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The Quantum Approximate Optimization Algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization problems whose performance can only improve with the number of layers $p$.
“Computational Hardness of Certifying Bounds on Constrained PCA Problems”
Afonso S. Bandeira, Dmitriy Kunisky, and Alexander S. Wein · 1902
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“The overlap gap property and approximate message passing algorithms for p p -spin models”
David Gamarnik and Aukosh Jagannath · 1911
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“Infinite number of order parameters for spin-glasses”
G. Parisi · 1979
Earlier work this paper cites.
“Some rigorous results on the Sherrington-Kirkpatrick spin glass model”
Michael Aizenman, Joel Lebowitz, and D. Ruelle · 1987
Earlier work this paper cites.
“Analysis of the ∞ \infty -replica symmetry breaking solution of the Sherrington-Kirkpatrick model”
A. Crisanti and T. Rizzo · 2002
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“Replica Symmetry Breaking at Low Temperatures”
Manuel J. Schmidt · 2008
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“Algorithmic Thresholds in Mean Field Spin Glasses” (2020)
Ahmed El Alaoui and Andrea Montanari · 2009
Earlier work this paper cites.
“The Sherrington-Kirkpatrick model”
Dmitry Panchenko · 2013
Cited alongside, same era.
“A Quantum Approximate Optimization Algorithm” (2014)
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2014
Cited alongside, same era.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2015
Cited alongside, same era.
Cedric Yen-Yu Lin and Yechao Zhu · 2016
Cited alongside, same era.
“Semidefinite programs on sparse random graphs and their application to community detection”
Andrea Montanari and Subhabrata Sen · 2016
“Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem” (2018)
Gavin E. Crooks · 2018
Later among the works it cites.
“Barren plateaus in quantum neural network training landscapes”
Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, and Hartmut Neven · 2018
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“Optimization of the Sherrington-Kirkpatrick Hamiltonian”
A. Montanari · 2019
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“Suboptimality of local algorithms for a class of max-cut problems”
Wei Kuo Chen, David Gamarnik, Dmitry Panchenko, and Mustazee Rahman · 2019
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“Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices”
Leo Zhou, Sheng-Tao Wang, Soonwon Choi, Hannes Pichler, and Mikhail D. Lukin · 2020
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Cited alongside, same era.
Fernando G. S. L. Brandao, Michael Broughton, Edward Farhi, Sam Gutmann, and Hartmut Neven · 2018
Cited alongside, same era.
G. Parisi. Private communication
Cited in the paper.
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Joao Basso, Edward Farhi, Kunal Marwaha, Benjamin Villalonga, and Leo Zhou · 2022
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