  We present a quantum algorithm for computing the Ramsey numbers whose
computational complexity grows super-exponentially with the number of vertices
of a graph on a classical computer. The problem is mapped to a decision problem
on a quantum computer, a probe qubit is coupled to a register that represents
the problem and detects the energy levels of the problem Hamiltonian. The
decision problem is solved by determining whether the probe qubit exhibits
resonance dynamics. The algorithm shows a quadratic speedup over its classical
counterparts, and the degenerate ground state problem in the adiabatic quantum
evolution algorithm for this problem is avoided.
