Method for applying adaptive control theory to quantum systems

Control in quantum systems is proving to be one of the top challenges in the computing world as scalability of qubits in quantum computers increase. This thesis has focused on understanding quantum control methods and contribute further understanding to progress this very important step in advancing computers. By applying principles from adaptive and Lyapunov-based control to the effect on particle states within a closed quantum system as defined by the Schrödinger equation, it will be possible to see the precise boundaries of creating various control laws as states change over time. The benefits for these methods will be used in trajectory tracking and state targeting as applied to Schrödinger’s time dependent equation and simulated with pre-defined evolving Hamiltonian eigenstates to create reference and error control between target and system states. The analysis of this closed quantum system will be useful in applying similar methods in more tedious, externally influenced, open quantum systems