Recent experimental progress has resulted in the development of mid-sized noisy quantum processors that realize short sequences of quantum gates which create quantum algorithms. Driven by utilitarian means, a merger of machine learning and quantum computation has rapidly developed to use these new processors. This new approach is known as the variational model of quantum computation, and relies on outer loop classical optimization to adjust or train the quantum gate sequence to minimize an objective function. While proven to be a universal model of quantum computation in theory, much remains unknown about the variational model and the power of noisy quantum processors in practice. Building on a merger between condensed matter and theoretical computer science, mathematical physics we’ll provide our setting to explore the variational model.