QuanONet: Quantum Neural Operator with Application to Differential Equation

Ruocheng Wang, Zhuo Xia, Ge Yan, Junchi Yan
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:64955-64975, 2025.

Abstract

Differential equations are essential and popular in science and engineering. Learning-based methods including neural operators, have emerged as a promising paradigm. We explore its quantum counterpart, and propose QuanONet – a quantum neural operator which has not been well studied in literature compared with their counterparts in other machine learning areas. We design a novel architecture as a hardware-efficient ansatz, in the era of noisy intermediate-scale quantum (NISQ). Its circuit is pure quantum. By lying its ground on the operator approximation theorem for its quantum counterpart, QuanONet in theory can fit various differential equation operators. We also propose its modified version TF-QuanONet with ability to adaptively fit the dominant frequency of the problem. The real-device empirical results on problems including anti-derivative operators, Diffusion-reaction Systems demonstrate that QuanONet outperforms peer quantum methods when their model sizes are set akin to QuanONet.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wang25dq, title = {{Q}uan{ON}et: Quantum Neural Operator with Application to Differential Equation}, author = {Wang, Ruocheng and Xia, Zhuo and Yan, Ge and Yan, Junchi}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {64955--64975}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wang25dq/wang25dq.pdf}, url = {https://proceedings.mlr.press/v267/wang25dq.html}, abstract = {Differential equations are essential and popular in science and engineering. Learning-based methods including neural operators, have emerged as a promising paradigm. We explore its quantum counterpart, and propose QuanONet – a quantum neural operator which has not been well studied in literature compared with their counterparts in other machine learning areas. We design a novel architecture as a hardware-efficient ansatz, in the era of noisy intermediate-scale quantum (NISQ). Its circuit is pure quantum. By lying its ground on the operator approximation theorem for its quantum counterpart, QuanONet in theory can fit various differential equation operators. We also propose its modified version TF-QuanONet with ability to adaptively fit the dominant frequency of the problem. The real-device empirical results on problems including anti-derivative operators, Diffusion-reaction Systems demonstrate that QuanONet outperforms peer quantum methods when their model sizes are set akin to QuanONet.} }
Endnote
%0 Conference Paper %T QuanONet: Quantum Neural Operator with Application to Differential Equation %A Ruocheng Wang %A Zhuo Xia %A Ge Yan %A Junchi Yan %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wang25dq %I PMLR %P 64955--64975 %U https://proceedings.mlr.press/v267/wang25dq.html %V 267 %X Differential equations are essential and popular in science and engineering. Learning-based methods including neural operators, have emerged as a promising paradigm. We explore its quantum counterpart, and propose QuanONet – a quantum neural operator which has not been well studied in literature compared with their counterparts in other machine learning areas. We design a novel architecture as a hardware-efficient ansatz, in the era of noisy intermediate-scale quantum (NISQ). Its circuit is pure quantum. By lying its ground on the operator approximation theorem for its quantum counterpart, QuanONet in theory can fit various differential equation operators. We also propose its modified version TF-QuanONet with ability to adaptively fit the dominant frequency of the problem. The real-device empirical results on problems including anti-derivative operators, Diffusion-reaction Systems demonstrate that QuanONet outperforms peer quantum methods when their model sizes are set akin to QuanONet.
APA
Wang, R., Xia, Z., Yan, G. & Yan, J.. (2025). QuanONet: Quantum Neural Operator with Application to Differential Equation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:64955-64975 Available from https://proceedings.mlr.press/v267/wang25dq.html.

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