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The quantum approximate optimization algorithm, also known in its generalization as the quantum alternating operator ansatz, (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to combinatorial optimization problems, such as maximum satisfiability.
“Optimizing QAOA: Success Probability and Runtime Dependence on Circuit Depth” (2019)
Murphy Yuezhen Niu, Sirui Lu, and Isaac L. Chuang · 1905
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“Beweis des Adiabatensatzes”
M. Born and V. Fock · 1928
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“A fast quantum mechanical algorithm for database search”
Lov K. Grover · 1996
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“Strengths and Weaknesses of Quantum Computing”
Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani · 1997
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“Quantum annealing in the transverse Ising model”
Tadashi Kadowaki and Hidetoshi Nishimori · 1998
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“A Quantum Algorithm for Finding the Minimum” (1999)
Christoph Durr and Peter Hoyer · 1999
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“Grover’s quantum searching algorithm is optimal”
Christof Zalka · 1999
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“Quantum lower bounds by polynomials”
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf · 2001
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“Quantum amplitude amplification and estimation”
Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp · 2002
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“Adiabatic Population Transfer with Control Fields”
Mustafa Demirplak and Stuart A. Rice · 2003
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“The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case” (2020)
Edward Farhi, David Gamarnik, and Sam Gutmann · 2004
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“Spatial search by quantum walk”
Andrew M. Childs and Jeffrey Goldstone · 2004
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Edward Farhi, David Gamarnik, and Sam Gutmann · 2005
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“Transitionless quantum driving”
M V Berry · 2009
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“Matrix Analysis”
Roger A. Horn and Charles R. Johnson · 2012
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“Shortcuts to adiabaticity by counterdiabatic driving”
Adolfo del Campo · 2013
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“A Quantum Approximate Optimization Algorithm” (2014)
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2014
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“Ising formulations of many NP problems”
Andrew Lucas · 2014
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“The Need for Structure in Quantum Speedups”
Scott Aaronson and Andris Ambainis · 2014
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Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2015
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“Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle”
Zhi-Cheng Yang, Armin Rahmani, Alireza Shabani, Hartmut Neven, and Claudio Chamon · 2017
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“Extremal eigenvalues of local Hamiltonians”
Aram W. Harrow and Ashley Montanaro · 2017
Cited alongside, same era.
“Near-optimal quantum circuit for Grover’s unstructured search using a transverse field”
Zhang Jiang, Eleanor G. Rieffel, and Zhihui Wang · 2017
Cited alongside, same era.
“From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz”
Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor G. Rieffel, Davide Venturelli, and Rupak Biswas · 2019
Cited alongside, same era.
“Shortcuts to adiabaticity: Concepts, methods, and applications”
D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga · 2019
Cited alongside, same era.
“A quantum walk-assisted approximate algorithm for bounded NP optimisation problems”
S. Marsh and J. B. Wang · 2019
Cited alongside, same era.
“Reachability Deficits in Quantum Approximate Optimization”
“Solving boolean satisfiability problems with the quantum approximate optimization algorithm” (2022)
Sami Boulebnane and Ashley Montanaro · 2022
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“Circuit depth scaling for quantum approximate optimization”
V. Akshay, H. Philathong, E. Campos, D. Rabinovich, I. Zacharov, Xiao-Ming Zhang, and J. D. Biamonte · 2022
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“Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models”
Joao Basso, David Gamarnik, Song Mei, and Leo Zhou · 2022
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“The QAOA gets stuck starting from a good classical string” (2022)
Madelyn Cain, Edward Farhi, Sam Gutmann, Daniel Ranard, and Eugene Tang · 2022
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“Counterdiabaticity and the quantum approximate optimization algorithm”
Jonathan Wurtz and Peter J. Love · 2022
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V. Akshay, H. Philathong, M. E. S. Morales, and J. D. Biamonte · 2020
Cited alongside, same era.
“Ultrafast critical ground state preparation via bang–bang protocols”
Luca Innocenti, Gabriele De Chiara, Mauro Paternostro, and Ricardo Puebla · 2020
Cited alongside, same era.
“Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation”
Andreas Bärtschi and Stephan Eidenbenz · 2020
Cited alongside, same era.
“Subdivided Phase Oracle for NISQ Search Algorithms”
Takahiko Satoh, Yasuhiro Ohkura, and Rodney Van Meter · 2020
Cited alongside, same era.
“Combinatorial optimization via highly efficient quantum walks”
S. Marsh and J. B. Wang · 2020
Cited alongside, same era.
“Polynomial scaling of the quantum approximate optimization algorithm for ground-state preparation of the fully connected p p -spin ferromagnet in a transverse field”
Matteo M. Wauters, Glen B. Mbeng, and Giuseppe E. Santoro · 2020
Cited alongside, same era.
“Grover Adaptive Search for Constrained Polynomial Binary Optimization”
Austin Gilliam, Stefan Woerner, and Constantin Gonciulea · 2021
Cited alongside, same era.
Later among the works it cites.
“Amplitude Amplification for Optimization via Subdivided Phase Oracle”
Naphan Benchasattabuse, Takahiko Satoh, Michal Hajdušek, and Rodney Van Meter · 2022
Later among the works it cites.
“Gaussian Amplitude Amplification for Quantum Pathfinding”
Daniel Koch, Massimiliano Cutugno, Samuel Karlson, Saahil Patel, Laura Wessing, and Paul M. Alsing · 2022
Later among the works it cites.
“Quadratic Speedup for Spatial Search by Continuous-Time Quantum Walk”
Simon Apers, Shantanav Chakraborty, Leonardo Novo, and Jérémie Roland · 2022
Later among the works it cites.
John Golden, Andreas Bärtschi, Stephan Eidenbenz, and Daniel O’Malley · 2023
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“The Quantum Alternating Operator Ansatz for Satisfiability Problems” (2023)
John Golden, Andreas Bärtschi, Daniel O’Malley, and Stephan Eidenbenz · 2023
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“Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations”
Anurag Anshu and Tony Metger · 2023
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“Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement”
Stefan H. Sack, Raimel A. Medina, Richard Kueng, and Maksym Serbyn · 2023
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Zichang He, Ruslan Shaydulin, Shouvanik Chakrabarti, Dylan Herman, Changhao Li, Yue Sun, and Marco Pistoia · 2023
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“Lower Bounds on Quantum Annealing Times”
Luis Pedro García-Pintos, Lucas T. Brady, Jacob Bringewatt, and Yi-Kai Liu · 2023
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“Variational Amplitude Amplification for Solving QUBO Problems” (2023)
Daniel Koch, Massimiliano Cutugno, Saahil Patel, Laura Wessing, and Paul M. Alsing · 2023
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“Optimizing the depth of variational quantum algorithms is strongly QCMA-hard to approximate” (2023)
Lennart Bittel, Sevag Gharibian, and Martin Kliesch · 2023
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“On eigenvalue singular value and norms of a real skew-symmetric matrix”
Ahmet İpek · 2023
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“Problem-size-independent angles for a Grover-driven quantum approximate optimization algorithm”
David Headley and Frank K. Wilhelm · 2023
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“Design of Heuristic Algorithms for Hard Optimization: With Python Codes for the Travelling Salesman Problem”
Éric D. Taillard · 2023
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“Analytical framework for quantum alternating operator ansätze”
Stuart Hadfield, Tad Hogg, and Eleanor G Rieffel · 2023
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