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.

翻译：数据驱动的代理模型可替代昂贵参数化偏微分方程的多物理场求解器，然而构建紧凑且精确的三维问题神经算子仍面临挑战：在傅里叶神经算子中，密集模态谱通道混合的参数量随保留傅里叶模态数线性增长，导致参数规模膨胀并限制实时部署能力。本文提出HQ-LP-FNO，一种混合量子-经典傅里叶神经算子，通过参数规模与傅里叶模态预算无关的紧凑型模态共享变分量子电路混合器，替代部分密集谱模块。我们协同设计了参数匹配的经典瓶颈控制模块，以提供严格评估框架。该模型在对高能激光加工（耦合传热、熔池对流、自由表面变形及相变）的三维代理建模中，相比经典基线方法减少15.6%可训练参数，同时将相分数平均绝对误差降低26%，并将相对温度平均绝对误差从2.89%降至2.56%。量子通道预算扫描实验表明，适度的变分量子电路分配在所有测试配置（包括完全经典基线）中均取得最佳温度指标，揭示了最优量子-经典划分方案。消融实验证实，变分量子电路通过紧凑电路结构自然实现的模态共享混合是性能提升的主要贡献因素。基于ibm-torino后校准噪声的噪声模拟器实验表明，量子混合器在测试采样范围内具有数值稳定性。这些结果表明，基于变分量子电路的参数高效谱混合方法可改进复杂多物理场问题的神经算子代理模型，并为混合量子算子学习的可控评估建立标准化协议。