Quantum annealing of the graph coloring problem

Quantum annealing extends simulated annealing by introducing artificial quantum fluctuations. The path-integral Monte Carlo version chosen is population-based and designed to be implemented on a classical computer. Its first application to the graph coloring problem is presented in this paper. It is shown by experiments that quantum annealing can outperform classical thermal simulated annealing for this particular problem. Moreover, quantum annealing proved competitive when compared with the best algorithms on most of the difficult instances from the DIMACS benchmarks. The quantum annealing algorithm has even found that the well-known benchmark graph dsjc1000.9 has a chromatic number of at most 222. This is an improvement on its best upper-bound from a large body of literature.