  We present a classical algorithm to find approximate solutions to instances
of quadratic unconstrained binary optimisation. The algorithm can be seen as an
analogue of quantum annealing under the restriction of a product state space,
where the dynamical evolution in quantum annealing is replaced with a
gradient-descent based method. This formulation is able to quickly find
high-quality solutions to large-scale problem instances, and can naturally be
accelerated by dedicated hardware such as graphics processing units. We
benchmark our approach for large scale problem instances with tuneable hardness
and planted solutions. We find that our algorithm offers a similar performance
to current state of the art approaches within a comparably simple
gradient-based and non-stochastic setting.
