[2603.22964] A PAC-Bayesian approach to generalization for quantum models

Quantum Physics arXiv:2603.22964 (quant-ph) [Submitted on 24 Mar 2026] Title:A PAC-Bayesian approach to generalization for quantum models Authors:Pablo Rodriguez-Grasa, Matthias C. Caro, Jens Eisert, Elies Gil-Fuster, Franz J. Schreiber, Carlos Bravo-Prieto View a PDF of the paper titled A PAC-Bayesian approach to generalization for quantum models, by Pablo Rodriguez-Grasa and 5 other authors View PDF HTML (experimental) Abstract:Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validat...