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Quantum algorithms have been widely studied in the context of combinatorial optimization problems.
M. Halldórsson and J. Radhakrishnan, Greed is good: Approximating independent sets in sparse and bounded-degree graphs, in Proceedings of the twenty-sixth annual ACM symposium on Theory of computing (1994) pp. 439–448
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T. Kadowaki and H. Nishimori, Quantum annealing in the transverse ising model, Physical Review E 58
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P. K. Agarwal, M. Van Kreveld, and S. Suri, Label placement by maximum independent set in rectangles, Computational Geometry 11
1998
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E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, Quantum computation by adiabatic evolution, arxiv (2000) , arXiv:quant-ph/0001106 [quant-ph]
2000
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S. Butenko, Maximum independent set and related problems, with applications (University of Florida, 2003)
2003
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S. Sakai, M. Togasaki, and K. Yamazaki, A note on greedy algorithms for the maximum weighted independent set problem, Discrete Applied Mathematics 126
2003
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2005
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C. Bazgan, B. Escoffier, and V. T. Paschos, Completeness in standard and differential approximation classes: Poly-(D) APX-and (D) PTAS-completeness, Theoretical Computer Science 339
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A. Vahdatpour, F. Dabiri, M. Moazeni, and M. Sarrafzadeh, Theoretical bound and practical analysis of connected dominating set in ad hoc and sensor networks, in Distributed Computing: 22nd International Symposium, DISC 2008, Arcachon, France, September 22-24, 2008. Proceedings 22 (Springer, 2008) pp. 481–495
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2011
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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and approximation: Combinatorial optimization problems and their approximability properties (Springer Science & Business Media, 2012)
2012
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E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm (2014)
2014
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A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, A variational eigenvalue solver on a photonic quantum processor, Nature Communications 5
2014
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While, as we have seen, the lowest depth quantum expectation values can be efficiently computed classically, efficient classical sampling from said circuits is not believed to be possible Farhi et al. 2014 ; Farhi and Harrow 2016 which hints at further possibilities for quantum advantage in practice
2016
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2016
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Approaches for MIS not directly related to QAOA have also been proposed such as Ref. Yu et al. 2021 ; Djidjev et al. 2018
2018
Earlier work this paper cites.
Z. Wang, S. Hadfield, Z. Jiang, and E. G. Rieffel, Quantum approximate optimization algorithm for maxcut: A fermionic view, Physical Review A 97
2018
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S. A. Hadfield, Quantum algorithms for scientific computing and approximate optimization (Columbia University, 2018)
2018
Cited alongside, same era.
T. Albash and D. A. Lidar, Adiabatic quantum computation, Reviews of Modern Physics 90
2018
Cited alongside, same era.
2018
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S. Hadfield, Z. Wang, B. O’Gorman, E. G. Rieffel, D. Venturelli, and R. Biswas, From the quantum approximate optimization algorithm to a quantum alternating operator ansatz, Algorithms 12
2019
Cited alongside, same era.
Z. H. Saleem, Max-independent set and the quantum alternating operator ansatz, International Journal of Quantum Information 18
2020
2022
Later among the works it cites.
R. Ayanzadeh, J. Dorband, M. Halem, and T. Finin, Quantum-assisted greedy algorithms, in IGARSS 2022-2022 IEEE International Geoscience and Remote Sensing Symposium (IEEE, 2022) pp. 4911–4914
2022
Later among the works it cites.
M. J. Schuetz, J. K. Brubaker, and H. G. Katzgraber, Combinatorial optimization with physics-inspired graph neural networks, Nature Machine Intelligence 4
2022
Later among the works it cites.
A. Ozaeta, W. van Dam, and P. L. McMahon, Expectation values from the single-layer quantum approximate optimization algorithm on Ising problems, Quantum Science and Technology 7
2022
Later among the works it cites.
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Cited alongside, same era.
M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al. , Variational quantum algorithms, Nature Reviews Physics 3
2021
Cited alongside, same era.
L. Bittel and M. Kliesch, Training variational quantum algorithms is NP-hard, Physical Review Letters 127
2021
Cited alongside, same era.
D. S. Wild, D. Sels, H. Pichler, C. Zanoci, and M. D. Lukin, Quantum sampling algorithms for near-term devices, Physical Review Letters 127
2021
Cited alongside, same era.
2021
Cited alongside, same era.
2021
Cited alongside, same era.
H. Yu, F. Wilczek, and B. Wu, Quantum algorithm for approximating maximum independent sets, Chinese Physics Letters 38
2021
Cited alongside, same era.
K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, et al. , Noisy intermediate-scale quantum algorithms, Reviews of Modern Physics 94
2022
Cited alongside, same era.
2022
Later among the works it cites.
S. Hadfield, T. Hogg, and E. G. Rieffel, Analytical framework for quantum alternating operator ansätze, Quantum Science and Technology 8
2022
Later among the works it cites.
2022
Later among the works it cites.
2023
Closest in time.
Z. H. Saleem, T. Tomesh, B. Tariq, and M. Suchara, Approaches to constrained quantum approximate optimization, SN Computer Science 4
2023
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M.-T. Nguyen, J.-G. Liu, J. Wurtz, M. D. Lukin, S.-T. Wang, and H. Pichler, Quantum optimization with arbitrary connectivity using rydberg atom arrays, PRX Quantum 4
2023
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M. Lanthaler, C. Dlaska, K. Ender, and W. Lechner, Rydberg-blockade-based parity quantum optimization, Physical Review Letters 130
2023
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2023
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M. C. Angelini and F. Ricci-Tersenghi, Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent set, Nature Machine Intelligence 5
2023
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M. J. Schuetz, J. K. Brubaker, and H. G. Katzgraber, Reply to: Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent set, Nature Machine Intelligence 5
2023
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2023
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