Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning
This work addresses the problem of efficient quantum-classical integration for scientific machine learning, offering a tunable hybrid method that is incremental in extending existing quantum Fourier neural operators.
The authors tackled the challenge of scaling quantum machine learning for scientific simulations by introducing the Partitioned Hybrid Quantum Fourier Neural Operator (PHQFNO), which partitions computations across classical and quantum resources, achieving higher accuracy than classical counterparts on incompressible Navier-Stokes equations and showing improved stability under input noise.
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.