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, "Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement", Physical Review A 107 6, 062404 (2023).

[2] Jiaqi Miao, Chang-Yu Hsieh, and Shi-Xin Zhang, "Neural-network-encoded variational quantum algorithms", Physical Review Applied 21 1, 014053 (2024).

[3] V. Vijendran, Aritra Das, Dax Enshan Koh, Syed M. Assad, and Ping Koy Lam, "An expressive ansatz for low-depth quantum approximate optimisation", Quantum Science and Technology 9 2, 025010 (2024).

[4] Samuel Duffield, Marcello Benedetti, and Matthias Rosenkranz, "Bayesian learning of parameterised quantum circuits", Machine Learning: Science and Technology 4 2, 025007 (2023).

[5] Lixue Cheng, Yu-Qin Chen, Shi-Xin Zhang, and Shengyu Zhang, "Quantum approximate optimization via learning-based adaptive optimization", Communications Physics 7 1, 83 (2024).

[6] Chae-Yeun Park and Nathan Killoran, "Hamiltonian variational ansatz without barren plateaus", Quantum 8, 1239 (2024).

[7] Brian Coyle, "Machine learning applications for noisy intermediate-scale quantum computers", arXiv:2205.09414, (2022).

[8] Ohad Amosy, Tamuz Danzig, Ely Porat, Gal Chechik, and Adi Makmal, "Iterative-Free Quantum Approximate Optimization Algorithm Using Neural Networks", arXiv:2208.09888, (2022).

[9] Linus Ekstrom, Hao Wang, and Sebastian Schmitt, "Variational Quantum Multi-Objective Optimization", arXiv:2312.14151, (2023).

[10] Slimane Thabet, Romain Fouilland, Mehdi Djellabi, Igor Sokolov, Sachin Kasture, Louis-Paul Henry, and Loïc Henriet, "Enhancing Graph Neural Networks with Quantum Computed Encodings", arXiv:2310.20519, (2023).

[11] Vivek Katial, Kate Smith-Miles, and Charles Hill, "On the Instance Dependence of Optimal Parameters for the Quantum Approximate Optimisation Algorithm: Insights via Instance Space Analysis", arXiv:2401.08142, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-05-25 02:15:15). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2024-05-25 02:15:14: Encountered the unhandled forward link type postedcontent_cite while looking for citations to DOI 10.22331/q-2022-11-17-861.