Quantum Graph Attention Networks: Trainable Quantum Encoders for Inductive Graph Learning

Graphs are a fundamental data structure for modeling relational systems, where entities (nodes) are connected by pairwise interactions (edges). This representation naturally arises in a wide range of domains, including chemistry (molecular structures) [2], social networks [3], Transportation & Logistics [4], Electrical Grids & Circuits [5], Communication Networks, Finance and Economics [6], and many more. Traditional machine learning models often struggle to process such non-Euclidean data due to their irregular topology. To address this, Graph Neural Networks (GNNs) have emerged as a powerful class of models that learn over graph-structured inputs by iteratively aggregating and transforming information from a node's neighborhood. By capturing both local structure and node features, GNNs enable tasks such as node classification, link prediction, and graph-level regression. Among their many variants, models like Graph Convolutional Networks (GCNs) [7], Graph Attention Networks (GATs) [8], and GraphSAGE [9] have demonstrated strong performance in both transductive and inductive settings, making GNNs a key building block in modern geometric deep learning. While classical GNNs have achieved remarkable success, their scalability and expressiveness can be limited by the classical nature of their computation [10], especially when modeling systems with inherent quantum structure, such as molecules or quantum materials. Quantum Graph Neural Networks (QGNNs) aim to address this by leveraging the computational power of parameterized quantum circuits to encode and process graph data in a quantum-enhanced latent space.