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Challenges and opportunities in quantum optimization
Abbas,Amira Ambainis,Andris Augustino,Brandon Baertschi,Andreas Buhrman,Harry Coffrin,Carleton Cortiana,Giorgio Dunjko,Vedran Egger,Daniel J. Elmegreen,Bruce G.
Abbas,Amira
Ambainis,Andris
Augustino,Brandon
Baertschi,Andreas
Buhrman,Harry
Coffrin,Carleton
Cortiana,Giorgio
Dunjko,Vedran
Egger,Daniel J.
Elmegreen,Bruce G.
Abstract
Quantum computers have demonstrable ability to solve problems at a scale beyond brute-force classical simulation. Interest in quantum algorithms has developed in many areas, particularly in relation to mathematical optimization - a broad field with links to computer science and physics. In this Review, we aim to give an overview of quantum optimization. Provably exact, provably approximate and heuristic settings are first explained using computational complexity theory, and we highlight where quantum advantage is possible in each context. Then, we outline the core building blocks for quantum optimization algorithms, define prominent problem classes and identify key open questions that should be addressed to advance the field. We underscore the importance of benchmarking by proposing clear metrics alongside suitable optimization problems, for appropriate comparisons with classical optimization techniques, and discuss next steps to accelerate progress towards quantum advantage in optimization.
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Publisher Copyright: © IBM, under exclusive licence to Springer Nature Limited 2024..
Date
2024-12
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s42254-024-00770-9.pdf
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Approximation algorithms, Computational-complexity, Traveling salesman, Simulations, Relaxation, Binary, Set, Cut
Citation
Abbas, A, Ambainis, A, Augustino, B, Baertschi, A, Buhrman, H, Coffrin, C, Cortiana, G, Dunjko, V, Egger, D J, Elmegreen, B G, Franco, N, Fratini, F, Fuller, B, Gacon, J, Gonciulea, C, Gribling, S, Gupta, S, Hadfield, S, Heese, R, Kircher, G, Kleinert, T, Koch, T, Korpas, G, Lenk, S, Marecek, J, Markov, V, Mazzola, G, Mensa, S, Mohseni, N, Nannicini, G, O'Meara, C, Tapia, E P, Pokutta, S, Proissl, M, Rebentrost, P, Sahin, E, Symons, B C B, Tornow, S, Valls, V, Woerner, S, Wolf-Bauwens, M L, Yard, J, Yarkoni, S, Zechiel, D, Zhuk, S & Zoufal, C 2024, 'Challenges and opportunities in quantum optimization', Nature Reviews Physics, vol. 6, no. 12, pp. 718-735. https://doi.org/10.1038/s42254-024-00770-9