A Laplacian-based quantum graph neural networks for quantum semi-supervised learning

Hamed Gholipour, Farid Bozorgnia, Kailash Hambarde, Hamzeh Mohammadigheymasi, Javier Mancilla, Andre Sequeira, João C. Neves, Hugo Proença, Moharram Challenger

Abstract: The Laplacian learning method has proven effective in classical graph-based semi-supervised learning, yet its quantum counterpart remains underexplored. This study systematically evaluates the Laplacian-based quantum semi-supervised learning (QSSL) approach across four benchmark datasets—Iris, Wine, Breast Cancer Wisconsin, and Heart Disease. By experimenting with varying qubit counts and entangling layers, we demonstrate that increased quantum resources do not necessarily lead to improved performance. Our findings reveal that the effectiveness of the method is highly sensitive to dataset characteristics, as well as the number of entangling layers. Optimal configurations, generally featuring moderate entanglement, strike a balance between model complexity and generalization. These results emphasize the importance of dataset-specific hyperparameter tuning in quantum semi-supervised learning frameworks.