Investigating constrained quantum control through a kinematic-to-dynamic- variable transformation

A search for the variables that control a quantum system's dynamics occurs over a landscape, defined as the target objective as a function of the variables. Prior studies show that upon satisfaction of three specific assumptions, the topology of the landscape is free of suboptimal traps that could prematurely halt the search for an optimal control. One key assumption is free access to all necessary control variables; however, in practice, the controls are always limited in some fashion which may result in constraint-induced traps on the landscape. This paper aims to introduce the means to systematically explore the nature of constrained controls that yield suboptimal outcomes. The procedure utilizes kinematic controls, which comprise a simple set of time-independent variables, and then performs a landscape topology-preserving transformation into corresponding dynamic controls. The equivalent landscape topology of these two formulations permits the study of a family of dynamic controls that reflect constrained control landscape behavior. In particular, constrained dynamic controls are identified as isolated points on the landscape or as suboptimal level sets. The wide range of such dynamic controls indicates the richness and complexity of constraint-induced features on the landscape.