Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs

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Autori principali: Tran, Ban Q., Dehaghani, Nahid Binandeh, Wisniewski, Rafal, Mengel, Susan, Aguiar, A. Pedro
Natura: Preprint
Pubblicazione: 2026
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author Tran, Ban Q.
Dehaghani, Nahid Binandeh
Wisniewski, Rafal
Mengel, Susan
Aguiar, A. Pedro
author_facet Tran, Ban Q.
Dehaghani, Nahid Binandeh
Wisniewski, Rafal
Mengel, Susan
Aguiar, A. Pedro
contents Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine learning have motivated hybrid quantum-classical extensions aimed at enhancing representational capacity while remaining compatible with near-term quantum hardware. In this work, we investigate trainable embedding strategies within quantum-assisted PINNs for solving parabolic PDEs, using one- and two-dimensional heat equations as canonical benchmarks. We introduce two quantum-assisted architectures that differ in their embedding components. In the first approach, a classical feed-forward neural network generates trainable feature maps for quantum data encoding (FNN-TE-QPINN). In the second, the embedding stage is realized entirely by a parameterized quantum circuit (QNN-TE-QPINN), yielding a fully quantum feature map. Our findings emphasize the critical role of embedding design and support hybrid quantum-classical approaches for parabolic PDE modeling in the NISQ era.
format Preprint
id arxiv_https___arxiv_org_abs_2602_14596
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs
Tran, Ban Q.
Dehaghani, Nahid Binandeh
Wisniewski, Rafal
Mengel, Susan
Aguiar, A. Pedro
Quantum Physics
Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine learning have motivated hybrid quantum-classical extensions aimed at enhancing representational capacity while remaining compatible with near-term quantum hardware. In this work, we investigate trainable embedding strategies within quantum-assisted PINNs for solving parabolic PDEs, using one- and two-dimensional heat equations as canonical benchmarks. We introduce two quantum-assisted architectures that differ in their embedding components. In the first approach, a classical feed-forward neural network generates trainable feature maps for quantum data encoding (FNN-TE-QPINN). In the second, the embedding stage is realized entirely by a parameterized quantum circuit (QNN-TE-QPINN), yielding a fully quantum feature map. Our findings emphasize the critical role of embedding design and support hybrid quantum-classical approaches for parabolic PDE modeling in the NISQ era.
title Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs
topic Quantum Physics
url https://arxiv.org/abs/2602.14596