Despite knowing the fundamental equations in most of the physics research areas, still there is an unceasing need for theoretical method development, thanks to the more and more challenging problems addressed by the research community. The investigation of post-silicon, non-classical information processing is one of the new and rapidly developing areas that requires tremendous amount of theoretical support, new understanding, and accurate theoretical predictions. My thesis focuses on theoretical method development for solid-state quantum information processing, mainly in the field of point defect quantum bits (qubits) in silicon carbide (SiC) and diamond. Due to recent experimental breakthroughs in this field, there are diverse theoretical problems, ranging from functional development for accurate first principles description of point defects, through complete theoretical characterization of qubits, to the modeling and simulation of actual quantum information protocols, that are needed to be addressed. The included articles of this thesis cover the development of (i) hybrid-DFT+Vw approach for the first principles description of mixed correlated and uncorrelated systems, (ii) zero-field-splitting tensor calculation for solid-state quantum bit characterization, (iii) a comprehensive model for dynamic nuclear spin polarization of solid-state qubits in semiconductors, and (iv) group theoretical description of qubits and novel twodimensional materials for topologically protected states.