Understanding Generalization in Quantum Machine Learning with Margins

Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform bounds, across both classical and quantum settings. In this work, we present a margin-based generalization bound for QML models, providing a more reliable framework for evaluating generalization. Our experimental studies on the quantum phase recognition dataset demonstrate that margin-based metrics are strong predictors of generalization performance, outperforming traditional metrics like parameter count. By connecting this margin-based metric to quantum information theory, we demonstrate how to enhance the generalization performance of QML through a classical-quantum hybrid approach when applied to classical data.

Quantum information processing presents exciting opportunities to push the boundaries of what machine learning can achieve. A central goal in machine learning is generalization—the ability of a model to learn from examples and make accurate predictions on new, unseen data. Generalization is a core characteristic of intelligent behavior and a critical measure of how useful a machine learning model will be in real-world applications.In this work, we contribute to a better understanding of generalization in quantum machine learning (QML). We build on a well-established idea from classical machine learning—called the margin—and develop new theoretical results for quantum models. Through both mathematical analysis and simulated experiments, we show that margin-based techniques offer a more effective way to predict generalization performance than traditional measures. Our results provide a new foundation for evaluating and improving quantum learning models, which may support the development of more reliable quantum algorithms in the future.