Hybrid quantum-classical control problems

The notion of hybrid quantum-classical control system was introduced as a control dynamical system which combined classical and quantum degrees of freedom. Classical and quantum objects were combined within a geometrical description of both types of systems. We also considered the notion of hybrid quantum-classical controllability by means of the usual definitions of geometric control theory, and we discussed how the different concepts associated to quantum controllability are lost in the hybrid context because of the nonlinearity of the dynamics. We also considered several examples of physically relevant problems, such as the spin-boson model or the notion of hybrid spline.