Graph neural network initialisation of quantum approximate optimisation
This work addresses optimization challenges in near-term quantum computing for combinatorial problems like MaxCut, offering incremental improvements in initialization and training methods.
The authors tackled the problem of initializing and training the Quantum Approximate Optimization Algorithm (QAOA) for the MaxCut problem by proposing graph neural networks (GNNs) as a warm-starting technique, which outperformed individual approaches and enabled generalization across graph instances and sizes, and they benchmarked various optimizers up to 16 qubits against vanilla gradient descent.
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.