Multiple solutions in the tracking control of quantum systems.

This paper demonstrates the existence of multiple solutions at each time point in tracking control of quantum systems. These solutions are shown to arise from the nonlinear dependence of the short-time propagators U(t + delta t,t) on the control field. The multiplicity of solutions depends on the parameters of the controlled system and the nature of the imposed track.

Optimal control landscapes for quantum observables.

The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density matrix and a Hermitian operator associated with the observable of interest. The optimal control landscape is the observable as a functional of the control field.

Quantum optimally controlled transition landscapes.

A large number of experimental studies and simulations show that it is surprisingly easy to find excellent quality control over broad classes of quantum systems. We now prove that for controllable quantum systems with no constraints placed on the controls, the only allowed extrema of the transition probability landscape correspond to perfect control or no control. Under these conditions, no suboptimal local extrema exist as traps that would impede the search for an optimal control.