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Main Authors: Marcandelli, Paolo, He, Yuanchun, Mariani, Stefano, Siena, Martina, Markidis, Stefano
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.08746
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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