  Approximate combinatorial optimisation has emerged as one of the most
promising application areas for quantum computers, particularly those in the
near term. In this work, we focus on the quantum approximate optimisation
algorithm (QAOA) for solving the MaxCut problem. Specifically, we address two
problems in the QAOA, how to initialise the algorithm, and how to subsequently
train the parameters to find an optimal solution. For the former, we propose
graph neural networks (GNNs) as a warm-starting technique for QAOA. We
demonstrate that merging GNNs with QAOA can outperform both approaches
individually. Furthermore, we demonstrate how graph neural networks enables
warm-start generalisation across not only graph instances, but also to
increasing graph sizes, a feature not straightforwardly available to other
warm-starting methods. For training the QAOA, we test several optimisers for
the MaxCut problem up to 16 qubits and benchmark against vanilla gradient
descent. These include quantum aware/agnostic and machine learning based/neural
optimisers. Examples of the latter include reinforcement and meta-learning.
With the incorporation of these initialisation and optimisation toolkits, we
demonstrate how the optimisation problems can be solved using QAOA in an
end-to-end differentiable pipeline.
