AI 中文总结
研究针对量子门最优控制，提出增强的PINNQOC方案，通过傅里叶特征嵌入等改进克服标准PINN框架瓶颈。与Krotov方法和PRONTO对比基准测试，在多能级量子比特上实现量子门，门保真度超99.9%，还分析了相关性能及权衡。
AI 中文摘要
实现可扩展量子计算需要高保真操作以减轻向非计算状态的粒子泄漏。物理信息神经网络（PINNs）已成为统一量子硬件表征（反问题）和脉冲工程（正问题）的强大范例，为自主量子处理器奠定基础架构。然而，标准PINN框架在同时解决高振荡多能级动力学和在严格全局相位约束下优化连续控制场时面临严重数值瓶颈。本文提出一种增强的量子最优控制PINN方案（PINNQOC），通过纳入傅里叶特征嵌入、动态轮次归一化和明智的预训练例程来规避这些限制。为严格评估其性能，将该框架与两种主要的连续控制求解器进行系统基准测试：一阶Krotov方法和二阶轨迹优化投影算子牛顿法（PRONTO）。这些技术应用于在截断的三能级磁通量子比特和与碳 - 13核自旋耦合的四能级氮空位中心上实现多个量子门。先进的PINNQOC方法成功抑制了粒子泄漏，同时实现了超过99.9%的门保真度，与传统求解器的效果相当。最后，对计算时间、迭代效率和平均泄漏进行了全面分析，突出了不同的权衡以及将物理引导的机器学习嵌入自动化量子硬件管道的途径。
英文摘要
Achieving scalable quantum computing demands high-fidelity operations capable of mitigating population leakage into non-computational states. Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful paradigm to unify quantum hardware characterization (inverse problems) and pulse engineering (direct problems), laying the foundational architecture for autonomous quantum processors. However, standard PINN frameworks face severe numerical bottlenecks, such as spectral bias, when attempting to simultaneously solve highly oscillatory multi-level dynamics and optimize continuous control fields under strict global phase constraints. In this work, we propose an enhanced PINN scheme for quantum optimal control (PINNQOC) that circumvents these limitations by incorporating Fourier feature embeddings, dynamic epoch normalization, and an informed pre-training routine. To rigorously evaluate its performance, we systematically benchmark our framework against two premier continuous control solvers: the first-order Krotov method and the second-order Projection Operator Newton Method for Trajectory Optimization (PRONTO). These techniques are applied to implement multiple quantum gates on a truncated three-level fluxonium qubit and a four-level Nitrogen-Vacancy center coupled to a Carbon-13 nuclear spin. Our advanced PINNQOC approach successfully suppresses population leakage while achieving gate fidelities exceeding 99.9$\%$, matching the efficacy of traditional solvers. Finally, we provide a comprehensive analysis of computational times, iteration efficiency, and mean leakage, highlighting the distinct trade-offs and avenues for embedding physics-guided machine learning into automated quantum hardware pipelines.
