Graph neural network initialisation of quantum approximate optimisation

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 Max-Cut problem. Specifically, we address two problems in the QAOA, how to select initial parameters, and how to subsequently train the parameters to find an optimal solution. For the former, we propose graph neural networks (GNNs) as an initialisation routine for the QAOA parameters, adding to the literature on warm-starting techniques. We show the GNN approach generalises across not only graph instances, but also to increasing graph sizes, a feature not available to other warm-starting techniques. For training the QAOA, we test several optimisers for the MaxCut problem. These include quantum aware/agnostic optimisers proposed in literature and we also incorporate machine learning techniques such as reinforcement and meta-learning. With the incorporation of these initialisation and optimisation toolkits, we demonstrate how the QAOA can be trained as an end-to-end differentiable pipeline