On the speed gradient method for generating unitary quantum operations for closed quantum systems

The speed gradient method [1] is widely applied for the design of control laws in various mechanical systems [2], including quantum systems [3], [4]. In this paper a general formulation of the speed gradient method is provided for the problem of generating unitary processes in n-level quantum systems isolated from the environment, and the stabilization condition is analyzed for the differential form of the speed gradient algorithm. The formulation of the problem includes defining an equation which determines the evolution of the system under the action of the control, and defining an objective function which determines the degree to which the control goal is attained.