Graph coloring with a distributed hybrid quantum annealing algorithm

Abstract

Quantum simulated annealing is analogous to a population of agents cooperating to optimize a shared cost function defined as the total energy between them. A hybridization of quantum annealing with mainstream evolutionary techniques is introduced to obtain an effective solver for the graph coloring problem. The state of the art is advanced by the description of a highly scalable distributed version of the algorithm. Most practical simulated annealing algorithms require the reduction of a control parameter over time to achieve convergence. The algorithm presented is able to keep all its parameters fixed at their initial value throughout the annealing schedule, and still achieve convergence to a global optimum in reasonable time. Competitive results are obtained on challenging problems from the standard DIMACS benchmarks. Furthermore, for some of the graphs, the distributed hybrid quantum annealing algorithm finds better results than those of any known algorithm. © 2011 Springer-Verlag.