk algorithm for mining critical links in static networks and its applications in dynamic unmanned aerial vehicle (UAV) networks, the continuous-time quantum walk algorithm for link prediction, and the simplified quantum walk algorithm for predicting missing links in complex networks.
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.
Prediction of missing links is an important part of many applications, such as friends' recommendations on social media, reduction of economic cost of protein functional modular mining, and implementation of accurate recommendations in the shopping platform. However, the existing algorithms for predicting missing links fall short in the accuracy and the efficiency. To ameliorate these, we propose a simplified quantum walk model whose Hilbert space dimension is only twice the number of nodes in a complex network. This property facilitates simultaneous consideration of the self-loop of each node and the common neighbour information between arbitrary pair of nodes. These effects decrease the negative effect generated by the interference effect in quantum walks while also recording the similarity between nodes and its neighbours. Consequently, the observed probability after the two-step walk is utilised to represent the score of each link as a missing link, by which extensive computations are omitted. Using the AUC index as a performance metric, the proposed model records the highest average accuracy in the prediction of missing links compared to 14 competing algorithms in nine real complex networks. Furthermore, experiments using the precision index show that our proposed model ranks in the first echelon in predicting missing links. These performances indicate the potential of our simplified quantum walk model for applications in network alignment and functional modular mining of protein-protein networks.
This chapter delineates potential research areas and challenges within the application domains of quantum walks and complex networks. These aspects entail the optimization of quantum walk computations on large-scale complex networks, the application of quantum walks across diverse types of complex networks, the exploration of quantitative relationships between quantum walk measurement outcomes and the statistical characteristics of complex networks, quantum walk algorithms for mining combined individuals within complex networks, and the requirement for a “dual-track” approach in the design of quantum walk algorithms on complex networks.
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links. Continuous-time quantum walk algorithms assume that we can simulate the dynamics of quantum systems where the Hamiltonian is given by the adjacency matrix of the graph. It is known that such can be simulated efficiently if the underlying graph is row-sparse and efficiently row-computable. While this is sufficient for many applications, it limits the applicability for this class of algorithms to study real world complex networks, which, among other properties, are characterized by the existence of a few densely connected nodes, called hubs. In other words, complex networks are typically not row-sparse, even though the average connectivity over all nodes can be very small. In this work, we extend the state-of-the-art results on quantum simulation to graphs that contain a small number of hubs, but that are otherwise sparse. Hopefully, our results may lead to new applications of quantum computing to network science.
Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize the explicit counting of even- and odd-length paths between nodes to quantify a score function and infer new or unobserved links. Here, we propose a quantum algorithm for path-based link prediction using a controlled continuous-time quantum walk to encode even and odd path-based prediction scores. Through classical simulations on a few real networks, we confirm that the quantum walk scoring function performs similarly to other path-based link predictors. In a brief complexity analysis we identify the potential of our approach in uncovering a quantum speedup for path-based link prediction.