  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 non-linear dynamics with
linear operators. In comparison with many machine learning paradigms, it
requires minimal data and the biDMD 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.
