arXiv:2604.04828quant-phcs.CE2026-04

用量子电路精简三维激光加工仿真模型的参数量,提升精度与实时性。

Hybrid Fourier Neural Operator for Surrogate Modeling of Laser Processing with a Quantum-Circuit Mixer

  • 用可变量子电路替代部分频域混合模块,参数量不随模式数增加
  • 相比纯经典模型减少15.6%参数,温度误差降低26%,相分数误差下降
  • 适合需要高精度实时仿真的复杂多物理场问题研究者

数据驱动的代理模型可替代昂贵的多物理场求解器,但构建三维问题的紧凑高精度神经算子仍具挑战:傅里叶神经算子中密集的模态混合层参数量随保留傅里叶模态数线性增长,导致参数膨胀并限制实时部署。本文提出HQ-LP-FNO,一种混合量子-经典傅里叶神经算子,将部分密集频域混合块替换为参数量独立于傅里叶模态数的紧凑型可变量子电路(VQC)混合器。同时设计参数匹配的经典瓶颈控制器以实现严格评估。在高能激光加工三维代理建模任务中,耦合热传导、熔池对流、自由表面变形与相变,该方法相较经典基线减少15.6%可训练参数,相分数平均绝对误差降低26%,相对温度MAE从2.89%降至2.56%。量子通道预算扫描显示,适度分配VQC可获得最优温度性能,优于全经典基线,表明存在最优经典-量子划分。消融实验确认,由VQC天然实现的模态共享混合是主要改进来源。基于ibm-torino后端校准噪声的噪声模拟器测试验证了量子混合器在测试采样范围内的数值稳定性。结果表明,基于VQC的参数高效频域混合可提升复杂多物理场神经算子的性能,并建立实用的混合量子算子学习评估协议。

原文摘要 · Abstract (English)

Data-driven surrogates can replace expensive multiphysics solvers for parametric PDEs, yet building compact, accurate neural operators for three-dimensional problems remains challenging: in Fourier Neural Operators, dense mode-wise spectral channel mixing scales linearly with the number of retained Fourier modes, inflating parameter counts and limiting real-time deployability. We introduce HQ-LP-FNO, a hybrid quantum-classical FNO that replaces a configurable fraction of these dense spectral blocks with a compact, mode-shared variational quantum circuit mixer whose parameter count is independent of the Fourier mode budget. A parameter-matched classical bottleneck control is co-designed to provide a rigorous evaluation framework. Evaluated on three-dimensional surrogate modeling of high-energy laser processing, coupling heat transfer, melt-pool convection, free-surface deformation, and phase change, HQ-LP-FNO reduces trainable parameters by 15.6% relative to a classical baseline while lowering phase-fraction mean absolute error by 26% and relative temperature MAE from 2.89% to 2.56%. A sweep over the quantum-channel budget reveals that a moderate VQC allocation yields the best temperature metrics across all tested configurations, including the fully classical baseline, pointing toward an optimal classical-quantum partitioning. The ablation confirms that mode-shared mixing, naturally implemented by the VQC through its compact circuit structure, is the dominant contributor to these improvements. A noisy-simulator study under backend-calibrated noise from ibm-torino confirms numerical stability of the quantum mixer across the tested shot range. These results demonstrate that VQC-based parameter-efficient spectral mixing can improve neural operator surrogates for complex multiphysics problems and establish a controlled evaluation protocol for hybrid quantum operator learning in practice.

量子计算神经算子激光加工代理模型

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