Systematic Investigations of Novel Quantum Control Landscapes

Abstract

The control of chemical phenomena through interactions with electromagnetic field pulses lends itself to applications from selective bond breaking to quantum computing. The conflation of advances in pulse generation, pulse shaping, and computer search algorithms has led to an impressive number of quantum control experiments. The surprising ease with which pulses can be identified to produce excellent control is attributed to not only technological improvements but also favorable trap-free topology of underlying quantum control landscapes, which functionally relate physical objectives to control variables. This dissertation explores three classes of novel quantum control landscapes.

While the number of successful quantum control experiments continues to grow, experiments are subject to constraints on the control variables. This dissertation studies the effects of constraints on achieving optimal control by systematically placing restrictions on control variables and exploring the resulting local landscape topology. When free landscape traversal is prohibited due to the imposition of constraints, suboptimal traps or saddles may be encountered. This dissertation presents mathematical tools to explore the local landscape near these constraint-induced topological features. The tools are capable of differentiating traps that exist as isolated points from those that reside on a manifold of suboptimal solutions. A practical methodology is developed to favorably alter local topology at a suboptimal critical point by systematically relaxing control constraints.

Quantum control experiments and landscape studies typically utilize control variables arising from electromagnetic field pulses. In such a setup, the quantum system is treated as fixed. However, one may consider allowing access to the molecular `stockroom', where a quantum system's Hamiltonian is treated as the control and the applied pulse is fixed. Hamiltonian structure control presents a unique avenue for molecular control, and this dissertation explores the Hamiltonian structure landscape.

Accurate prediction of quantum system dynamics requires knowledge of the system's Hamiltonian. The search for a Hamiltonian that reproduces experimental data occurs on an inversion landscape, which this dissertation investigates using data obtained through simulated quantum control experiments. Local convexity about the true Hamiltonian is observed even when significant noise is incorporated, and Hamiltonians can be identified with the use of a simple gradient-based search algorithm.