Graph neural network initialisation of quantum approximate optimisation

TL;DR

This paper introduces a novel approach combining graph neural networks with the quantum approximate optimisation algorithm to improve initialisation and training for MaxCut problems, demonstrating enhanced performance and generalisation.

Contribution

It proposes using GNNs as a warm-start for QAOA, enabling better initialisation and transferability across graph sizes, and benchmarks various optimisers for QAOA training.

Findings

GNNs outperform traditional initialisation methods for QAOA.

GNN-based warm-start generalises across graph instances and sizes.

Meta-learning and reinforcement learning optimisers improve QAOA training.

Abstract

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.