Approximation rates of quantum neural networks for periodic functions via Jackson's inequality

• URL: http://arxiv.org/abs/2511.16149v2
• Date: Wed, 26 Nov 2025 13:02:50 GMT
• Title: Approximation rates of quantum neural networks for periodic functions via Jackson's inequality
• Authors: Ariel Neufeld, Philipp Schmocker, Viet Khoa Tran,
• Abstract summary: Quantum neural networks (QNNs) are an analog of classical neural networks in the world of quantum computing.<n>We study the approximation capabilities of QNNs for periodic functions.
• Score: 2.217547045999963
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum neural networks (QNNs) are an analog of classical neural networks in the world of quantum computing, which are represented by a unitary matrix with trainable parameters. Inspired by the universal approximation property of classical neural networks, ensuring that every continuous function can be arbitrarily well approximated uniformly on a compact set of a Euclidean space, some recent works have established analogous results for QNNs, ranging from single-qubit to multi-qubit QNNs, and even hybrid classical-quantum models. In this paper, we study the approximation capabilities of QNNs for periodic functions with respect to the supremum norm. We use the Jackson inequality to approximate a given function by implementing its approximating trigonometric polynomial via a suitable QNN. In particular, we see that by restricting to the class of periodic functions, one can achieve a quadratic reduction of the number of parameters, producing better approximation results than in the literature. Moreover, the smoother the function, the fewer parameters are needed to construct a QNN to approximate the function.

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