This article covers quantum computing from the angle of adiabatic quantum computing [7,13], which has proven to have the shortest horizon to real-world applications, partly due to a slightly easier path to development2 than alternative approaches such as gate-model quantum computers. In this article we cover background on quantum annealing computing generally, the canonical problem formulation necessary to program the D-Wave quantum processing unit (QPU), and discuss how such a problem is compiled onto the QPU. We also cover recent joint work solving a problem from topological data analysis on the DWave quantum computer. The goal of the article is to cover the above from a mathematical viewpoint, accessible to a wide range of levels, and introduce as many people as possible to a small portion of the mathematics encountered in this industry.