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Node representation learning with discrete-time quantum walks (Master thesis)

Καραγιάννης, Αριστοτέλης/ Karagiannis, Aristotelis/ Quantum Computing and Quantum Technologies/ Κβαντική Υπολογιστική και Κβαντικές Τεχνολογίες

Graphs are fundamental structures for modeling complex relationships in domains such as social networks, bioinformatics, and finance, but traditional machine learning struggles with graph-structured, non-Euclidean data. Graph embedding methods address this by mapping nodes to low-dimensional vector spaces, yet classical approaches like DeepWalk and node2vec rely on Markovian assumptions that can limit their ability to capture global structure and subtle relational patterns. This thesis investigates discrete-time quantum walks (DTQWs) as an alternative approach to graph representation learning: unlike classical random walks, DTQWs use unitary quantum dynamics, enabling richer encoding of global connectivity and long-range correlations. We develop a Python toolkit for simulating DTQWs on arbitrary graphs and implement an embedding pipeline that produces both linear and nonlinear node embeddings. We evaluate DTQW-based embeddings on link prediction and node classification using benchmark datasets such as ego-Facebook and Cora, and we find that DTQW embeddings, especially when combined with nonlinear post-processing techniques such as kernel principal component analysis, outperform classical baselines in link prediction under edge sparsity and achieve competitive multi-class node classification.