Graph Representation Learning (GRL) has emerged as a cornerstone technique for analysing complex, networked data across diverse domains, including biological systems, social networks, and data analysis. Traditional GRL methods often struggle to capture intricate relationships within complex graphs, particularly those exhibiting non-trivial structural properties such as power-law distributions or hierarchical structures. This paper introduces a novel quantum-inspired algorithm for GRL, utilizing hybrid Quantum-Classical Walks to overcome these limitations. Our approach combines the benefits of both quantum and classical dynamics, allowing the walker to simultaneously explore both highly local and far-reaching connections within the graph. Preliminary results for a case study in network community detection shows that this hybrid dynamic enables the algorithm to adapt effectively to complex graph topologies, offering a robust and versatile solution for GRL tasks.Graph Representation Learning (GRL) has emerged as a cornerstone technique for analysing complex, networked data across diverse domains, including biological systems, social networks, and data analysis. Traditional GRL methods often struggle to capture intricate relationships within complex graphs, particularly those exhibiting non-trivial structural properties such as power-law distributions or hierarchical structures. This paper introduces a novel quantum-inspired algorithm for GRL, utilizing hybrid Quantum-Classical Walks to overcome these limitations. Our approach combines the benefits of both quantum and classical dynamics, allowing the walker to simultaneously explore both highly local and far-reaching connections within the graph. Preliminary results for a case study in network community detection shows that this hybrid dynamic enables the algorithm to adapt effectively to complex graph topologies, offering a robust and versatile solution for GRL tasks.

arXiv:2510.01918Oct 2, 20250 citations

Community detection in network using Szegedy quantum walk

Md Samsur Rahaman, Supriyo Dutta

In a network, the vertices with similar characteristics construct communities. The vertices in a community are well-connected. Detecting the communities in a network is a challenging and important problem in the theory of complex networks. One approach to solving this problem uses the classical random walks on graphs. In quantum computing, quantum walks are the quantum mechanical counterparts of classical random walks. In this article, we employ a variant of Szegedy's quantum walk to develop a procedure for discovering the communities in networks. The limiting probability distribution of quantum walks assists us in determining the inclusion of a vertex in a community. We apply our community detection procedure to a variety of graphs and social networks, including the relaxed caveman graph, $l$ -partition graph, Karate club graph, and the dolphin's social network, among others.In a network, the vertices with similar characteristics construct communities. The vertices in a community are well-connected. Detecting the communities in a network is a challenging and important problem in the theory of complex networks. One approach to solving this problem uses the classical random walks on graphs. In quantum computing, quantum walks are the quantum mechanical counterparts of classical random walks. In this article, we employ a variant of Szegedy's quantum walk to develop a procedure for discovering the communities in networks. The limiting probability distribution of quantum walks assists us in determining the inclusion of a vertex in a community. We apply our community detection procedure to a variety of graphs and social networks, including the relaxed caveman graph, $l$-partition graph, Karate club graph, and the dolphin's social network, among others.

quant-pharXiv:2601.21152Jan 30, 20260 citations

Quantum Walk Neural Networks for Graph-Structured Data

Stefan Dernbach, Arman Mohseni-Kabir, Siddharth Pal +1 more

Studies in computational intelligenceDec 4, 201811 citations

Discrete quantum-classical walks for link prediction

A. Marin, M. Soto-Gomez, Giorgio Valentini +3 more

Link prediction is a fundamental task in network science that involves estimating the likelihood of missing or future connections between nodes based on the structural patterns of a graph. While Graph Neural Networks (GNNs) have become a dominant approach, Random Walk (RW)-based methods remain highly relevant due to their lower computational demands in large-scale networks. Although recent hybrid quantum-classical walks have shown promise in exploring graph structures, existing continuous-time models are computationally expensive as they require solving high-dimensional systems of differential equations. In this paper, we propose a discrete version of a recent hybrid quantum-classical random walk algorithm that significantly improves computational efficiency by utilizing state vector representations instead of density matrices. Our method, inspired by the Quantum Jumps approach, alternates between coherent evolution and measurement-driven state collapse to generate trajectories for node embeddings. We integrate this algorithm into a link prediction pipeline and evaluate its performance across various synthetic topologies, including Grid, Power-Law, Erdös-Rényi, Barabási-Albert, and Community graphs. The experimental results demonstrate that the proposed discrete hybrid walks consistently outperform classical random walk approaches in Community and Grid topologies, showing that quantum-inspired dynamics can capture complex structural information more effectively than classical dynamics for specific topologies.Link prediction is a fundamental task in network science that involves estimating the likelihood of missing or future connections between nodes based on the structural patterns of a graph. While Graph Neural Networks (GNNs) have become a dominant approach, Random Walk (RW)-based methods remain highly relevant due to their lower computational demands in large-scale networks. Although recent hybrid quantum-classical walks have shown promise in exploring graph structures, existing continuous-time models are computationally expensive as they require solving high-dimensional systems of differential equations. In this paper, we propose a discrete version of a recent hybrid quantum-classical random walk algorithm that significantly improves computational efficiency by utilizing state vector representations instead of density matrices. Our method, inspired by the Quantum Jumps approach, alternates between coherent evolution and measurement-driven state collapse to generate trajectories for node embeddings. We integrate this algorithm into a link prediction pipeline and evaluate its performance across various synthetic topologies, including Grid, Power-Law, Erdös-Rényi, Barabási-Albert, and Community graphs. The experimental results demonstrate that the proposed discrete hybrid walks consistently outperform classical random walk approaches in Community and Grid topologies, showing that quantum-inspired dynamics can capture complex structural information more effectively than classical dynamics for specific topologies.

IEEE Conference on Artificial Intelligence (CAI)May 8, 20260 citations

l

-partition graph, Karate club graph, and the dolphin's social network, among others.