Pulse control of affine systems with applications to quantum control

Motivated by problems in quantum control, we introduce a novel method for studying time-optimal control problems of affine systems with unbounded controls. Intuitively, we construct a relaxation of our problem as follows: for each control of finite amplitude, we appropriately rescale the time variable so that, in the limit, an instantaneous jump in the state of the system becomes a trajectory containing both the state before and after the jump. The main advantage of this method is the direct applicability of the classical Pontryagin maximum principle. Several examples, including the generation of noiseless and noisy qubit gates, as well as population transfer in open two-level systems, are discussed.