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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.08746 |
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| _version_ | 1866916839008763904 |
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| author | Marcandelli, Paolo He, Yuanchun Mariani, Stefano Siena, Martina Markidis, Stefano |
| author_facet | Marcandelli, Paolo He, Yuanchun Mariani, Stefano Siena, Martina Markidis, Stefano |
| contents | We introduce the Partitioned Hybrid Quantum Fourier Neural Operator (PHQFNO), a generalization of the Quantum Fourier Neural Operator (QFNO) for scientific machine learning. PHQFNO partitions the Fourier operator computation across classical and quantum resources, enabling tunable quantum-classical hybridization and distributed execution across quantum and classical devices. The method extends QFNOs to higher dimensions and incorporates a message-passing framework to distribute data across different partitions. Input data are encoded into quantum states using unary encoding, and quantum circuit parameters are optimized using a variational scheme. We implement PHQFNO using PennyLane with PyTorch integration and evaluate it on Burgers' equation, incompressible and compressible Navier-Stokes equations. We show that PHQFNO recovers classical FNO accuracy. On incompressible Navier-Stokes, PHQFNO achieves higher accuracy than its classical counterparts. Finally, we perform a sensitivity analysis under input noise, confirming improved stability of PHQFNO over classical baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning Marcandelli, Paolo He, Yuanchun Mariani, Stefano Siena, Martina Markidis, Stefano Machine Learning Quantum Physics We introduce the Partitioned Hybrid Quantum Fourier Neural Operator (PHQFNO), a generalization of the Quantum Fourier Neural Operator (QFNO) for scientific machine learning. PHQFNO partitions the Fourier operator computation across classical and quantum resources, enabling tunable quantum-classical hybridization and distributed execution across quantum and classical devices. The method extends QFNOs to higher dimensions and incorporates a message-passing framework to distribute data across different partitions. Input data are encoded into quantum states using unary encoding, and quantum circuit parameters are optimized using a variational scheme. We implement PHQFNO using PennyLane with PyTorch integration and evaluate it on Burgers' equation, incompressible and compressible Navier-Stokes equations. We show that PHQFNO recovers classical FNO accuracy. On incompressible Navier-Stokes, PHQFNO achieves higher accuracy than its classical counterparts. Finally, we perform a sensitivity analysis under input noise, confirming improved stability of PHQFNO over classical baselines. |
| title | Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning |
| topic | Machine Learning Quantum Physics |
| url | https://arxiv.org/abs/2507.08746 |