|Researchers||Saman Naseer, B.Sc. Honours Physics, University of the Punjab|
Contact me for a copy of the thesis.
The technique of nuclear magnetic resonance (NMR) makes use of various radio frequency pulses for the transference of the nuclear magnetization vector form one state to the other. In addition, one form of quantum information processing (QIP) utilizes NMR to implement unitary (and non-unitary) dynamics with the far-reaching goal of realizing computers that can surpass their classical counterparts. NMR based QIP, that is the focus of this dissertation, involves designing accurate unitary transformations of the spin state. The overlap of the theoretical and experimentally achieved values, called the fidelity, is an important parameter in the design of robust, accurate unitary transformations. Besides, the transformations need also be time optimal.
In this one year undergraduate research project we used gradient-based optimization methods for designing pulse sequences for NMR based QIP. These sequences implement unitary operations. The goal of the optimization was to achieve high fidelities. Specially, we used gradient ascent pulse engineering (GRAPE) as the optimization paradigm.
An introduction to the basics of NMR is given in Chapter 1. Chapter 2 covers basic gradient-based optimization techniques and line search methods, especially the methods that are relevant to the present work. The next two chapters cover the formulation and implementation of the GRAPE algorithm. We have used the GRAPE algorithm along with line search to engineer pulse sequences for state-to-state transfer as well as the more general problem of unitary transformation design. We study the role of algorithmic parameters in quantum fidelity maximization, the number of steps required to achieve maximal fidelity and the robustness of the algorithm with respect to the choice of initial controls. We determine that the algorithm also returns results that are known to be optimal from the analytical perspective. This work helps us in understanding better the modus operandi of the GRAPE algorithm itself. Last, the present work also includes the design of pulse sequences that are robust against pulse width errors.