Quantum control consists in tuning in real-time a set of knobs which set the intensity of
some interactions or couplings of a control Hamiltonian. The control Hamiltonian dictates the dynamical state of a quantum state
and, as the controls are changed, the quantum state evolves following Schrödinger's dynamic. Ultimately, the goal of quantum control is to prepare certain quantum states with desirable properties (an entangled state for instance). This is of fundamental interest for cold-atom systems, quantum computing and many "hot" fields of quantum sciences.
Below is an artistic impression of a non-convex optimization landscape that may be encountered when optimizing quantum control. In our work we explore the different geometry that this landscape can take as different constraints are impose on the system. We show in particular that quantum control undergoes multiple phase transitions from smooth phases to rugged and glassy phases. Our exploration is guided by reinforcement learning methods along with stochastic descent optimization.