CTQWformer: A CTQW-based Transformer for Graph Classification

TL;DR

CTQWformer introduces a novel hybrid framework combining continuous-time quantum walks with GNNs and Transformers, effectively capturing global structure and dynamic information for improved graph classification.

Contribution

It is the first to integrate CTQW-based quantum dynamics with Transformer and recurrent modules for enhanced graph representation learning.

Findings

Outperforms existing graph kernel and GNN methods on benchmark datasets.

Effectively captures both structural dependencies and temporal evolution in graphs.

Demonstrates the potential of quantum-inspired models 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.