Exploring Quantum Control Landscapes

Abstract

Recent developments in the fields of ultrashort pulse generation, frequency-based pulse shaping techniques, and evolutionary machine learning algorithms have made it possible to control chemical phenomena at the molecular scale. The unexpected ease of finding successful controls in the laboratory has been ascribed to the favorable topology and structure of the control landscape, which is the physical observable defined as a function of the control variables.

In this regard, a set of so called D-MORPH homotopy algorithms for landscape explorations are presented within this work. The first-order D-MORPH algorithm explores control level sets that exist away from the landscape top and bottom. The algorithm also has the ability to climb to the landscape top in order to identify controls producing perfect yields. The second-order D-MORPH algorithm operates to explore the level sets at the landscape top and bottom, which is especially important as these locations have particular physical relevance -- the top is the most desired location while at the bottom the goal is to climb away as rapidly as possible. At the top, an attractive control is one that consistently produces high yields even in the presence of some degree of noise. This work shows that a robustness criteria can be built into landscape explorations at the top in order to identify such controls. The Pareto D-MORPH algorithm is used to explore the trade-off between laser resources (e.g., bandwidth) and the ability to discriminate between similar systems. Within this work, the algorithm is geared toward detecting and differentiating between similar chemical species.

Finally, many sections of this work address the notion that chemical or material composition itself can be exploited as controls. From this perspective the goal of property optimization in chemistry or material science can be viewed in a control context, and Hamiltonian structure controls may be optimized by drawing on the chemical `stockroom'. The D-MORPH algorithms are extended to the case of dual controls (i.e., field and Hamiltonian structure together) and the freedom is shown to offer prospects for new and exciting control applications.