Designing Quantum Controls Efficiently

Abstract

Optimal control theory has played an important role in many areas of science and engineering including aerospace, manufacturing, and chemical processing. More recently, these concepts have been applied to quantum systems, with the aim of determining the optimal controls to achieve a desired target, which can range from the breakage of a specific chemical bond to the application of a quantum logic gate. Emerging applications of quantum optimal control often involve complex quantum systems. To date, capabilities for studying these control problems from a theoretical perspective have been limited by two factors: (1) the high cost of iterative control field optimization, and (2) the prohibitive cost of simulating many-body quantum dynamics from first principles, a problem which is plagued by the so-called {curse of dimensionality}. These two issues present a significant challenge to the development of new quantum experiments and technologies that would require precise, accurate control. The goal of this thesis is to explore methods for addressing them. A means for addressing the iterative control field identification problem (1) is explored through a tracking control approach for faster control field identification without the need for iteration. Studies are presented that utilize tracking control to design fields to control the orientation of rotating linear and symmetric top molecules in 2D and 3D. In all cases considered, it is shown that the resulting fields are free of singularities. Following this, the problem of chemical mixture characterization is considered. In this setting, a scalable, single-shot mixture characterization procedure based on tracking control principles is introduced, which enables the sequential suppression of the optical responses of the chemical species in the mixture, enhancing their distinguishability. The resultant optical response data can then be used to infer the concentrations of the mixture constituents. Numerical illustrations are presented involving systems of diatomic molecules in the gas phase. The complexity of the many-body quantum dynamics problem (2) is first explored through the substitution of first-principles models by the lower cost Time-Dependent Hartree approximation, in order to scalably model the controlled dynamics of interacting molecular rotors in the weak dipole-dipole coupling regime. Following this, it is studied how (1) could alternatively be addressed by offloading the classically-difficult task of quantum dynamics simulation to a quantum computer, where it could be performed in polynomial time. To this end, a hybrid quantum-classical algorithm is developed for the task of computing quantum optimal control fields, and numerical illustrations are presented involving vibrational, rotational, and biological systems.