Experimental determination of Ramsey numbers with quantum annealing

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. It has found applications in mathematics, theoretical computer science, information theory, and classical error correcting codes. Ramsey numbers mark the threshold at which order first appears and are notoriously difficult to calculate due to their explosive rate of growth. Recently, a quantum algorithm has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm based on quantum annealing and show that it correctly determines the Ramsey numbers R(3, 3) and R(m, 2) for 4 ≤ m ≤ 8. The R(8, 2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful quantum algorithm that has been done to date.