Quantum control landscape for a two-level system near the quantum speed limit

Abstract

The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expected value of some physical observable. The complexity of this procedure is given by the structural and topological features of the quantum control landscape (QCL) - i.e. the functional which maps the control field into a given value of the observable. In this work, we analyze the rich structure of the QCL in the paradigmatic Landau-Zener two-level model, and focus in particular on characterizing the QCL when the total evolution time is severely constrained. By studying several features of the optimized solutions, such as their abundance, spatial distribution and fidelities, we are able to rationalize several geometrical and topological aspects of the QCL of this simple model and identify the effects produced by different types of constraint.