Ramsey numbers and adiabatic quantum computing

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, only nine Ramsey numbers are currently known, with knowledge of other Ramsey numbers limited to bounds on their possible value. We describe a quantum algorithm for the computation of Ramsey numbers. We show how the problem of computing a Ramsey number can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution (AQE). We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for s $\leq$ 6. We also discuss experimental implementation of an adiabatic quantum computation of R(3,3).