Optimal control theory has played an important role in many areas of science and engineering including aviation, 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 molecular bond to the application of a quantum logic gate. Emerging applications of quantum optimal control often involve complex, many-body quantum systems; capabilities for studying such control scenarios from a theoretical perspective are 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 which would require precise, accurate control. The goal of this thesis is to explore, develop, and implement methods to address them.
To this end, 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, where tracking control is utilized to design fields to control the orientation of rotating linear and symmetric top molecules in 2D and 3D. Following this, the problem of mixture characterization is considered, and to this end, a scalable, single-shot mixture characterization procedure based on tracking control principles is introduced.
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. 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.