Quantum computation (QC) is a novel way of information processing that allows, for certain classes of problems, exponential speedup over classical computation. Various frameworks of quantum computation exist, such as the circuit, adiabatic, and measurement-based models, but operate very differently and may suit different physical realizations. I will discuss some of these frameworks and a few selected results, such as universal resource using AKLT states in measurement-based QC (and the gap issue of 2D AKLT Hamiltonians) and algorithms for spectral projection that allow simulations of quantum annealing. I will also discuss tomographic tools in characterizing states, process and measurement, focusing on the so-called detector tomography, and present some results obtained from runs on IBM Q Experience. Characterization of detection allows us to mitigation imperfection detection.