Work

Universal Approximation Theorem and Error Bounds for Quantum Neural Networks and Quantum Reservoirs

Year: 2025

Type: article

Abstract: Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a quantum setting, whereby classical functions can be approximated by parameterized quantum circuits. We provide here precise error bounds for specific classes of functions and extend these results to the interesting new setup of randomized quantum circuits, mimicking classical reservoir neural networks. Our results show in particular that a quantum neural network with ${\mathcal {O}}(\varepsilon ^{-2})$ weights and ${\mathcal {O}} (\lceil \log _{2}(\varepsilon ^{-1})\rceil)$ qubits suffices to achieve approximation error $\varepsilon \gt 0$ when approximating functions with integrable Fourier transforms.

Source: IEEE Transactions on Neural Networks and Learning Systems

DOI: 10.1109/tnnls.2025.3552223

Authors: Lukas Gonon, Antoine Jacquier

Institutions: University of St.Gallen, Imperial College London

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: G1089084160, Rough Volatility: A Trojan horse into modern Financial computing, G460110269, Distributed Quantum Computing and Applications