AI 中文总结
该研究将HHL与QSVT算法用于FDTD离散麦克斯韦方程的线性系统求解，在工业电磁学用例中验证了量子计算的适用性，发现QSVT精度更高且矩阵条件数饱和可适配工业规模。
AI 中文摘要
计算电磁学在众多工业应用中处于核心地位，但往往需要大量计算资源，尤其是在需要精细空间离散化时。尽管经典方法仍是主流，但量子计算可通过用有限数量的量子比特对大规模模拟进行编码，具备加速这类模拟的潜力。本研究针对采用有限差分时域（FDTD）方法离散化麦克斯韦方程所生成的线性系统，探究了Harrow-Hassidim-Lloyd（HHL）算法与量子奇异值变换（QSVT）算法的性能及资源缩放情况，并在雷达传播、透镜模拟和波束成形流程等具有代表性的工业用例中对其性能进行了基准测试。研究结果验证了这些方法的有效性：其状态保真度小于$2\cdot 10^{-3}$，成功概率大于$10^{-3}$，与实际量子状态采样兼容。总体而言，QSVT方法始终能提供更高的精度。研究还发现，作为量子求解器性能关键影响因素的线性矩阵条件数，会随空间格点数量增加而趋于饱和，这意味着空间网格可扩展至实际工业规模，而不会因矩阵病态性导致HHL或QSVT的电路深度增加。
英文摘要
Computational electromagnetics plays a central role in many industrial applications but often requires substantial computational resources, particularly when fine spatial discretizations are needed. While classical approaches remain the standard, quantum computing offers the potential to accelerate large-scale simulations by encoding them with a limited number of qubits. Here, we investigate the performance and resource scaling of the Harrow-Hassidim-Lloyd (HHL) and Quantum Singular Value Transformation (QSVT) algorithms for solving linear systems generated by the finite-difference time-domain (FDTD) method, a widely adopted numerical scheme for discretizing Maxwell's equations. We benchmark their performance across representative industrial use cases, including radar propagation, lens simulations, and beamforming processes. Our results demonstrate the validity of the approaches, achieving state infidelities smaller than $2\cdot 10^{-3}$ with success probabilities greater than $10^{-3}$, compatible with practical quantum state sampling. Overall, we observe that the QSVT method consistently delivers higher accuracy. We further observe that the condition number of the linear matrix, a key factor governing the performance of quantum solvers, saturates as the number of spatial lattice points increases. This implies that the spatial grid can be scaled to realistic industrial dimensions without increasing the HHL or QSVT circuit depth due to ill-conditioned matrices.
Comments19 pages, 13 figures
