GraphQWalk: Learning Structural Node Embeddings via Continuous Quantum Walk

Structural node embedding is a fundamental technique for encoding the topology of a graph into low-dimensional vectors. However, many existing methods generate position-dependent embeddings, meaning that structurally similar nodes are represented dissimilarly merely due to their distance in the graph. Furthermore, these approaches often lack interpretability and robustness against structural noise. To address these challenges, this paper introduces GraphQWalk, an interpretable, unsupervised, and position-independent method that leverages the continuous quantum walk to capture structural features. Inspired by quantum physics, GraphQWalk first computes initial node features from the average transition probabilities of a particle in a continuous quantum walk. These features, encoding multi-scale structural information, are then aggregated within multi-hop neighborhoods to incorporate local context. Extensive experiments demonstrate that GraphQWalk effectively captures diverse structural roles, achieving superior robustness and performance over baseline models in downstream tasks from classification to cross-graph alignment.