Systematically altering the apparent topology of constrained quantum control landscapes

Abstract

A quantum control experiment typically seeks a shaped electromagnetic field to drive a system towards a specified observable objective. The large number of successful experiments can be understood through an exploration of the underlying quantum control landscape, which maps the objective as a function of the control variables. Specifically, under certain assumptions, the control landscape lacks suboptimal traps that could prevent identification of an optimal control. One of these assumptions is that there are no restrictions on the control variables, however, in practice control resources are inevitably constrained. The associated constrained quantum control landscape may be difficult to freely traverse due to the presence of limited resource induced traps. This work develops algorithms to (1) seek optimal controls under restricted resources, (2) explore the nature of apparent suboptimal landscape topology, and (3) favorably alter trap topology through systematic relaxation of the constraints. A set of mathematical tools are introduced to meet these needs by working directly with dynamic controls, rather than the prior studies that employed intermediate so-called kinematic control variables. The new tools are illustrated using few-level systems showing the capability of systematically relaxing constraints to convert an isolated trap into a level set or saddle feature on the landscape, thereby opening up the ability to find new solutions including those of higher fidelity. The results indicate the richness and complexity of the constrained quantum control landscape upon considering the tradeoff between resources and freedom to move on the landscape.