Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.

使用针对特定量子动力学系统和所需控制目标定制的时间相关控制脉冲来建立量子最优控制(QOC) 的数据驱动方法对于许多新兴的量子技术至关重要。我们开发了一个数据驱动的回归程序，双线性动态模式分解(biDMD)，它利用时间序列测量来建立 QOC 的量子系统识别。biDMD 优化框架是一种基于物理的回归，它利用了已知的潜在哈密顿结构。此外，可以修改 biDMD 以对控制信号的快速和慢速采样进行建模，后者通过频闪采样策略进行建模。biDMD 方法为量子系统中的实时在线实现提供了灵活、可解释和自适应的回归框架。此外，该方法与 Koopman 理论有很强的理论联系，后者用线性算子近似非线性动力学。与许多机器学习范式相比，构建 biDMD 模型所需的数据最少，并且随着新数据的收集，模型很容易更新。