We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. For any control protocol, the goal is to find the mapping between the offset and the distance. This mapping is interpolated using a neural network. The estimate is global in the sense that no a priori knowledge is required on the relation to be determined. Different neural network algorithms are tested on a series of data sets. We show that the mapping can be reproduced with very high precision in the direct case when the offset is known, while obstacles appear in the indirect case starting from the distance to the target. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results.

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We investigate two different formulations of gradient-based algorithms for the robust control of quantum systems. We consider the simultaneous control of an ensemble of systems which differ by the value of a constant Hamiltonian parameter. The two versions of the iterative algorithm, called concurrent and sequential, correspond respectively to a joint update of the control at each iteration for all the elements of the ensemble or to a successive correction of the control in which the control law is different for each system. We analyze the relative efficiency of the two optimization procedures on two benchmark examples, namely the control of two-level quantum systems and Bose-Eistein Condensates in a one-dimensional optical lattice. Intensive numerical simulations show the superiority of the sequential-update formulation with respect to the concurrent one for a similar numerical cost.