Generalization analysis of quantum neural networks using dynamical Lie algebras

Hiroshi Ohno

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arXiv · 2504.09771

Generalization analysis of quantum neural networks using dynamical Lie algebras

Hiroshi Ohno

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Abstract

The paper presents a generalization bound for quantum neural networks based on a dynamical Lie algebra. Using covering numbers derived from a dynamical Lie algebra, the Rademacher complexity is derived to calculate the generalization bound. The obtained result indicates that the generalization bound is scaled by O(sqrt(dim(g))), where g denotes a dynamical Lie algebra of generators. Additionally, the upper bound of the number of the trainable parameters in a quantum neural network is presented. Numerical simulations are conducted to confirm the validity of the obtained results.

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Hiroshi Ohno. 2025-04-14. Generalization analysis of quantum neural networks using dynamical Lie algebras. https://arxiv.org/abs/2504.09771

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