Quantum control landscape analysis including its application in NMR experiments

Abstract

Scientists have attempted for decades to efficiently control the dynamics of quantum systems on the atomic and molecular scale with modulated electromagnetic fields, such as femtosecond laser pulses. The success of such experiments in achieving specified control objectives will rely on finding the optimal pulse shapes. The search for optimal solutions in such a high-dimensional control parameter space is usually accomplished by learning algorithms. The success of quantum optimal control in a wide range of applications motivated the analysis of the underlying control landscape, defined by the objective value as a functional of the control field, whose topology (e.g., local optima and saddle points) will dictate the ease of finding globally optimal control fields by iterative searches with gradient-based

algorithms. Based on some assumptions theoretical analysis revealed many topological properties of the landscapes, which are both experimentally assessed and theoretically developed in this dissertation.

The experimental works focus on the landscapes in controlling nuclear spins by pulsed magnetic fields, with nuclear magnetic resonance (NMR) spectroscopy as a testbed. We choose this type of experimental settings because of its desirable physical properties and potential application in realizing quantum computation. A set of methodology for control

landscape studies in NMR systems is constructed, leading to the first observation of landscape saddles in the laboratory. The dissertation also discusses a variety of theoretical topics about the control landscape in general, including (i) measuring “distances” from the landscape saddle points and driving to locate them; (ii) simultaneous optimization of multiple

control objectives in the same quantum system; and (iii) generalizing the landscape concept from the semiclassical setting to the full quantum setting. All these works aim to further enrich and develop the landscape theory in quantum optimal control, and apply it to physical systems with practical importance.