|M.Sc Student||Shalyt Michael|
|Subject||Control of a 2-Level System to Reduce Colored Noise|
|Department||Department of Physics||Supervisor||Professor Emeritus Joseph Avron|
|Full Thesis text|
Quantum computation is one of the most popular and rapidly expanding research topics in past two decades. The possibility of performing tasks that are believed to be unfeasible using classical computation made quantum information wide spread even in popular culture, and there are other - less widely known - applications of pure quantum systems. Unfortunately, experimental realization of a system capable performing even basic calculations is still far from reality. One of the main obstacles is the susceptability to unwanted interaction with the environment (noise) of any quantum system (especially if it is large or for example should act as a measuring apparatus). This interaction causes information stored in the system to “leak” to its sorroundings, thus reducing the system quantum purity (creating decoherence). One possible method of battling this effect is dynamical decoupling (DD) - the use of a deterministic field (control) to act upon the quantum system and effectively reduce the effect of the environment. In the past 15 years dynamical decoupling has proven itself as one of the main methods for maintaining quantum coherence. The DD schemes became increasingly elaborate, the theoretical foundations strengthened and qubit lifetime extension by more than an order of magnitude was measured.
Our research focuses on DD schemes under an energy constraint - a limiting factor mostly ignored in the field until recently. Starting from fundamental principles and using a perturbative approach, we develop a geometric framework for studying a general control scheme for combating noise. We discuss higher perturbation orders - translating the problem to Feynman diagram calculation and proving convergence. We proceed to discuss several specific examples, notably showing entropy reversal. Next we show that decoherence minimization is ill defined without adding constraints and introduce a constraint on the total amount of energy applied to the system. We study the integro-differential equation for constrained optimal control and provide new insights. Using simple geometric and algebraic tools we derive an upper bound on the improvement (decoherence reduction) achievable by any DD scheme constrained by finite energy. We proceed to prove that for the case of square pulses a wide pulse is more efficient in decoupling the system from its environment than a sharp one - in contrast to most of the DD schemes used today. Finally, we show a few limits where a constant control field saturates the improvement bound, making it asymptotically optimal.