Enhancement of Quantum Semi-Supervised Learning via Improved Laplacian and Poisson Methods

This paper develops a hybrid quantum approach for graph-based semi-supervised learning to enhance performance in scenarios where labeled data is scarce. We introduce two enhanced quantum models, the Improved Laplacian Quantum Semi-Supervised Learning (ILQSSL) and the Improved Poisson Quantum Semi-Supervised Learning (IPQSSL), that incorporate advanced label propagation strategies within variational quantum circuits. These models utilize QR decomposition to embed graph structure directly into quantum states, thereby enabling more effective learning in low-label settings. We validate our methods across four benchmark datasets like Iris, Wine, Heart Disease, and German Credit Card -- and show that both ILQSSL and IPQSSL consistently outperform leading classical semi-supervised learning algorithms, particularly under limited supervision. Beyond standard performance metrics, we examine the effect of circuit depth and qubit count on learning quality by analyzing entanglement entropy and Randomized Benchmarking (RB). Our results suggest that while some level of entanglement improves the model's ability to generalize, increased circuit complexity may introduce noise that undermines performance on current quantum hardware. Overall, the study highlights the potential of quantum-enhanced models for semi-supervised learning, offering practical insights into how quantum circuits can be designed to balance expressivity and stability. These findings support the role of quantum machine learning in advancing data-efficient classification, especially in applications constrained by label availability and hardware limitations.