A Laplacian-based Quantum Graph Neural Network for Semi-Supervised Learning

Abstract: Laplacian learning method is a well-established technique in classical graph-based semi-supervised learning, but its potential in the quantum domain remains largely unexplored. This study investigates the performance of the Laplacian-based Quantum Semi-Supervised Learning (QSSL) method across four benchmark datasets -- Iris, Wine, Breast Cancer Wisconsin, and Heart Disease. Further analysis explores the impact of increasing Qubit counts, revealing that adding more Qubits to a quantum system doesn't always improve performance. The effectiveness of additional Qubits depends on the quantum algorithm and how well it matches the dataset. Additionally, we examine the effects of varying entangling layers on entanglement entropy and test accuracy. The performance of Laplacian learning is highly dependent on the number of entangling layers, with optimal configurations varying across different datasets. Typically, moderate levels of entanglement offer the best balance between model complexity and generalization capabilities. These observations highlight the crucial need for precise hyperparameter tuning tailored to each dataset to achieve optimal performance in Laplacian learning methods.