Numerical and Algebraic Studies for the Control of Quantum Systems

The thesis explores the application of controllability and optimal control within quantum systems using group theoretical techniques and numerical studies. It reveals how symmetry limits full controllability and establishes guidelines for designing new control systems. The research optimizes quantum channel capacities through gradient flows, challenging a longstanding additivity conjecture. Additionally, it benchmarks the GRAPE modular optimal control algorithm against a Krotov-type algorithm, demonstrating GRAPE's superior performance in achieving high-quality outcomes.