将量子傅里叶神经算子分块，实现跨设备混合计算，提升科学机器学习精度与稳定性。
Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning
- 分块设计量子-经典混合计算，支持分布式执行
- 在不可压缩纳维-斯托克斯方程上优于经典模型
- 对输入噪声更鲁棒，适合高精度科学模拟场景
我们提出分区混合量子傅里叶神经算子（PHQFNO），是面向科学机器学习的量子傅里叶神经算子（QFNO）的推广。PHQFNO将傅里叶算子计算分派至经典与量子资源，支持可调的量子-经典混合及跨设备分布式执行。该方法拓展了QFNO至高维场景，并引入消息传递框架实现数据分片。输入数据通过一元编码映射为量子态，量子电路参数采用变分优化。我们基于PennyLane与PyTorch集成实现，评估了其在Burgers方程、不可压缩与可压缩纳维-斯托克斯方程上的表现。结果表明，PHQFNO可复现经典FNO精度；在不可压缩纳维-斯托克斯问题中，其精度高于经典基线。此外，在输入噪声下的敏感性分析显示，PHQFNO相比经典模型具有更强的稳定性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。