Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning

TL;DR

The paper presents PHQFNO, a hybrid quantum-classical neural operator that extends FNOs to higher dimensions, enabling distributed quantum-classical computation for scientific machine learning tasks.

Contribution

It introduces a partitioned hybrid quantum Fourier neural operator that generalizes QFNOs, allowing for scalable, higher-dimensional, and more stable quantum-enhanced scientific modeling.

Findings

PHQFNO recovers classical FNO accuracy.

PHQFNO outperforms classical models on Navier-Stokes equations.

PHQFNO shows improved stability under input noise.

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.