Generalization bounds in hybrid quantum-classical machine learning models
Year: 2025
Type: article
Abstract: Hybrid quantum-classical models aim to harness the strengths of both quantum computing and classical machine learning, but their practical potential remains poorly understood. In this work, we develop a unified mathematical framework for analyzing generalization in hybrid models, offering insight into how these systems learn from data. We establish a generalization bound of the form O ̃ ( α k N ( k 3 2 m n + T log T ) ) for N training data points, T trainable quantum gates, n -dimensional quantum circuit output, and k bounded linear layers ∥ F i ∥ F ≤ α , where i = 1 , ⋯ , k and F ∈ R m × n interspersed with activation functions. This generalization bound decomposes into quantum and classical contributions, providing a theoretical framework to separate their influence and clarifying their interaction. Alongside the bound, we highlight conceptual limitations of applying classical statistical learning theory in the hybrid setting and suggest promising directions for future theoretical work.
Source: Physical Review A
DOI: 10.1103/6ckt-hlh8
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,675
OpenAlex ID: W7117130439