  Branch-and-bound is a widely used technique for solving combinatorial
optimisation problems where one has access to two procedures: a branching
procedure that splits a set of potential solutions into subsets, and a cost
procedure that determines a lower bound on the cost of any solution in a given
subset. Here we describe a quantum algorithm that can accelerate classical
branch-and-bound algorithms near-quadratically in a very general setting. We
show that the quantum algorithm can find exact ground states for most instances
of the Sherrington-Kirkpatrick model in time $O(2^{0.226n})$, which is
substantially more efficient than Grover's algorithm.
