Exploring the impact of constraints in quantum optimal control through a kinematic formulation

The control of quantum dynamics with tailored laser fields is finding growing experimental success. In practice, experiments will be subject to constraints on the controls that may prevent full optimization of the objective. A framework is presented for systematically investigating the impact of constraints in quantum optimal control simulations using a two-stage process starting with simple time-independent kinematic controls, which act as stand-ins for the traditional dynamic controls. The objective is a state-to-state transition probability, and constraints are introduced by restricting the kinematic control variables during optimization. As a second stage, the means to map from kinematic to dynamic controls is presented, thus enabling a simplified overall procedure for exploring how limited resources affect the ability to optimize the objective. A demonstration of the impact of imposing several types of kinematic constraints is investigated, thereby offering insight into constrained quantum controls.