{"ID":2838971,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.16149","arxiv_id":"2511.16149","title":"Approximation rates of quantum neural networks for periodic functions via Jackson's inequality","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.","short_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...","url_abs":"https://arxiv.org/abs/2511.16149","url_pdf":"https://arxiv.org/pdf/2511.16149v2","authors":"[\"Ariel Neufeld\",\"Philipp Schmocker\",\"Viet Khoa Tran\"]","published":"2025-11-20T08:44:24Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.LG\",\"math.NA\",\"stat.ML\"]","methods":"[]","has_code":false}