Adaptive experimental quantum control (${\min }_{a\in \mathcal{A}}{J}_{\exp }(a)$)

Parametrize a reproducible pulse by a finite vector $a$ and evaluate its objective experimentally on freshly prepared systems. Repeatedly update the pulse from measured objective values or finite-difference derivatives, including penalties for resources. This is closed-loop control across experimental runs, even when each pulse is open-loop control within a run. It reduces reliance on an inaccurate dynamical model but still requires preparation reproducibility, sufficient measurement statistics and stability of the experimental conditions.