Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise

TL;DR

This paper develops data-dependent generalization bounds for noisy parameterized quantum models using quantum Fisher information, aiding understanding of their robustness and capacity in quantum machine learning.

Contribution

It introduces a novel quantum Fisher information-based generalization bound that accounts for noise and model complexity in quantum machine learning.

Findings

Bound relates model complexity to training data and quantum Fisher information.

Analysis of the tradeoff between model expressiveness and generalization.

Structured characterization of quantum model complexity via local neighborhoods.

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.