  Model-based quantum optimal control promises to solve a wide range of
critical quantum technology problems within a single, flexible framework. The
catch is that highly-accurate models are needed if the optimized controls are
to meet the exacting demands set by quantum engineers. A practical alternative
is to directly calibrate control parameters by taking device data and tuning
until success is achieved. In quantum computing, gate errors due to inaccurate
models can be efficiently polished if the control is limited to a few (usually
hand-designed) parameters; however, an alternative tool set is required to
enable efficient calibration of the complicated waveforms potentially returned
by optimal control. We propose an automated model-based framework for
calibrating quantum optimal controls called Learning Iteratively for Feasible
Tracking (LIFT). LIFT achieves high-fidelity controls despite parasitic model
discrepancies by precisely tracking feasible trajectories of quantum
observables. Feasible trajectories are set by combining black-box optimal
control and the bilinear dynamic mode decomposition, a physics-informed
regression framework for discovering effective Hamiltonian models directly from
rollout data. Any remaining tracking errors are eliminated in a non-causal way
by applying model-based, norm-optimal iterative learning control to subsequent
rollout data. We use numerical experiments of qubit gate synthesis to
demonstrate how LIFT enables calibration of high-fidelity optimal control
waveforms in spite of model discrepancies.
