Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912907075256320 |
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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 |