# Quantum speedup of branch-and-bound algorithms

## TL;DR

This paper introduces a quantum algorithm that significantly accelerates classical branch-and-bound methods for combinatorial optimization, achieving near-quadratic speedup and efficiently solving complex models like the Sherrington-Kirkpatrick.

## Contribution

It presents a novel quantum algorithm that enhances branch-and-bound techniques, providing a near-quadratic speedup over classical approaches in a broad setting.

## Key findings

- Quantum algorithm achieves near-quadratic speedup.
- Efficiently finds ground states of the Sherrington-Kirkpatrick model.
- Outperforms Grover's algorithm in specific instances.

## Abstract

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.