Warm-starting quantum optimization
Open accessAbstract
There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Preconditioning of quantum algorithms for VQAs is provided by warm-starting with classical solvers for relaxed CO problems.
“Concerning the former, a preconditioning of the quantum algorithm for VQAs is provided by warm-starting with classical solvers for relaxed CO problems [42], e.g., an SDP solver [137].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [42]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
Einstein, A., Podolsky, B., & Rosen, N. (1935) · Physical Review · doi:10.1103/physrev.47.777 · Cited by 16,654 · see citing works
Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., & Lloyd, S. (2017) · Nature · doi:10.1038/nature23474 · Cited by 4,779 · see citing works
Markowitz, H. M. (1952) · The Journal of Finance · doi:10.2307/2975974 · Cited by 4,606 · see citing works
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587 · see citing works
A second course in stochastic processes
Karlin, S., & Taylor, H. E. (1981) · Cited by 2,819 · see citing works
Supervised learning with quantum-enhanced feature spaces
Havlíček, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019) · Nature · doi:10.1038/s41586-019-0980-2 · Cited by 2,572 · see citing works
Ising formulations of many NP problems
Lucas, A. (2014) · Frontiers in Physics · doi:10.3389/fphy.2014.00005 · Cited by 2,512 · see citing works
Global Optimization with Polynomials and the Problem of Moments
Lasserre, J. B. (2001) · SIAM Journal on Optimization · doi:10.1137/s1052623400366802 · Cited by 2,412 · see citing works
Computational Complexity: A Modern Approach
Arora, S., & Barak, B. (2009) · Cited by 2,375 · see citing works
Some optimal inapproximability results
Håstad, J. (2001) · Journal of the ACM · doi:10.1145/502090.502098 · Cited by 1,902 · see citing works
Quantum annealing with manufactured spins
Johnson, M. W., Amin, M. H. S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A. J., Johansson, J., Bunyk, P., et al. (2011) · Nature · doi:10.1038/nature10012 · Cited by 1,891 · see citing works
Quantum generalizations of Bell's inequality
Cirel'son, B. S. (1980) · Letters in Mathematical Physics · doi:10.1007/bf00417500 · Cited by 1,788 · see citing works
P-Complete Approximation Problems
Sahni, S. K., & Gonzalez, T. F. (1976) · Journal of the ACM · doi:10.1145/321958.321975 · Cited by 1,725 · see citing works
Computational Complexity: A Modern Approach
Arora, S., & Barak, B. (2009) · doi:10.1017/cbo9780511804090 · Cited by 1,690 · see citing works
Strengths and Weaknesses of Quantum Computing
Bennett, C. H., Bernstein, E., Brassard, G., & Vazirani, U. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539796300933 · Cited by 1,470 · see citing works
Qiskit: An Open-source Framework for Quantum Computing
Aleksandrowicz, G., Alexander, T., Barkoutsos, P. K., Bello, L., Ben-Haim, Y., Bucher, D., Cabrera-Hernández, F. J., Carballo-Franquis, J., Chen, A., Chen, C.-F., et al. (2019) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.2562110 · Cited by 1,454 · see citing works
Proof verification and the hardness of approximation problems
Arora, S., Lund, C., Motwani, R., Sudan, M., & Szegedy, M. (1998) · Journal of the ACM · doi:10.1145/278298.278306 · Cited by 1,449 · see citing works
Qiskit: An Open-source Framework for Quantum Computing
Aleksandrowicz, G., Alexander, T., Barkoutsos, P. K., et al. (2019) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.2562111 · Cited by 1,314 · see citing works
Complexity and real computation
Blum, L. (1998) · Choice Reviews Online · doi:10.5860/choice.35-6275c · Cited by 1,266 · see citing works
Probabilistic checking of proofs
Arora, S., & Safra, M. (1998) · Journal of the ACM · doi:10.1145/273865.273901 · Cited by 1,158 · see citing works
Randomized rounding: A technique for provably good algorithms and algorithmic proofs
Raghavan, P., & Tompson, C. D. (1987) · COMBINATORICA · doi:10.1007/bf02579324 · Cited by 1,021 · see citing works
Zhou, L., Wang, S.-T., Choi, S., Pichler, H., & Lukin, M. D. (2020) · Physical Review X · doi:10.1103/physrevx.10.021067 · Cited by 913 · see citing works
Error mitigation extends the computational reach of a noisy quantum processor
Kandala, A., Temme, K., Corcoles, A. D., Mezzacapo, A., Chow, J. M., & Gambetta, J. (2019) · Nature · doi:10.1038/s41586-019-1040-7 · Cited by 870 · see citing works
Complexity and Real Computation
Blum, L., Felipe Cucker, B., Shub, M., & Smale, S. (1998) · Springer eBooks · doi:10.1007/978-1-4612-0701-6 · Cited by 869 · see citing works
On the power of unique 2-prover 1-round games
Khot, S. (2002) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/509907.510017 · Cited by 825 · see citing works
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
Hadfield, S., Wang, Z., O’Gorman, B., Rieffel, E. G., Venturelli, D., & Biswas, R. (2019) · Algorithms · doi:10.3390/a12020034 · Cited by 772 · see citing works
Quantum optimization using variational algorithms on near-term quantum devices
Moll, N., Barkoutsos, P., Bishop, L. S., Chow, J. M., Cross, A., Egger, D. J., Filipp, S., Fuhrer, A., Gambetta, J. M., Ganzhorn, M., et al. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aab822 · Cited by 744 · see citing works
Self-citationQuantum computing for finance: Overview and prospects
Orús, R., Mugel, S., & Lizaso, E. (2019) · Reviews in Physics · doi:10.1016/j.revip.2019.100028 · Cited by 714 · see citing works
Optimal Inapproximability Results for MAX‐CUT and Other 2‐Variable CSPs?
Khot, S., Kindler, G., Mossel, E., & O’Donnell, R. (2007) · SIAM Journal on Computing · doi:10.1137/s0097539705447372 · Cited by 592 · see citing works
Computational Complexity: ADVANCED TOPICS
Arora, S., & Barak, B. (2009) · Cited by 578 · see citing works
Quantum approximate optimization of non-planar graph problems on a planar superconducting processor
Harrigan, M. P., Sung, K. J., Neeley, M., Satzinger, K. J., Arute, F., Arya, K., Atalaya, J., Bardin, J. C., Barends, R., Boixo, S., et al. (2021) · Nature Physics · doi:10.1038/s41567-020-01105-y · Cited by 564 · see citing works
Boolean Methods in Operations Research and Related Areas
Hammer, P. L., & Rudeanu, S. (1968) · Ökonometrie und Unternehmensforschung · doi:10.1007/978-3-642-85823-9 · Cited by 529 · see citing works
The PCP theorem by gap amplification
Dinur, I. (2006) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/1132516.1132553 · Cited by 506 · see citing works
Digitized adiabatic quantum computing with a superconducting circuit
Barends, R., Shabani, A., Lamata, L., Kelly, J., Mezzacapo, A., Heras, U. L., Babbush, R., Fowler, A. G., Campbell, B., Chen, Y., et al. (2016) · Nature · doi:10.1038/nature17658 · Cited by 455 · see citing works
Quantum Computing for Finance: State-of-the-Art and Future Prospects
Egger, D. J., Gambella, C., Marecek, J., McFaddin, S., Mevissen, M., Raymond, R., Simonetto, A., Woerner, S., & Yndurain, E. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.3030314 · Cited by 422 · see citing works
Self-citationOptimal algorithms and inapproximability results for every CSP?
Raghavendra, P. (2008) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/1374376.1374414 · Cited by 390 · see citing works
Barkoutsos, P. K., Gonthier, J. F., Sokolov, I., Moll, N., Salis, G., Fuhrer, A., Ganzhorn, M., Egger, D. J., Troyer, M., Mezzacapo, A., et al. (2018) · Physical Review A · doi:10.1103/physreva.98.022322 · Cited by 363 · see citing works
Self-citationQuantum approximate optimization algorithm for MaxCut: A fermionic view
Wang, Z., Hadfield, S., Jiang, Z., & Rieffel, E. G. (2018) · Physical Review A · doi:10.1103/physreva.97.022304 · Cited by 353 · see citing works
Handbook on Semidefinite, Conic and Polynomial Optimization
Lasserre, J.-B., & Miguel, A. (2011) · International series in management science/operations research/International series in operations research & management science · doi:10.1007/978-1-4614-0769-0 · Cited by 325 · see citing works
Woerner, S., & Egger, D. J. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0130-6 · Cited by 298 · see citing works
Self-citationConvergent SDP‐Relaxations in Polynomial Optimization with Sparsity
Lasserre, J. B. (2006) · SIAM Journal on Optimization · doi:10.1137/05064504x · Cited by 292 · see citing works
Rigorous location of phase transitions in hard optimization problems
Achlioptas, D., Naor, A., & Peres, Y. (2005) · Nature · doi:10.1038/nature03602 · Cited by 284 · see citing works
Option Pricing using Quantum Computers
Stamatopoulos, N., Egger, D. J., Sun, Y., Zoufal, C., Iten, R., Shen, N., & Woerner, S. (2020) · Quantum · doi:10.22331/q-2020-07-06-291 · Cited by 278 · see citing works
Self-citationObstacles to Variational Quantum Optimization from Symmetry Protection
Bravyi, S., Kliesch, A., Koenig, R., & Tang, E. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.260505 · Cited by 278 · see citing works
Improving Variational Quantum Optimization using CVaR
Barkoutsos, P. K., Nannicini, G., Robert, A., Tavernelli, I., & Woerner, S. (2020) · Quantum · doi:10.22331/q-2020-04-20-256 · Cited by 263 · see citing works
Self-citationQuantum computational finance: Monte Carlo pricing of financial derivatives
Rebentrost, P., Gupt, B., & Bromley, T. R. (2018) · Physical Review A · doi:10.1103/physreva.98.022321 · Cited by 262 · see citing works
Exploring Entanglement and Optimization within the Hamiltonian Variational Ansatz
Wiersema, R., Zhou, C., de Sereville, Y., Carrasquilla, J., Kim, Y. B., & Yuen, H. (2020) · PRX Quantum · doi:10.1103/prxquantum.1.020319 · Cited by 248 · see citing works
Zhu, L., Tang, H. L., Barron, G. S., Calderon-Vargas, F. A., Mayhall, N. J., Barnes, E., & Economou, S. E. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033029 · Cited by 245 · see citing works
Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle
Yang, Z.-C., Rahmani, A., Shabani, A., Neven, H., & Chamon, C. (2017) · Physical Review X · doi:10.1103/physrevx.7.021027 · Cited by 210 · see citing works
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
Charikar, M., & Wirth, A. I. (2004) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2004.39 · Cited by 204 · see citing works
A recipe for semidefinite relaxation for (0,1)-quadratic programming
Poljak, S., Rendl, F., & Wolkowicz, H. (1995) · Journal of Global Optimization · doi:10.1007/bf01100205 · Cited by 200 · see citing works
Wang, Z., Rubin, N. C., Dominy, J. M., & Rieffel, E. G. (2020) · Physical Review A · doi:10.1103/physreva.101.012320 · Cited by 190 · see citing works
Checking local optimality in constrained quadratic programming is NP-hard
Pardalos, P. M., & Schnitger, G. (1988) · Operations Research Letters · doi:10.1016/0167-6377(88)90049-1 · Cited by 187 · see citing works
Qiskit pulse: programming quantum computers through the cloud with pulses
Alexander, T., Kanazawa, N., Egger, D. J., Capelluto, L., Wood, C. J., Javadi-Abhari, A., & McKay, D. C. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/aba404 · Cited by 183 · see citing works
Self-citationPerformance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem
Crooks, G. E. (2018) · arXiv · doi:10.48550/arxiv.1811.08419 · Cited by 158 · see citing works
Reachability Deficits in Quantum Approximate Optimization
Akshay, V., Philathong, H., Morales, M. E. S., & Biamonte, J. D. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.090504 · Cited by 151 · see citing works
Credit Risk Analysis Using Quantum Computers
Egger, D. J., Gutiérrez, R. G., Mestre, J. C., & Woerner, S. (2020) · IEEE Transactions on Computers · doi:10.1109/tc.2020.3038063 · Cited by 146 · see citing works
Self-citationGate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer
Ganzhorn, M., Egger, D. J., Barkoutsos, P., Ollitrault, P. J., Salis, G., Moll, N., Roth, M., Fuhrer, A., Mueller, P., Woerner, S., et al. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.11.044092 · Cited by 142 · see citing works
Self-citationA Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem
Farhi, E., Goldstone, J., & Gutmann, S. (2014) · arXiv · doi:10.48550/arxiv.1412.6062 · Cited by 131 · see citing works
What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO
Dunning, I., Gupta, S., & Silberholz, J. (2018) · INFORMS Journal on Computing · doi:10.1287/ijoc.2017.0798 · Cited by 128 · see citing works
Benchmarking the quantum approximate optimization algorithm
Willsch, M., Willsch, D., Jin, F., De Raedt, H., & Michielsen, K. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02692-8 · Cited by 128 · see citing works
Near-optimal algorithms for unique games
Charikar, M., Makarychev, K., & Makarychev, Y. (2006) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/1132516.1132547 · Cited by 124 · see citing works
Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation
Bartschi, A., & Eidenbenz, S. (2020) · 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce49297.2020.00020 · Cited by 122 · see citing works
Rounding Semidefinite Programming Hierarchies via Global Correlation
Barak, B., Raghavendra, P., & Steurer, D. (2011) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2011.95 · Cited by 119 · see citing works
Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems
Khairy, S., Shaydulin, R., Cincio, L., Alexeev, Y., & Balaprakash, P. (2020) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v34i03.5616 · Cited by 117 · see citing works
Scalable Semidefinite Programming
Yurtsever, A., Tropp, J. A., Fercoq, O., Udell, M. R., & Cevher, V. (2021) · SIAM Journal on Mathematics of Data Science · doi:10.1137/19m1305045 · Cited by 111 · see citing works
Multistart Methods for Quantum Approximate optimization
Shaydulin, R., Safro, I., & Larson, J. (2019) · 2019 IEEE High Performance Extreme Computing Conference (HPEC) · doi:10.1109/hpec.2019.8916288 · Cited by 110 · see citing works
Benchmarking the quantum approximate optimization algorithm
Willsch, M., Willsch, D., Jin, F., Raedt, H. A. D., & Michielsen, K. F. L. (2020) · RWTH Publications (RWTH Aachen) · Cited by 109 · see citing works
Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer
Ganzhorn, M., Egger, D. J., Tavernelli, I., Filipp, S., Barkoutsos, P. K., Ollitrault, P. J., Salis, G., Moll, N., Roth, M., Fuhrer, A., et al. (2019) · RWTH Publications (RWTH Aachen) · Cited by 109 · see citing works
Self-citationQiskit Backend Specifications for OpenQASM and OpenPulse ExperimentsPreprint
McKay, D. C., Alexander, T., Bello, L., Biercuk, M. J., Bishop, L. S., Chen, J., Chow, J. M., Corcoles, A. D., Egger, D. J., Filipp, S., et al. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1809.03452 · Cited by 101 · see citing works
Self-citationQuantum SDP-Solvers: Better upper and lower bounds
van Apeldoorn, J., Gilyén, A., Gribling, S., & de Wolf, R. (2020) · Quantum · doi:10.22331/q-2020-02-14-230 · Cited by 100 · see citing works
Majumdar, A., Hall, G., & Ahmadi, A. A. (2019) · Annual Review of Control Robotics and Autonomous Systems · doi:10.1146/annurev-control-091819-074326 · Cited by 97 · see citing works
Classical and Quantum Bounded Depth Approximation Algorithms
Hastings, M. B. (2019) · arXiv · doi:10.48550/arxiv.1905.07047 · Cited by 96 · see citing works
Quantum Algorithms for Fixed Qubit Architectures
Farhi, E., Goldstone, J., Gutmann, S., & Neven, H. (2017) · arXiv · doi:10.48550/arxiv.1703.06199 · Cited by 93 · see citing works
Warm start of the primal-dual method applied in the cutting-plane scheme
Gondzio, J. (1998) · Mathematical Programming · doi:10.1007/bf02680554 · Cited by 91 · see citing works
Optimized Quantum Compilation for Near-Term Algorithms with OpenPulse
Gokhale, P., Javadi-Abhari, A., Earnest, N., Shi, Y., & Chong, F. T. (2020) · IEEE/ACM International Symposium on Microarchitecture (MICRO) · doi:10.1109/micro50266.2020.00027 · Cited by 89 · see citing works
Scalable Semidefinite Programming
Yurtsever, A., Tropp, J. A., Fercoq, O., Udell, M. R., & Cevher, V. (2019) · CaltechAUTHORS (California Institute of Technology) · Cited by 89 · see citing works
Brandao, F. G. S. L., Broughton, M., Farhi, E., Gutmann, S., & Neven, H. (2018) · arXiv · doi:10.48550/arxiv.1812.04170 · Cited by 88 · see citing works
On the Complexity of Semidefinite Programs
Porkolab, L., & Khachiyan, L. (1997) · Journal of Global Optimization · doi:10.1023/a:1008203903341 · Cited by 85 · see citing works
Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware
Earnest, N., Tornow, C., & Egger, D. J. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043088 · Cited by 85 · see citing works
Self-citationKhot, S., & Vishnoi, N. K. (2015) · Journal of the ACM · doi:10.1145/2629614 · Cited by 83 · see citing works
Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets
Lacroix, N., Hellings, C., Andersen, C. K., Paolo, A. D., Remm, A., Lazar, S., Krinner, S., Norris, G. J., Gabureac, M. S., Heinsoo, J., et al. (2020) · PRX Quantum · doi:10.1103/prxquantum.1.020304 · Cited by 83 · see citing works
Reinforcement-learning-assisted quantum optimization
Wauters, M. M., Panizon, E., Mbeng, G. B., & Santoro, G. E. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033446 · Cited by 80 · see citing works
Random MAX SAT, random MAX CUT, and their phase transitions
Coppersmith, D., Gamarnik, D., Hajiaghayi, M., & Sorkin, G. B. (2004) · Random Structures and Algorithms · doi:10.1002/rsa.20015 · Cited by 79 · see citing works
The detectability lemma and quantum gap amplification
Aharonov, D., Arad, I., Landau, Z. A., & Vazirani, U. V. (2009) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/1536414.1536472 · Cited by 77 · see citing works
A polynomial case of unconstrained zero-one quadratic optimization
Allemand, K., Fukuda, K., Liebling, T. M., & Steiner, E. (2001) · Mathematical Programming · doi:10.1007/s101070100233 · Cited by 76 · see citing works
On the Unique Games Conjecture (Invited Survey)
Khot, S. (2010) · IEEE Conference on Computational Complexity (CCC) · doi:10.1109/ccc.2010.19 · Cited by 76 · see citing works
Unique Games with Entangled Provers Are Easy
Kempe, J., Regev, O., & Toner, B. (2010) · SIAM Journal on Computing · doi:10.1137/090772885 · Cited by 74 · see citing works
Toward pricing financial derivatives with an IBM quantum computer
Martin, A., Candelas, B., Rodríguez-Rozas, Á., Martín-Guerrero, J. D., Chen, X., Lamata, L., Orús, R., Solano, E., & Sanz, M. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.013167 · Cited by 74 · see citing works
How Good is the Goemans--Williamson MAX CUT Algorithm?
Karloff, H. J. (1999) · SIAM Journal on Computing · doi:10.1137/s0097539797321481 · Cited by 71 · see citing works
Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion
Subhash, K., Minzer, D., & Safra, M. (2018) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2018.00062 · Cited by 70 · see citing works
Classical and quantum bounded depth approximation algorithms
Hastings, M. B. (2019) · Quantum Information and Computation · doi:10.26421/qic19.13-14-3 · Cited by 65 · see citing works
Bridging Classical and Quantum with SDP initialized warm-starts for QAOA
Tate, R., Farhadi, M., Herold, C. D., Mohler, G., & Gupta, S. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3549554 · Cited by 64 · see citing works
Efficient State Preparation for Quantum Amplitude Estimation
Vazquez, A. C., & Woerner, S. (2021) · Physical Review Applied · doi:10.1103/physrevapplied.15.034027 · Cited by 63 · see citing works
Self-citationQuantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning
Brandão, F. G. S. L., Kalev, A., Li, T., Lin, C. Y.-Y., Svore, K. M., & Wu, X. (2019) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/lipics.icalp.2019.27 · Cited by 60 · see citing works
Raghavendra, P., & Steurer, D. (2009) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2009.74 · Cited by 59 · see citing works
Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets
Lacroix, N., Hellings, C., Andersen, C. K., Paolo, A. D., Remm, A., Lazar, S., Krinner, S., Norris, G. J., Gabureac, M. S., Heinsoo, J., et al. (2020) · Repository for Publications and Research Data (ETH Zurich) · doi:10.3929/ethz-b-000464528 · Cited by 59 · see citing works
Evaluating Quantum Approximate Optimization Algorithm: A Case Study
Shaydulin, R., & Alexeev, Y. (2019) · 2019 Tenth International Green and Sustainable Computing Conference (IGSC) · doi:10.1109/igsc48788.2019.8957201 · Cited by 55 · see citing works
Quantum Algorithms for Mixed Binary Optimization Applied to Transaction Settlement
Braine, L., Egger, D. J., Glick, J., & Woerner, S. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3063635 · Cited by 51 · see citing works
Self-citationQuantum Annealing versus Digital Computing
Jünger, M., Lobe, E., Mutzel, P., Reinelt, G., Rendl, F., Rinaldi, G., & Stollenwerk, T. (2021) · ACM Journal of Experimental Algorithmics · doi:10.1145/3459606 · Cited by 51 · see citing works
Local classical MAX-CUT algorithm outperforms p=2 QAOA on high-girth regular graphs
Marwaha, K. (2021) · Quantum · doi:10.22331/q-2021-04-20-437 · Cited by 49 · see citing works
Random MAX SAT, Random MAX CUT, and Their Phase TransitionsPreprint
Coppersmith, D., Gamarnik, D., Hajiaghayi, M., & Sorkin, G. B. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0306047 · Cited by 47 · see citing works
Low-Degree Testing for Quantum States, and a Quantum Entangled Games PCP for QMA
Natarajan, A., & Vidick, T. (2018) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2018.00075 · Cited by 39 · see citing works
Unique Games with Entangled Provers are Easy
Kempe, J., Regev, O., & Toner, B. (2008) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2008.9 · Cited by 38 · see citing works
Quantum Annealing: a journey through Digitalization, Control, and hybrid Quantum Variational schemesPreprint
Mbeng, G. B., Fazio, R., & Santoro, G. E. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.08948 · Cited by 35 · see citing works
Lower bounds on circuit depth of the quantum approximate optimization algorithm
Herrman, R., Ostrowski, J., Humble, T. S., & Siopsis, G. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03001-7 · Cited by 35 · see citing works
Alam, M., Ash-Saki, A., & Ghosh, S. (2019) · arXiv · doi:10.48550/arxiv.1907.09631 · Cited by 33 · see citing works
A MAX-CUT formulation of 0/1 programs
Lasserre, J. B. (2015) · Operations Research Letters · doi:10.1016/j.orl.2015.12.014 · Cited by 32 · see citing works
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
Ghaddar, B., Vera, J. C., & Anjos, M. F. (2011) · SIAM Journal on Optimization · doi:10.1137/100802190 · Cited by 21 · see citing works
Robust Control Optimization for Quantum Approximate Optimization Algorithms
Dong, Y., Meng, X., Lin, L., Kosut, R. L., & Whaley, K. B. (2020) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2020.12.130 · Cited by 19 · see citing works
Gondzio, J., & Grothey, A. (2006) · WIT transactions on modelling and simulation · doi:10.2495/cf060101 · Cited by 15 · see citing works
Lodewijks, B. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.08043 · Cited by 15 · see citing works
Quantum-Inspired Sublinear Algorithm for Solving Low-Rank Semidefinite Programming.
Chia, N.-H., Li, T., Lin, H. H., & Wang, C. (2020) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/lipics.mfcs.2020.23 · Cited by 10 · see citing works
Subexponential LPs Approximate Max-Cut
Hopkins, S. B., Schramm, T., & Trevisan, L. (2020) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs46700.2020.00092 · Cited by 9 · see citing works
Fair Dimensionality Reduction and Iterative Rounding for SDPsPreprint
Morgenstern, J., Samadi, S., Singh, M., Tantipongpipat, U. T., & Vempala, S. (2019) · arXiv (Cornell University) · Cited by 8 · see citing works
Krivine diffusions attain the Goemans--Williamson approximation ratioPreprint
Eldan, R., & Naor, A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.10615 · Cited by 7 · see citing works
Entropy-Penalized Semidefinite Programming
Krechetov, M., Mareček, J., Maximov, Y., & Takáč, M. (2019) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2019/157 · Cited by 6 · see citing works
Self-citationLarkin, J. M., Jonsson, M., Justice, D., & Guerreschi, G. G. (2020) · arXiv (Cornell University) · Cited by 6 · see citing works
The Unique Games Conjecture with Entangled Provers is False
Kempe, J., Regev, O., & Toner, B. (2008) · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · doi:10.4230/dagsemproc.07411.6 · Cited by 5 · see citing works
Reachability Deficits Implicit in Google's Quantum Approximate Optimization of Graph ProblemsPreprint
Akshay, V., Philathong, H., Zacharov, I., & Biamonte, J. (2020) · arXiv (Cornell University) · Cited by 5 · see citing works
Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems
Zadeh, S. A., Bansal, N., Guruganesh, G., Nikolov, A., Schwartz, R., & Singh, M. (2019) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611975994.52 · Cited by 4 · see citing works
A new polynomially solvable class of quadratic optimization problems with box constraints
Hladík, M., Černý, M., & Rada, M. (2021) · Optimization Letters · doi:10.1007/s11590-021-01711-6 · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- Edward Farhi, Jeffrey Goldstone, and Sam Gut- mann. A quantum approximate optimization al- gorithm, 2014. URL https://arxiv.org/abs/ 1411.4028.
- Michael Juenger, Elisabeth Lobe, Petra Mutzel, Gerhard Reinelt, Franz Rendl, Giovanni Ri- naldi, and Tobias Stollenwerk. Performance of a quantum annealer for Ising ground state computations on chimera graphs, 2019. URL https://arxiv.org/abs/1904.11965. · arXiv
- Sergey Bravyi, Alexander Kliesch, Robert Koenig, and Eugene Tang. Hybrid quantum- classical algorithms for approximate graph col- oring, 2020. URL https://arxiv.org/abs/ 2011.13420.
- Michael Mitzenmacher and Eli Upfal. Probabil- ity and computing: Randomization and proba- bilistic techniques in algorithms and data anal- ysis. Cambridge university press, 2017.
Cited by
Sorted by citations
A review on Quantum Approximate Optimization Algorithm and its variants
Blekos, K., Brand, D., Ceschini, A., Chou, C.-H., Li, R.-H., Pandya, K., & Summer, A. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.03.002 · Cited by 444 · see citing works
Quantum Computing for High-Energy Physics: State of the Art and Challenges
Meglio, A. D., Jansen, K., Tavernelli, I., Alexandrou, C., Arunachalam, S., Bauer, C., Borras, K., Carrazza, S., Crippa, A., Croft, V. A., et al. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.037001 · Cited by 257 · see citing works
Self-citationChallenges and opportunities in quantum optimization
Abbas, A., Ambainis, A., Augustino, B., Bärtschi, A., Buhrman, H., Coffrin, C., Cortiana, G., Dunjko, V., Egger, D. J., Elmegreen, B. G., et al. (2024) · Nature Reviews Physics · doi:10.1038/s42254-024-00770-9 · Cited by 201 · see citing works
Self-citationNoisy intermediate-scale quantum (NISQ) algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2021) · arXiv · doi:10.48550/arxiv.2101.08448 · Cited by 166 · see citing works
Grover Adaptive Search for Constrained Polynomial Binary Optimization
Gilliam, A., Woerner, S., & Gonciulea, C. (2021) · Quantum · doi:10.22331/q-2021-04-08-428 · Cited by 153 · see citing works
Self-citationQuantum annealing initialization of the quantum approximate optimization algorithm
Sack, S. H., & Serbyn, M. (2021) · Quantum · doi:10.22331/q-2021-07-01-491 · Cited by 145 · see citing works
Multi-angle quantum approximate optimization algorithm
Herrman, R., Lotshaw, P. C., Ostrowski, J., Humble, T. S., & Siopsis, G. (2022) · Scientific Reports · doi:10.1038/s41598-022-10555-8 · Cited by 117 · see citing works
Counterdiabaticity and the quantum approximate optimization algorithm
Wurtz, J., & Love, P. J. (2022) · Quantum · doi:10.22331/q-2022-01-27-635 · Cited by 103 · see citing works
Hybrid quantum-classical algorithms for approximate graph coloring
Bravyi, S. B., Kliesch, A., König, R., & Tang, E. (2022) · Quantum · doi:10.22331/q-2022-03-30-678 · Cited by 105 · see citing works
Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
Weidenfeller, J., Valor, L. C., Gacon, J., Tornow, C., Bello, L., Woerner, S., & Egger, D. J. (2022) · Quantum · doi:10.22331/q-2022-12-07-870 · Cited by 97 · see citing works
Self-citationHuang, H.-L., Xu, X., Guo, C., Tian, G., Wei, S.-J., Sun, X., Bao, W., & Long, G. (2023) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-022-2057-y · Cited by 101 · see citing works
Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware
Earnest, N., Tornow, C., & Egger, D. J. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043088 · Cited by 85 · see citing works
Self-citationQuantum Distributed Unit Commitment: An Application in Microgrids
Nikmehr, N., Zhang, P., & Bragin, M. A. (2022) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2022.3141794 · Cited by 88 · see citing works
Matrix product state pre-training for quantum machine learning
Dborin, J., Barratt, F., Wimalaweera, V., Wright, L., & Green, A. G. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac7073 · Cited by 71 · see citing works
Transferability of optimal QAOA parameters between random graphs
Galda, A., Liu, X., Lykov, D., Alexeev, Y., & Safro, I. (2021) · 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00034 · Cited by 72 · see citing works
Bridging Classical and Quantum with SDP initialized warm-starts for QAOA
Tate, R., Farhadi, M., Herold, C. D., Mohler, G., & Gupta, S. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3549554 · Cited by 64 · see citing works
Quantum Optimization: Potential, Challenges, and the Path Forward
Abbas, A., (NNSA), U. N. N. S. A., Ambainis, A., Augustino, B., Bärtschi, A., Buhrman, H., Coffrin, C., Cortiana, G., Dunjko, V., Egger, D., et al. (2023) · doi:10.2172/2229681 · Cited by 63 · see citing works
Self-citationEfficient Encoding of the Weighted MAX $$k$$-CUT on a Quantum Computer Using QAOA
Fuchs, F. G., Kolden, H. Ø., Aase, N. H., & Sartor, G. (2021) · SN Computer Science · doi:10.1007/s42979-020-00437-z · Cited by 56 · see citing works
QUARK: A Framework for Quantum Computing Application Benchmarking
Finžgar, J. R., Ross, P., Hölscher, L., Klepsch, J., & Luckow, A. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00042 · Cited by 51 · see citing works
Quantum Algorithms for Mixed Binary Optimization Applied to Transaction Settlement
Braine, L., Egger, D. J., Glick, J., & Woerner, S. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3063635 · Cited by 51 · see citing works
Self-citationGraph neural network initialisation of quantum approximate optimisation
Jain, N., Coyle, B., Kashefi, E., & Kumar, N. (2022) · Quantum · doi:10.22331/q-2022-11-17-861 · Cited by 50 · see citing works
Challenges of variational quantum optimization with measurement shot noise
Scriva, G., Astrakhantsev, N., Pilati, S., & Mazzola, G. (2024) · Physical Review A · doi:10.1103/physreva.109.032408 · Cited by 49 · see citing works
Alignment between initial state and mixer improves QAOA performance for constrained optimization
He, Z., Shaydulin, R., Chakrabarti, S., Herman, D., Li, C., Sun, Y., & Pistoia, M. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00787-5 · Cited by 51 · see citing works
Constraint Preserving Mixers for the Quantum Approximate Optimization Algorithm
Fuchs, F. G., Lye, K. O., Nilsen, H. M., Stasik, A. J., & Sartor, G. (2022) · Algorithms · doi:10.3390/a15060202 · Cited by 47 · see citing works
Short-depth QAOA circuits and quantum annealing on higher-order ising models
Pelofske, E., Bärtschi, A., & Eidenbenz, S. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00825-w · Cited by 49 · see citing works
Dalyac, C., Henriet, L., Jeandel, E., Lechner, W., Perdrix, S., Porcheron, M., & Veshchezerova, M. (2021) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-021-00100-3 · Cited by 46 · see citing works
Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space
Fischer, L. E., Miller, D., Tacchino, F., Barkoutsos, P. K., Egger, D. J., & Tavernelli, I. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033027 · Cited by 45 · see citing works
Self-citationQuantum Artificial Intelligence: A Brief Survey
Klusch, M., Lässig, J., Müssig, D., Macaluso, A., & Wilhelm, F. K. (2024) · Künstliche Intell. · doi:10.1007/s13218-024-00871-8 · Cited by 52 · see citing works
Tate, R., Moondra, J., Gard, B., Mohler, G., & Gupta, S. (2023) · Quantum · doi:10.22331/q-2023-09-26-1121 · Cited by 44 · see citing works
NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems
Au-Yeung, R., Chancellor, N., & Halffmann, P. (2023) · Frontiers in Quantum Science and Technology · doi:10.3389/frqst.2023.1128576 · Cited by 46 · see citing works
A Conceptual Architecture for a Quantum-HPC Middleware
Saurabh, N., Jha, S., & Luckow, A. (2023) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw59989.2023.00023 · Cited by 41 · see citing works
Classically Optimal Variational Quantum Algorithms
Wurtz, J., & Love, P. J. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3122568 · Cited by 42 · see citing works
Sack, S. H., & Egger, D. J. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013223 · Cited by 40 · see citing works
Self-citationLyapunov-control-inspired strategies for quantum combinatorial optimization
Magann, A. B., Rudinger, K., Grace, M., & Sarovar, M. (2022) · Physical Review A · doi:10.1103/physreva.106.062414 · Cited by 37 · see citing works
A practitioner’s guide to quantum algorithms for optimisation problems
Symons, B. C. B., Galvin, D., Sahin, E., Alexandrov, V., & Mensa, S. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad00f0 · Cited by 37 · see citing works
An expressive ansatz for low-depth quantum approximate optimisation
Vijendran, V., Das, A., Koh, D. E., Assad, S. M., & Lam, P. K. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad200a · Cited by 41 · see citing works
Variational quantum algorithms: fundamental concepts, applications and challenges
Qi, H., Xiao, S., Liu, Z., Gong, C., & Gani, A. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04438-2 · Cited by 40 · see citing works
Scaling quantum approximate optimization on near-term hardware
Lotshaw, P. C., Nguyen, T., Santana, A., McCaskey, A., Herrman, R., Ostrowski, J., Siopsis, G., & Humble, T. S. (2022) · Scientific Reports · doi:10.1038/s41598-022-14767-w · Cited by 37 · see citing works
Lykov, D., Wurtz, J., Poole, C., Saffman, M. E., Noel, T., & Alexeev, Y. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00718-4 · Cited by 37 · see citing works
Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices
Bechtold, M., Barzen, J., Leymann, F., Mandl, A., Obst, J., Truger, F., & Weder, B. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acf59c · Cited by 35 · see citing works
Evaluation of QAOA based on the approximation ratio of individual samples
Larkin, J. M., Jonsson, M., Justice, D., & Guerreschi, G. G. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac6973 · Cited by 40 · see citing works
Approximate Solutions of Combinatorial Problems via Quantum Relaxations
Fuller, B., Hadfield, C. F., Glick, J. R., Imamichi, T., Itoko, T., Thompson, R. J., Jiao, Y., Kagele, M., Blom, A. W., Raymond, R., et al. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3421294 · Cited by 35 · see citing works
Quantum Computing Techniques for Multi-knapsack Problems
Awasthi, A., Bär, F., Doetsch, J. A., Ehm, H., Erdmann, M., Hess, M., Klepsch, J., Limacher, P. A., Luckow, A., Niedermeier, C. A., et al. (2023) · Lecture notes in networks and systems · doi:10.1007/978-3-031-37963-5_19 · Cited by 34 · see citing works
Similarity-based parameter transferability in the quantum approximate optimization algorithm
Galda, A., Gupta, E., Falla, J., Liu, X., Lykov, D., Alexeev, Y., & Safro, I. (2023) · Frontiers in Quantum Science and Technology · doi:10.3389/frqst.2023.1200975 · Cited by 30 · see citing works
Pulse variational quantum eigensolver on cross-resonance-based hardware
Egger, D. J., Capecci, C., Pokharel, B., Barkoutsos, P. K., Fischer, L. E., Guidoni, L., & Tavernelli, I. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.033159 · Cited by 31 · see citing works
Self-citationBenchmarking Digital Quantum Simulations Above Hundreds of Qubits Using Quantum Critical Dynamics
Miessen, A., Egger, D. J., Tavernelli, I., & Mazzola, G. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.040320 · Cited by 29 · see citing works
Self-citationPatterns for Hybrid Quantum Algorithms
Weigold, M., Barzen, J., Leymann, F., & Vietz, D. (2021) · Communications in computer and information science · doi:10.1007/978-3-030-87568-8_2 · Cited by 29 · see citing works
Architectural Vision for Quantum Computing in the Edge-Cloud Continuum
Furutanpey, A., Barzen, J., Bechtold, M., Dustdar, S., Leymann, F., Raith, P., & Truger, F. (2023) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw59989.2023.00021 · Cited by 29 · see citing works
Improving the Solving of Optimization Problems: A Comprehensive Review of Quantum Approaches
Volpe, D., Orlandi, G., & Turvani, G. (2025) · Quantum Reports · doi:10.3390/quantum7010003 · Cited by 32 · see citing works
Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing
Harwood, S. M., Trenev, D., Stober, S. T., Barkoutsos, P. K., Gujarati, T. P., Mostame, S., & Greenberg, D. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3479197 · Cited by 29 · see citing works
Meta-learning digitized-counterdiabatic quantum optimization
Chandarana, P., Vieites, P. S., Hegade, N. N., Solano, E., Ban, Y., & Chen, X. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace54a · Cited by 28 · see citing works
Quantum Optimization Heuristics with an Application to Knapsack Problems
van Dam, W., Eldefrawy, K., Genise, N., & Parham, N. (2021) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00033 · Cited by 26 · see citing works
Zoufal, C., Mishmash, R. V., Sharma, N., Kumar, N., Sheshadri, A., Deshmukh, A. A., Ibrahim, N., Gacon, J., & Woerner, S. (2023) · Quantum · doi:10.22331/q-2023-01-26-909 · Cited by 26 · see citing works
Self-citationWarm-Starting and Quantum Computing: A Systematic Mapping Study
Truger, F., Barzen, J., Bechtold, M., Beisel, M., Leymann, F., Mandl, A., & Yussupov, V. (2024) · ACM Computing Surveys · doi:10.1145/3652510 · Cited by 28 · see citing works
Approaches to Constrained Quantum Approximate Optimization
Saleem, Z. H., Tomesh, T., Tariq, B., & Suchara, M. (2023) · SN Computer Science · doi:10.1007/s42979-022-01638-4 · Cited by 25 · see citing works
Provable bounds for noise-free expectation values computed from noisy samples
Barron, S. V., Egger, D. J., Pelofske, E., Bärtschi, A., Eidenbenz, S., Lehmkuehler, M., & Woerner, S. (2024) · Nature Computational Science · doi:10.1038/s43588-024-00709-1 · Cited by 25 · see citing works
Self-citationQuantum approximate multi-objective optimization
Kotil, A., Pelofske, E., Riedmüller, S., Egger, D. J., Eidenbenz, S., Koch, T., & Woerner, S. (2025) · Nature Computational Science · doi:10.1038/s43588-025-00873-y · Cited by 27 · see citing works
Self-citationEvolving objective function for improved variational quantum optimization
Kolotouros, I., & Wallden, P. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023225 · Cited by 24 · see citing works
Quantum approximate optimization for combinatorial problems with constraints
Ruan, Y., Yuan, Z., Xue, X., & Liu, Z. (2022) · Information Sciences · doi:10.1016/j.ins.2022.11.020 · Cited by 26 · see citing works
Quantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem
Palackal, L., Poggel, B., Wulff, M., Ehm, H., Lorenz, J. M., & Mendl, C. B. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00080 · Cited by 24 · see citing works
Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs
Pelofske, E., Bärtschi, A., Cincio, Ł., Golden, J. K., & Eidenbenz, S. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00906-w · Cited by 24 · see citing works
Performance Evaluation and Acceleration of the QTensor Quantum Circuit Simulator on GPUs
Lykov, D., Chen, A., Chen, H., Keipert, K., Zhang, Z., Gibbs, T., & Alexeev, Y. (2021) · IEEE/ACM International Workshop on Quantum Computing Software (QCS) · doi:10.1109/qcs54837.2021.00007 · Cited by 23 · see citing works
Falla, J., Langfitt, Q., Alexeev, Y., & Safro, I. (2024) · Quantum Machine Intelligence · doi:10.1007/s42484-024-00178-9 · Cited by 22 · see citing works
An introduction to variational quantum algorithms for combinatorial optimization problems
Grange, C., Poss, M., & Bourreau, E. (2023) · 4OR · doi:10.1007/s10288-023-00549-1 · Cited by 21 · see citing works
Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study
Gemeinhardt, F., Garmendia, A., Wimmer, M., Weder, B., & Leymann, F. (2024) · ACM Computing Surveys · doi:10.1145/3620668 · Cited by 22 · see citing works
“Concerning the former, a preconditioning of the quantum algorithm for VQAs is provided by warm-starting with classical solvers for relaxed CO problems [42], e.g., an SDP solver [137].”
BackgroundMethodSack, S. H., Medina, R. A., Kueng, R., & Serbyn, M. (2023) · Physical Review A · doi:10.1103/physreva.107.062404 · Cited by 21 · see citing works
Data re-uploading with a single qudit
Wach, N. L., Rudolph, M. S., Jendrzejewski, F., & Schmitt, S. (2023) · Quantum Machine Intelligence · doi:10.1007/s42484-023-00125-0 · Cited by 19 · see citing works
Error mitigation for quantum approximate optimization
Weidinger, A., Mbeng, G. B., & Lechner, W. (2023) · Physical Review A · doi:10.1103/physreva.108.032408 · Cited by 21 · see citing works
Quantum Approximate Optimization Algorithm (QAOA)
Fakhimi, R., & Validi, H. (2023) · Springer eBooks · doi:10.1007/978-3-030-54621-2_854-1 · Cited by 22 · see citing works
Transfer learning of optimal QAOA parameters in combinatorial optimization
Montañez-Barrera, J. A., Willsch, D., & Michielsen, K. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04743-4 · Cited by 19 · see citing works
Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer
Chalupnik, M., Melo, H., Alexeev, Y., & Galda, A. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00028 · Cited by 21 · see citing works
Quantum Computing for High-Energy Physics: State of the Art and ChallengesPreprint
Meglio, A. D., Jansen, K., Tavernelli, I., Alexandrou, C., Arunachalam, S., Bauer, C., Borras, K., Carrazza, S., Crippa, A., Croft, V. A., et al. (2023) · arXiv (Cornell University) · doi:10.3204/pubdb-2023-04595 · Cited by 24 · see citing works
Self-citationFermionic quantum approximate optimization algorithm
Yoshioka, T., Sasada, K., Nakano, Y., & Fujii, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023071 · Cited by 17 · see citing works
Solution of SAT problems with the adaptive-bias quantum approximate optimization algorithm
Yu, Y., Cao, C., Wang, X., Shannon, N., & Joynt, R. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023147 · Cited by 17 · see citing works
Bias-field digitized counterdiabatic quantum algorithm for higher-order binary optimization
Romero, S. V., Visuri, A.-M., Cadavid, A. G., Simen, A., Solano, E., & Hegade, N. N. (2025) · Communications Physics · doi:10.1038/s42005-025-02270-3 · Cited by 18 · see citing works
“Several warm-starting techniques have been proposed,wherearelaxedversionoftheproblemissolvedclassicallyandits solutionfedintothequantumalgorithm,leveragingthecomplexityandcost ofthequantumroutinewhileensuringabetterperformance 71,72 .”
Quantum approximate optimization algorithm for Bayesian network structure learning
Soloviev, V. P., Bielza, C., & Larrañaga, P. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03769-2 · Cited by 18 · see citing works
Wulff, A., Chen, B., Steinberg, M., Tang, Y., Möller, M., & Feld, S. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117380 · Cited by 16 · see citing works
Markov chain Monte Carlo enhanced variational quantum algorithms
Patti, T. L., Shehab, O., Najafi, K., & Yelin, S. F. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/aca821 · Cited by 16 · see citing works
Truger, F., Beisel, M., Barzen, J., Leymann, F., & Yussupov, V. (2022) · Electronics · doi:10.3390/electronics11071033 · Cited by 15 · see citing works
Quantum Local Search with the Quantum Alternating Operator Ansatz
Tomesh, T., Saleem, Z. H., & Suchara, M. (2022) · Quantum · doi:10.22331/q-2022-08-22-781 · Cited by 15 · see citing works
Sawaya, N. P. D., Schmitz, A. T., & Hadfield, S. (2023) · Quantum · doi:10.22331/q-2023-09-14-1111 · Cited by 16 · see citing works
From Digital Humanities to Quantum Humanities: Potentials and Applications
Barzen, J. (2022) · Springer eBooks · doi:10.1007/978-3-030-95538-0_1 · Cited by 15 · see citing works
Quantum-Enabled Distributed Unit Commitment
Nikmehr, N., Zhang, P., & Bragin, M. A. (2022) · IEEE Power Engineering Society General Meeting · doi:10.1109/pesgm48719.2022.9917029 · Cited by 14 · see citing works
Warm-started quantum sphere decoding via reverse annealing for massive IoT connectivity
Kim, M., Venturelli, D., Kaewell, J., & Jamieson, K. (2022) · ACM Annual International Conference on Mobile Computing and Networking (MobiCom) · doi:10.1145/3495243.3560516 · Cited by 14 · see citing works
Govia, L. C. G., Poole, C., Saffman, M. E., & Krovi, H. (2021) · Physical Review A · doi:10.1103/physreva.104.062428 · Cited by 14 · see citing works
The Quantum Alternating Operator Ansatz for Satisfiability Problems
Golden, J., Bärtschi, A., O'Malley, D., & Eidenbenz, S. (2023) · 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00042 · Cited by 13 · see citing works
“Recent work has argued in favor of using classical algorithms to generate initial states which are weighted in favor of likely good solutions [6, 7], and the effect of this”
MethodVariational quantum multiobjective optimization
Ekstrøm, L., Wang, H., & Schmitt, S. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.023141 · Cited by 13 · see citing works
A Quantum Computing Approach for the Unit Commitment Problem
Halffmann, P., Holzer, P., Plociennik, K., & Trebing, M. E. (2023) · Lecture notes in operations research · doi:10.1007/978-3-031-24907-5_14 · Cited by 13 · see citing works
Hybrid Quantum-Classical Multilevel Approach for Maximum Cuts on Graphs
Angone, A., Liu, X., Shaydulin, R., & Safro, I. (2023) · IEEE High Performance Extreme Computing Conference · doi:10.1109/hpec58863.2023.10363584 · Cited by 13 · see citing works
Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering
Zhang, Z., Paredes, R., Sundar, B., Quiroga, D., Kyrillidis, A., Dueñas‐Osorio, L., Pagano, G., & Hazzard, K. R. A. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad895c · Cited by 17 · see citing works
Mixer-phaser Ansätze for quantum optimization with hard constraints
LaRose, R., Rieffel, E. G., & Venturelli, D. (2022) · Quantum Machine Intelligence · doi:10.1007/s42484-022-00069-x · Cited by 14 · see citing works
The Role of Entanglement in Quantum-Relaxation Based Optimization Algorithms
Teramoto, K., Raymond, R., & Imai, H. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00068 · Cited by 12 · see citing works
Camur, M. C., Bollapragada, S., Thanos, A. E., Dülgeroğlu, O., & Gemici-Ozkan, B. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.124304 · Cited by 12 · see citing works
Schuster, S., Kühn, S., Funcke, L., Hartung, T., Pleinert, M.-O., von Zanthier, J., & Jansen, K. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.114508 · Cited by 12 · see citing works
Low-depth Clifford circuits approximately solve MaxCut
Muñoz-Arias, M. H., Kourtis, S., & Blais, A. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023294 · Cited by 12 · see citing works
Lyngfelt, I., & García-Álvarez, L. (2025) · Physical Review A · doi:10.1103/physreva.111.022418 · Cited by 12 · see citing works
Initial State Encoding via Reverse Quantum Annealing and H-Gain Features
Pelofske, E., Hahn, G., & Djidjev, H. N. (2023) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2023.3319586 · Cited by 15 · see citing works
Convergence of digitized-counterdiabatic QAOA: circuit depth versus free parameters
Vizzuso, M., Passarelli, G., Cantele, G., & Lucignano, P. (2023) · New Journal of Physics · doi:10.1088/1367-2630/ad1536 · Cited by 12 · see citing works
JuliQAOA: Fast, Flexible QAOA Simulation
Golden, J. K., Bärtschi, A., O’Malley, D., Pelofske, E., & Eidenbenz, S. (2023) · International Conference for High Performance Computing, Networking, Storage and Analysis (SC) · doi:10.1145/3624062.3624220 · Cited by 11 · see citing works
Perelshtein, M. R., Pakhomchik, A. I., Мельников, А. А., Podobrii, M., Termanova, A., Kreidich, I., Nuriev, B., Iudin, S., Mansell, C., & Vinokur, V. M. (2023) · Quantum · doi:10.22331/q-2023-11-21-1186 · Cited by 11 · see citing works
- Authors
- Egger, D. J., Mareček, J., & Woerner, S.
- Affiliations
- IBM Research - Zurich (CH)
- Czech Technical University in Prague (CZ)
- Venue
- Quantum
- Published
- 2021-06-17
- Volume
- 5
- Pages
- 479
- ISSN
- 2521-327X (ISSN-L)
- OpenAlex
- W3088409280
- Cited by
- 269
- References
- 122
- Citations by year
- 2026: 44 · 2025: 61 · 2024: 57 · 2023: 56 · 2022: 34 · 2021: 16 · 2020: 1
- FWCI
- 14.35
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Bulletin of the American Physical Society
- Funders
- OP RDE project Research Center for Informatic (CZ.02.1.01/0.0/0.0/16_019/0000765)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Keywords
- warm start, quantum optimization, quantum approximate optimization algorithm, MaxCut, portfolio optimization, semidefinite relaxation, Unique Games Conjecture, randomized rounding, integer programming, combinatorial optimization, performance guarantees
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
