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Quantum annealing is a powerful tool for solving and approximatingcombinatorial optimization problems such as graph partitioning, communitydetection, centrality, routing problems, and more. In this paper we explore theuse of quantum annealing as a tool for use in exploring combinatorialmathematics research problems. We consider the monochromatic triangle problemand the Ramsey number problem, both examples of graph coloring. Conversion toquadratic unconstrained binary optimization (QUBO) form is required to run onquantum hardware. While the monochromatic triangle problem is quadratic bynature, the Ramsey number problem requires the use of order reduction methodsfor a quadratic formulation. We discuss implementations, limitations, andresults when running on the D-Wave Advantage quantum annealer.

Toward Computing Bounds for Ramsey Numbers Using Quantum Annealing