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Graph neural network initialisation of quantum approximate optimisation


Nishant Jain1, Brian Coyle2, Elham Kashefi2,3, and Niraj Kumar2

1Indian Institute of Technology, Roorkee, India.
2School of Informatics, University of Edinburgh, EH8 9AB Edinburgh, United Kingdom.
3LIP6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France.

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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.

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Cited by

[1] Stefan H. Sack, Raimel A. Medina, Richard Kueng, and Maksym Serbyn, “Transition states and greedy exploration of the QAOA optimization landscape”, arXiv:2209.01159.

[2] Samuel Duffield, Marcello Benedetti, and Matthias Rosenkranz, “Bayesian Learning of Parameterised Quantum Circuits”, arXiv:2206.07559.

[3] Brian Coyle, “Machine learning applications for noisy intermediate-scale quantum computers”, arXiv:2205.09414.

[4] Ohad Amosy, Tamuz Danzig, Ely Porat, Gal Chechik, and Adi Makmal, “Iterative-Free Quantum Approximate Optimization Algorithm Using Neural Networks”, arXiv:2208.09888.

[5] Ioannis Kolotouros, Ioannis Petrongonas, and Petros Wallden, “Adiabatic quantum computing with parameterized quantum circuits”, arXiv:2206.04373.

The above citations are from SAO/NASA ADS (last updated successfully 2022-11-18 02:57:39). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2022-11-18 02:57:38).


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