Quantum speedup of branch-and-bound algorithms

06/25/2019

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by   Ashley Montanaro, et al.

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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.