In this talk I will introducing the most basic concepts in quantum computing and describe one type of quantum computing hardware (a transmon) and how it is modeled. We will then outline the computationally challenging tasks that are needed for making a quantum computer run and introduce numerical methods tailored especially for these tasks. Time permitting I will take you on a comprehensive journey through a real-world example involving characterization, control, and experimental validation, showcasing our experiences with a qutrit device within the Lawrence Livermore QUDIT testbed.