Quantum Optimal Control: Landscape Structure and Topology

Understand

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 expectation of value of some physical observable.

• The functional which maps the control field into a given value of the observable defines a Quantum Control Landscape (QCL).
• Studying the topological and structural features of these landscapes is of critical importance for understanding the process of finding the optimal fields required to effectively control the system, specially when external constraints are placed on both the field $\epsilon(t)$ and the available control duration $T$.
• In this work we analyze the rich structure of the $QCL$ of the paradigmatic Landau-Zener two-level model, studying several features of the optimized solutions, such as their abundance, spatial distribution and fidelities.