QPI-DeepONet-MAC: A Scalable and Stable Hybrid Classical-Quantum Architecture for Physics-Informed Deep Operator Networks
Abstract
General operator learning for parametric partial differential equations (PDEs) is a fundamental challenge at the intersection of artificial intelligence and physics-based modeling. Physics-informed Deep Operator Networks (PI-DeepONets) incorporate governing equations into learning, but face optimization difficulties in high dimensions. Quantum extensions offer additional representational capacity, yet their trainability can be hindered by barren plateaus. Here, we introduce QPI-DeepONet-MAC, a hybrid quantum-classical architecture that integrates parameterized quantum circuits into PI-DeepONets through a multiplicative-and-additive coupling (MAC) of classical representations and quantum expectation values. We prove analytically that the proposed architecture retains universal operator approximation capabilities. Furthermore, we derive bounds on quantum parameter gradients, establishing explicit conditions to avoid barren plateaus alongside a scaling criterion for trainability. Additionally, we derive a lower bound on the number of sensors required for a target accuracy, directly linking sampling requirements to input function regularity, domain dimension, and PDE dynamical growth. Finally, we propose an informational regularization scheme based on quantum coherence and state fidelity dynamics to prevent coherence loss and preserve quantum structure during training. Together, these results establish a theoretical foundation for quantum-enhanced physics-informed operator learning and position QPI-DeepONet-MAC as a scalable, stable framework for solving parametric PDEs.
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BibTeX
@misc{lantigua2026qpideeponetmac,
title = {{QPI-DeepONet-MAC: A Scalable and Stable Hybrid Classical-Quantum Architecture for Physics-Informed Deep Operator Networks}},
author = {Said Lantigua and José Valencia and Gilson Giraldi and Renato Portugal and Jonas Maziero},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01824},
eprint = {2610.01824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01824},
}
RIS
TY - UNPB
TI - QPI-DeepONet-MAC: A Scalable and Stable Hybrid Classical-Quantum Architecture for Physics-Informed Deep Operator Networks
AU - Said Lantigua
AU - José Valencia
AU - Gilson Giraldi
AU - Renato Portugal
AU - Jonas Maziero
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01824
UR - https://arxiv.org/abs/2610.01824
AB - General operator learning for parametric partial differential equations (PDEs) is a fundamental challenge at the intersection of artificial intelligence and physics-based modeling. Physics-informed Deep Operator Networks (PI-DeepONets) incorporate governing equations into learning, but face optimization difficulties in high dimensions. Quantum extensions offer additional representational capacity, yet their trainability can be hindered by barren plateaus. Here, we introduce QPI-DeepONet-MAC, a hybrid quantum-classical architecture that integrates parameterized quantum circuits into PI-DeepONets through a multiplicative-and-additive coupling (MAC) of classical representations and quantum expectation values. We prove analytically that the proposed architecture retains universal operator approximation capabilities. Furthermore, we derive bounds on quantum parameter gradients, establishing explicit conditions to avoid barren plateaus alongside a scaling criterion for trainability. Additionally, we derive a lower bound on the number of sensors required for a target accuracy, directly linking sampling requirements to input function regularity, domain dimension, and PDE dynamical growth. Finally, we propose an informational regularization scheme based on quantum coherence and state fidelity dynamics to prevent coherence loss and preserve quantum structure during training. Together, these results establish a theoretical foundation for quantum-enhanced physics-informed operator learning and position QPI-DeepONet-MAC as a scalable, stable framework for solving parametric PDEs.
ER -