Toward Computing Bounds for Ramsey Numbers Using Quantum Annealing

Abstract

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum annealing as a tool for use in exploring combinatorial mathematics research problems. We consider the monochromatic triangle problem and the Ramsey number problem, both examples of graph coloring. Conversion to quadratic unconstrained binary optimization (QUBO) form is required to run on quantum hardware. While the monochromatic triangle problem is quadratic by nature, the Ramsey number problem requires the use of order reduction methods for a quadratic formulation. We discuss implementations, limitations, and results when running on the D-Wave Advantage quantum annealer.