  The maximum-cut problem is one of the fundamental problems in combinatorial
optimization. With the advent of quantum computers, both the maximum-cut and
the equivalent quadratic unconstrained binary optimization problem have
experienced much interest in recent years.
  This article aims to advance the state of the art in the exact solution of
both problems -- by using mathematical programming techniques on digital
computers. The main focus lies on sparse problem instances, although also dense
ones can be solved. We enhance several algorithmic components such as reduction
techniques and cutting-plane separation algorithms, and combine them in an
exact branch-and-cut solver. Furthermore, we provide a parallel implementation.
The new solver is shown to significantly outperform existing state-of-the-art
software for sparse MaxCut and QUBO instances. Furthermore, we improve the best
known bounds for several instances from the 7th DIMACS Challenge and the QPLIB,
and solve some of them (for the first time) to optimality.
