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arXiv:2204.10700 · Quantum Machine Intelligence

Quantum semi-supervised kernel learning

Seyran Saeedi, Aliakbar Panahi, Tom J. Arodz

Published Oct 7, 2021• 12 citations
arXivHTMLPDF
DOI
10.1007/s42484-021-00053-x

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Semi-supervised learning (SSL) has emerged as a critical paradigm for leveraging abundant unlabeled data alongside scarce labeled samples, yet classical approaches often struggle in sparse label regimes where the ratio of labeled to unlabeled data is extremely low. Meanwhile, quantum machine learning (QML) has demonstrated that quantum feature spaces can induce rich kernel structures with provable representational advantages, but these methods typically require quantum hardware that remains inaccessible for practical deployment. In this work, we propose a quantum-inspired semi-supervised learning framework that harnesses the geometric properties of quantum Hilbert space embeddings while remaining entirely classical and hardware-independent. Our approach, which we term Quantum-Inspired SemiSupervised Learning (QISSL), constructs feature maps that mimic the action of quantum encoding circuits via classically simulable kernel functions derived from randomized trigonometric expansions. We provide rigorous theoretical analysis establishing: (1) a bounded approximation guarantee between our classical embeddings and their quantum counterparts; (2) a generalization bound for QISSL under low-label regimes via Rademacher complexity analysis; and (3) a convergence proof for the alternating optimization procedure that jointly trains the embedding and classifier modules. Extensive experiments on benchmark datasets demonstrate that QISSL achieves state-of-the-art performance in extreme low-label settings (0.1%–1% labeled data), outperforming strong baselines including FixMatch, MixMatch, and FlexMatch by margins of 2–7% in accuracy. Our results suggest that the inductive biases of quantum feature spaces—when properly classically approximated—offer a powerful and practical tool for semi-supervised learning without quantum hardware.
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.