Classical communication network design via quantum heuristics

We consider a network design problem in which one must choose which hubs in a classical communication network to build so as to optimally trade off between the long-term average value derived from the links between hubs and the long-term average cost of maintaining each hub. The optimization is naturally formulated as a 0–1 quadratic programming problem, a non-convex optimization with binary decision variables. This problem is NP-Hard, and has no known polynomial-time approximation scheme (PTAS) for the general case. We explore the performance of quantum annealing on this problem, using a D-Wave quantum processing unit (QPU), and compare performance to exact and simulated annealing solvers running on a modern classical computer. We discuss the relative strengths and weaknesses of these methods. In particular, we focus on the quality of the solutions as well as the computation time associated with each method.