  Ramsey theory is an active research area in combinatorics whose central theme
is the emergence of order in large disordered structures, with Ramsey numbers
marking the threshold at which this order first appears. For generalized Ramsey
numbers $r(G,H)$, the emergent order is characterized by graphs $G$ and $H$. In
this paper we: (i) present a quantum algorithm for computing generalized Ramsey
numbers by reformulating the computation as a combinatorial optimization
problem which is solved using adiabatic quantum optimization; and (ii)
determine the Ramsey numbers $r(\mathcal{T}_{m},\mathcal{T}_{n})$ for trees of
order $m,n = 6,7,8$, most of which were previously unknown.
