Classical computation over quantum architectures

Abstract The lack of purely Quantum Programming Languages constitutes a hurdle in the general description of quantum computational processes; the implementation is heavily dependent on the considered quantum computational model. To bypass the obstacle, this paper pursues a new direction, investigating the compilation of classical programming paradigms over different quantum computational models: Gate-Based, Measurement-Based and Adiabatic Quantum Computation. Since graphs can be exploited to describe both classical and quantum computations, the problem of graph encoding on quantum hardware is tightly connected to our purposes. As such, it holds a major relevance in our quest for quantum compilation. While studying these topics through the lenses of Graph Theory, declarative programming emerges as the ideal candidate for such endeavour. In this paper we consider some existing quantum computational models and for each of them we identify the main subtleties in the compilation of classical languages. In turn, we break these complexities down into easier problems to stimulate further developments in this area of research. As it turns out, the observations for each model differ widely. Nevertheless, as for the tasks here considered, no model seems to claim supremacy over the others. In contrast, declarative programming maintains the spot as the ideal candidate for quantum compilation, independently of the model.