Experimental determination of Ramsey numbers

Abstract

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers $R(m,n)$. Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and $R(m,2)$ for $4\leq m\leq 8$. 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 adiabatic evolution algorithm that has been done to date.Comment: manuscript: 5 pages; 1 table, 3 figures; Supplementary Information: 18 pages, 1 table, 13 figures; version to appear in Physical Review Letter