CTQWformer: A CTQW-based Transformer for Graph Classification

2026-05-10

AI Summary

This work addresses the challenge that existing graph neural networks and Transformers struggle to jointly capture global structural dependencies and dynamic information propagation in graphs. The authors propose a hybrid architecture that integrates continuous-time quantum walks (CTQWs) with Graph Transformers, embedding both graph topology and node features into a quantum dynamical evolution process via a trainable Hamiltonian. A graph recurrent module is further incorporated to explicitly model temporal dynamics. This approach introduces CTQWs into graph representation learning for the first time, offering a physically inspired paradigm that combines structural bias with dynamic modeling capabilities. Experimental results demonstrate that the proposed model significantly outperforms graph kernel methods and state-of-the-art GNNs across multiple graph classification benchmarks, validating the effectiveness of quantum dynamical mechanisms in deep graph learning.

Abstract

Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In this paper, we propose CTQWformer, a hybrid graph learning framework that integrates continuous-time quantum walks (CTQW) with GNN. CTQWformer employs a trainable Hamiltonian that fuses graph topology and node features, enabling physically grounded modeling of quantum walk dynamics that captures rich and intricate graph structure information. The extracted CTQW-based representations are incorporated into two complementary modules:(i) a Graph Transformer module that embeds final-time propagation probabilities as structural biases in the self-attention mechanism, and (ii) a Graph Recurrent Module that captures temporal evolution patterns with bidirectional recurrent networks. Extensive experiments on benchmark graph classification datasets demonstrate that CTQWformer outperforms graph kernel and GNN-based methods, demonstrating the potential of integrating quantum dynamics into trainable deep learning frameworks for graph representation learning. To the best of our knowledge, CTQWformer is the first hybrid CTQW-based Transformer, integrating CTQW-derived structural bias with temporal evolution modeling to advance graph learning.

Problem

• graph classification
• global structural dependencies
• dynamic information propagation
• graph representation learning

Innovation

• Continuous-Time Quantum Walks
• Graph Transformer
• Trainable Hamiltonian
• Structural Bias
• Graph Representation Learning