Sequential versus concurrent gradient-based optimal algorithms for the robust control of quantum systems

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-Einstein 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.