Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise

Abstract: Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the generalizability of quantum circuit models. Designing robust quantum machine learning models under noise requires a principled understanding of complexity and generalization, extending beyond classical capacity measures. This study investigates the generalization properties of parameterized quantum machine learning models under the influence of noise. We present a data-dependent generalization bound grounded in the quantum Fisher information matrix. We leverage statistical learning theory to relate the parameter space volumes and training sizes to estimate the generalization capability of the trained model. We provide a structured characterization of complexity in quantum models by integrating local parameter neighborhoods and effective dimensions defined through quantum Fisher information matrix eigenvalues. We also analyze the tightness of the bound and discuss the tradeoff between model expressiveness and generalization performance.