  Experimentally engineering high-dimensional quantum states is a crucial task
for several quantum information protocols. However, a high degree of precision
in the characterization of experimental noisy apparatus is required to apply
existing quantum state engineering protocols. This is often lacking in
practical scenarios, affecting the quality of the engineered states. Here, we
implement experimentally an automated adaptive optimization protocol to
engineer photonic Orbital Angular Momentum (OAM) states. The protocol, given a
target output state, performs an online estimation of the quality of the
currently produced states, relying on output measurement statistics, and
determines how to tune the experimental parameters to optimize the state
generation. To achieve this, the algorithm needs not be imbued with a
description of the generation apparatus itself. Rather, it operates in a fully
black-box scenario, making the scheme applicable in a wide variety of
circumstances. The handles controlled by the algorithm are the rotation angles
of a series of waveplates and can be used to probabilistically generate
arbitrary four-dimensional OAM states. We showcase our scheme on different
target states both in classical and quantum regimes, and prove its robustness
to external perturbations on the control parameters. This approach represents a
powerful tool for automated optimizations of noisy experimental tasks for
quantum information protocols and technologies.
