{"ID":2895791,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.08746","arxiv_id":"2507.08746","title":"Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning","abstract":"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.","short_abstract":"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 di...","url_abs":"https://arxiv.org/abs/2507.08746","url_pdf":"https://arxiv.org/pdf/2507.08746v1","authors":"[\"Paolo Marcandelli\",\"Yuanchun He\",\"Stefano Mariani\",\"Martina Siena\",\"Stefano Markidis\"]","published":"2025-07-11T16:56:37Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"quant-ph\"]","methods":"[]","has_code":false}