SAQNN: Spectral Adaptive Quantum Neural Network as a Universal Approximator

Jialiang Tang, Jialin Zhang, Xiaoming Sun
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:119423-119442, 2026.

Abstract

Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete theoretical foundations for the expressivity of quantum neural networks (QNNs). In this paper we propose a constructive QNN model and demonstrate that it possesses the universal approximation property (UAP), which means it can approximate any square-integrable function up to arbitrary accuracy. Furthermore, it supports switching function bases, thus adaptable to various scenarios in numerical approximation and machine learning. Our model has asymptotic advantages over the best classical feed-forward neural networks in terms of circuit size and achieves optimal parameter complexity when approximating Sobolev functions under $L_2$ norm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-tang26af, title = {{SAQNN}: Spectral Adaptive Quantum Neural Network as a Universal Approximator}, author = {Tang, Jialiang and Zhang, Jialin and Sun, Xiaoming}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {119423--119442}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/tang26af/tang26af.pdf}, url = {https://proceedings.mlr.press/v306/tang26af.html}, abstract = {Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete theoretical foundations for the expressivity of quantum neural networks (QNNs). In this paper we propose a constructive QNN model and demonstrate that it possesses the universal approximation property (UAP), which means it can approximate any square-integrable function up to arbitrary accuracy. Furthermore, it supports switching function bases, thus adaptable to various scenarios in numerical approximation and machine learning. Our model has asymptotic advantages over the best classical feed-forward neural networks in terms of circuit size and achieves optimal parameter complexity when approximating Sobolev functions under $L_2$ norm.} }
Endnote
%0 Conference Paper %T SAQNN: Spectral Adaptive Quantum Neural Network as a Universal Approximator %A Jialiang Tang %A Jialin Zhang %A Xiaoming Sun %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-tang26af %I PMLR %P 119423--119442 %U https://proceedings.mlr.press/v306/tang26af.html %V 306 %X Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete theoretical foundations for the expressivity of quantum neural networks (QNNs). In this paper we propose a constructive QNN model and demonstrate that it possesses the universal approximation property (UAP), which means it can approximate any square-integrable function up to arbitrary accuracy. Furthermore, it supports switching function bases, thus adaptable to various scenarios in numerical approximation and machine learning. Our model has asymptotic advantages over the best classical feed-forward neural networks in terms of circuit size and achieves optimal parameter complexity when approximating Sobolev functions under $L_2$ norm.
APA
Tang, J., Zhang, J. & Sun, X.. (2026). SAQNN: Spectral Adaptive Quantum Neural Network as a Universal Approximator. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:119423-119442 Available from https://proceedings.mlr.press/v306/tang26af.html.

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