Optimization and application of the quantum adiabatic theorem, and the quantum origin of classical interference

Abstract

In this master’s thesis, we developed three different topics. In the first topic, we studied the quantum adiabatic brachistochrone method (QAB) for optimizing adiabatic dynamics. In the first part of this study, we reported the investigation of the charging and discharging processes of a transmon superconducting three-level quantum battery. The charging process was enhanced using the QAB method, in which we analyzed the effect of constraining the interpolation functions. We completed the battery study by showing that its self-discharging process, which is how the device loses its charge to the environment, is non- Ohmic. Furthermore, we considered the application of the QAB method to the adiabatic Grover algorithm for times when there are limited resources for its execution, for instance when there is a limit on the maximum power of the external fields or in the available total energy. The second part is concerned with the theory of the D-Wave’s quantum annealer and its limitations, as the lack of global connections between the qubits. For evaluating the state-of-the-art of this quantum simulator, we solved the traveling salesman problem on it. Moreover, we did a literature review about problems this processor can handle and different strategies to avoid its limitations. Finally, in the third topic, we proved that describing light-matter interaction using quantum fluctuations yields ambiguities for multi-modes of light. We showed that classical interference emerges in quantum optics due to collective bright and dark states of light. In a multi-mode case, the criterion for a ground-state atom to be excited is the existence of a projection on non-dark states rather than quantum fluctuations.