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There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization.
Fair dimensionality reduction and iterative rounding for SDPs
Jamie Morgenstern, Samira Samadi, Mohit Singh, Uthaipon Tantipongpipat, and Santosh Vempala · 1902
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Performance of a quantum annealer for Ising ground state computations on chimera graphs, 2019
Michael Juenger, Elisabeth Lobe, Petra Mutzel, Gerhard Reinelt, Franz Rendl, Giovanni Rinaldi, and Tobias Stollenwerk · 1904
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Classical and quantum bounded depth approximation algorithms, 2019
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Krivine diffusions attain the goemans–williamson approximation ratio
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Mahabubul Alam, Abdullah Ash-Saki, and Swaroop Ghosh · 1907
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A new polynomially solvable class of quadratic optimization problems with box constraints
Milan Hladík, Michal Černý, and Miroslav Rada · 1911
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Bas Lodewijks · 1911
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Can quantum-mechanical description of physical reality be considered complete?
Albert Einstein, Boris Podolsky, and Nathan Rosen · 1935
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Portfolio selection
Harry Markowitz · 1952
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Boolean methods in operations research and related areas
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P-complete approximation problems
Sartaj Sahni and Teofilo Gonzalez · 1976
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Quantum generalizations of Bell’s inequality
Boris S. Cirel’son · 1980
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A second course in stochastic processes
Samuel Karlin and Howard E. Taylor · 1981
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Randomized rounding: A technique for provably good algorithms and algorithmic proofs
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Checking local optimality in constrained quadratic programming is np-hard
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
Michel X. Goemans and David P. Williamson · 1995
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A recipe for semidefinite relaxation for (0, 1)-quadratic programming
Svatopluk Poljak, Franz Rendl, and Henry Wolkowicz · 1995
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On the complexity of semidefinite programs
Lorant Porkolab and Leonid Khachiyan · 1997
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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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Warm start of the primal-dual method applied in the cutting-plane scheme
Jacek Gondzio · 1998
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Probabilistic checking of proofs: A new characterization of np
Sanjeev Arora and Shmuel Safra · 1998
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Proof verification and the hardness of approximation problems
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy · 1998
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How good is the Goemans–Williamson MAX CUT algorithm?
Howard Karloff · 1999
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A polynomial case of unconstrained zero-one quadratic optimization
Kim Allemand, Komei Fukuda, Thomas M Liebling, and Erich Steiner · 2001
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Global optimization with polynomials and the problem of moments
Jean B. Lasserre · 2001
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Some optimal inapproximability results
Johan Håstad · 2001
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On the power of unique 2-prover 1-round games
Subhash Khot · 2002
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Maximizing quadratic programs: Extending Grothendieck’s inequality
Moses Charikar and Anthony Wirth · 2004
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Random MAX SAT, random MAX CUT, and their phase transitions
Don Coppersmith, David Gamarnik, Mohammad T. Hajiaghayi, and Gregory B. Sorkin · 2004
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Linghua Zhu, Ho Lun Tang, George S. Barron, Nicholas J. Mayhall, Edwin Barnes, and Sophia E. Economou · 2005
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Rigorous location of phase transitions in hard optimization problems
Dimitris Achlioptas, Assaf Naor, and Yuval Peres · 2005
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Solving nonlinear financial planning problems with 10 9 10^{9} decision variables on massively parallel architectures
Jacek Gondzio and Andreas Grothey · 2006
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Convergent SDP-relaxations in polynomial optimization with sparsity
Jean B. Lasserre · 2006
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Jason Larkin, Matías Jonsson, Daniel Justice, and Gian Giacomo Guerreschi · 2006
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Near-optimal algorithms for unique games
Moses Charikar, Konstantin Makarychev, and Yury Makarychev · 2006
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Optimal inapproximability results for MAX-CUT and other 2-variable CSPs?
Subhash Khot, Guy Kindler, Elchanan Mossel, and Ryan O’Donnell · 2007
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The unique games conjecture with entangled provers is false
Julia Kempe, Oded Regev, and Ben Toner · 2007
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Reachability deficits implicit in google’s quantum approximate optimization of graph problems, 2020b
Vishwanathan Akshay, Hariphan Philathong, Igor Zacharov, and Jacob D. Biamonte · 2007
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The PCP theorem by gap amplification
Irit Dinur · 2007
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Optimal algorithms and inapproximability results for every CSP?
Prasad Raghavendra · 2008
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Computational complexity: a modern approach
Sanjeev Arora and Boaz Barak · 2009
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How to round any CSP
Prasad Raghavendra and David Steurer · 2009
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Quantum computing for finance: Overview and prospects
Roman Orus, Samuel Mugel, and Enrique Lizaso · 2019
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From the quantum approximate optimization algorithm to a quantum alternating operator ansatz
Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor Rieffel, Davide Venturelli, and Rupak Biswas · 2019
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Multistart methods for quantum approximate optimization
Ruslan Shaydulin, Ilya Safro, and Jeffrey Larson · 2019
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Evaluating quantum approximate optimization algorithm: A case study
Ruslan Shaydulin and Yuri Alexeev · 2019
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Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning
Fernando G. S. L. Brandão, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu · 2019
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Entropy-penalized semidefinite programming
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The detectability lemma and quantum gap amplification
Dorit Aharonov, Itai Arad, Zeph Landau, and Umesh Vazirani · 2009
Cited alongside, same era.
On the unique games conjecture (invited survey)
Subhas Khot · 2010
Cited alongside, same era.
Unique games with entangled provers are easy
Julia Kempe, Oded Regev, and Ben Toner · 2010
Cited alongside, same era.
Bridging classical and quantum with SDP initialized warm-starts for QAOA, 2020
Reuben Tate, Majid Farhadi, Creston Herold, Greg Mohler, and Swati Gupta · 2010
Cited alongside, same era.
Quantum annealing with manufactured spins
Mark W. Johnson, Mohammad HS Amin, Suzanne Gildert, Trevor Lanting, Firas Hamze, Neil Dickson, Richard Harris, Andrew J. Berkley, Jan Johansson, Paul Bunyk, and et al · 2011
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Hybrid quantum-classical algorithms for approximate graph coloring, 2020b
Sergey Bravyi, Alexander Kliesch, Robert Koenig, and Eugene Tang · 2011
Cited alongside, same era.
Mikhail Krechetov, Jakub Mareček, Yury Maximov, and Martin Takáč · 2019
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Qiskit: An open-source framework for quantum computing, 2019
H. Abraham et al · 2019
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Quantum computing for finance: State-of-the-art and future prospects
Daniel J. Egger, Claudio Gambella, Jakub Mareček, Scott McFaddin, Martin Mevissen, Rudy Raymond, Aandrea Simonetto, Sefan Woerner, and Elena Yndurain · 2020
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Option pricing using quantum computers
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Credit risk analysis using quantum computers
Daniel J. Egger, Ricardo G. Gutierrez, Jordi Cahue Mestre, and Stefan Woerner · 2020
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Improving variational quantum optimization using cvar
Panagiotis Kl. Barkoutsos, Giacomo Nannicini, Anton Robert, Ivano Tavernelli, and Stefan Woerner · 2020
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Benchmarking the quantum approximate optimization algorithm
Madita Willsch, Dennis Willsch, Fengping Jin, Hans De Raedt, and Kristel Michielsen · 2020
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XY mixers: Analytical and numerical results for the quantum alternating operator ansatz
Zhihui Wang, Nicholas C. Rubin, Jason M. Dominy, and Eleanor G. Rieffel · 2020
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Learning to optimize variational quantum circuits to solve combinatorial problems
Sami Khairy, Ruslan Shaydulin, Lukasz Cincio, Yuri Alexeev, and Prasanna Balaprakash · 2020
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Reinforcement-learning-assisted quantum optimization
Matteo M. Wauters, Emanuele Panizon, Glen B. Mbeng, and Giuseppe E. Santoro · 2020
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Exploring entanglement and optimization within the hamiltonian variational ansatz
Roeland Wiersema, Cunlu Zhou, Yvette de Sereville, Juan Felipe Carrasquilla, Yong Baek Kim, and Henry Yuen · 2020
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Robust control optimization for quantum approximate optimization algorithms
Yulong Dong, Xiang Meng, Lin Lin, Robert Kosut, and K. Birgitta Whaley · 2020
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Improving the performance of deep quantum optimization algorithms with continuous gate sets
Nathan Lacroix, Christoph Hellings, Christian Kraglund Andersen, Agustin Di Paolo, Ants Remm, Stefania Lazar, Sebastian Krinner, Graham J. Norris, Mihai Gabureac, Johannes Heinsoo, and et al · 2020
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Optimized quantum compilation for near-term algorithms with openpulse, 2020
Pranav Gokhale, Ali Javadi-Abhari, Nathan Earnest, Yunong Shi, and Frederic T. Chong · 2020
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Recent scalability improvements for semidefinite programming with applications in machine learning, control, and robotics
Anirudha Majumdar, Georgina Hall, and Amir Ali Ahmadi · 2020
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Quantum SDP-solvers: Better upper and lower bounds
Joran Van Apeldoorn, András Gilyén, Sander Gribling, and Ronald de Wolf · 2020
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Quantum-Inspired Sublinear Algorithm for Solving Low-Rank Semidefinite Programming
Nai-Hui Chia, Tongyang Li, Han-Hsuan Lin, and Chunhao Wang · 2020
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Sticky brownian rounding and its applications to constraint satisfaction problems
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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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Grover mixers for qaoa: Shifting complexity from mixer design to state preparation
Andreas Bärtschi and Stephan Eidenbenz · 2020
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Subexponential LPs approximate max-cut
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Toward pricing financial derivatives with an ibm quantum computer
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Quantum algorithms for mixed binary optimization applied to transaction settlement
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Quantum approximate optimization of non-planar graph problems on a planar superconducting processor
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Local classical MAX-CUT algorithm outperforms p = 2 p=2 QAOA on high-girth regular graphs
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Lower bounds on circuit depth of the quantum approximate optimization algorithm
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https://github.com/Qiskit/qiskit-optimization
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