Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers
Open accessAbstract
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, for example, the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). In this article, we present a decomposition-based approach to extend the applicability of current approaches to “quadratic plus convex” mixed binary optimization (MBO) problems, so as to solve a broad class of real-world optimization problems. In the MBO framework, we show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms), and continuous constrained convex subproblems (that can be solved cheaply with classical optimization solvers). The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit, an open-source quantum computing software development framework.
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?
A certain amount of noise in the quantum solver can be beneficial for the final solution quality.
“In this context, a certain amount of noise in the quantum solver has turned out to be even beneficial for the final solution quality [50, 61].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [50]
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
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075 · see citing works
Rockafellar, R. T. (1970) · Princeton University Press eBooks · doi:10.1515/9781400873173 · Cited by 10,843 · see citing works
A variational eigenvalue solver on a photonic quantum processor
Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014) · Nature Communications · doi:10.1038/ncomms5213 · Cited by 4,552 · cited 3× · see citing works
“Research directed to apply the resulting algorithms to early generation of universal quantum computers has mainly focused on quantum variational approaches [6], which have been applied to chemistry [11], [12], machine learning [13], [14], and mathematical optimization [7], [15], [16].”
BackgroundMethodInfluentialHardware-efficient variational quantum eigensolver for small molecules and quantum magnets
Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017) · Nature · doi:10.1038/nature23879 · Cited by 2,982 · see citing works
A dual algorithm for the solution of nonlinear variational problems via finite element approximation
Gabay, D., & Mercier, B. (1976) · Computers & Mathematics with Applications · doi:10.1016/0898-1221(76)90003-1 · Cited by 2,638 · see citing works
Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
Spall, J. C. (1992) · IEEE Transactions on Automatic Control · doi:10.1109/9.119632 · Cited by 2,283 · see citing works
The theory of variational hybrid quantum-classical algorithms
McClean, J. R., Romero, J., Babbush, R., & Aspuru-Guzik, A. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/2/023023 · Cited by 2,227 · see citing works
SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
Toh, K.-C., Todd, M. J., & Tütüncü, R. H. (1999) · Optimization methods & software · doi:10.1080/10556789908805762 · Cited by 1,939 · see citing works
Kellerer, H. G., Pferschy, U., & Pisinger, D. (2004) · Springer eBooks · doi:10.1007/978-3-540-24777-7 · Cited by 1,827 · see citing works
A Quantum Approximate Optimization Algorithm
Farhi, E., Goldstone, J., & Gutmann, S. (2014) · arXiv · doi:10.48550/arxiv.1411.4028 · Cited by 1,789 · see citing works
Attouch, H., Bolte, J., & Svaiter, B. F. (2011) · Mathematical Programming · doi:10.1007/s10107-011-0484-9 · Cited by 1,485 · see citing works
Global Convergence of ADMM in Nonconvex Nonsmooth Optimization
Wang, Y., Yin, W., & Zeng, J. (2018) · Journal of Scientific Computing · doi:10.1007/s10915-018-0757-z · Cited by 1,221 · see citing works
Attouch, H., Bolte, J., Redont, P., & Soubeyran, A. (2010) · Mathematics of Operations Research · doi:10.1287/moor.1100.0449 · Cited by 1,175 · see citing works
Bolaño, L. J. C., Uribe-Martes, C., Coronado-Hernández, J. R., Ramirez-Ríos, D. G., Herazo-Padilla, N., Paez-Logreira, H., & Gatica, G. (2014) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611973594 · Cited by 1,141 · see citing works
Integer programming formulations of discrete hub location problems
Campbell, J. F. (1994) · European Journal of Operational Research · doi:10.1016/0377-2217(94)90318-2 · Cited by 920 · 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
Classification with Quantum Neural Networks on Near Term Processors
Farhi, E., & Neven, H. (2020) · doi:10.37686/qrl.v1i2.80 · Cited by 909 · see citing works
Hong, M., Luo, Z.-Q., & Razaviyayn, M. (2016) · SIAM Journal on Optimization · doi:10.1137/140990309 · Cited by 894 · see citing works
Andersen, E. D., & Andersen, K. D. (2000) · Applied Optimization · doi:10.1007/978-1-4757-3216-0_8 · Cited by 766 · 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
Mixed-integer nonlinear optimization
Belotti, P., Kirches, C., Leyffer, S., Linderoth, J., Luedtke, J., & Mahajan, A. (2013) · Acta Numerica · doi:10.1017/s0962492913000032 · Cited by 715 · see citing works
Bolte, J., Daniilidis, A., & Lewis, A. S. (2007) · SIAM Journal on Optimization · doi:10.1137/050644641 · Cited by 713 · see citing works
Consensus in Ad Hoc WSNs With Noisy Links—Part I: Distributed Estimation of Deterministic Signals
Schizas, I. D., Ribeiro, A., & Giannakis, G. B. (2007) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2007.906734 · Cited by 709 · see citing works
A Branch-and-Cut Algorithm for the Dial-a-Ride Problem
Cordeau, J. (2006) · Operations Research · doi:10.1287/opre.1060.0283 · Cited by 704 · see citing works
On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers
Deng, W., & Yin, W. (2015) · Journal of Scientific Computing · doi:10.1007/s10915-015-0048-x · Cited by 698 · see citing works
Quantum autoencoders for efficient compression of quantum data
Romero, J., Olson, J. P., & Aspuru-Guzik, A. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa8072 · Cited by 559 · see citing works
Ghadimi, E., Teixeira, A. M. H., Shames, I., & Johansson, M. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2354892 · Cited by 529 · see citing works
Fiacco, A. V., & McCormick, G. P. (1990) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971316 · Cited by 470 · see citing works
Fischetti, M., Glover, F., & Lodi, A. (2005) · Mathematical Programming · doi:10.1007/s10107-004-0570-3 · Cited by 404 · see citing works
Bin packing and cutting stock problems: Mathematical models and exact algorithms
Delorme, M., Iori, M., & Martello, S. (2016) · European Journal of Operational Research · doi:10.1016/j.ejor.2016.04.030 · Cited by 384 · see citing works
QAOA for Max-Cut requires hundreds of qubits for quantum speed-up
Guerreschi, G. G., & Matsuura, A. Y. (2019) · Scientific Reports · doi:10.1038/s41598-019-43176-9 · Cited by 337 · see citing works
Advances in Optimization and Numerical Analysis
Gómez, S., & Hennart, J.-P. (1994) · Springer eBooks · doi:10.1007/978-94-015-8330-5 · Cited by 327 · see citing works
Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem
Schöll, A., Klein, R., & Jürgens, C. (1997) · Computers & Operations Research · doi:10.1016/s0305-0548(96)00082-2 · Cited by 295 · 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
Splitting methods for monotone operators with applications to parallel optimization
Eckstein, J. (1989) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 250 · see citing works
Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM
Giselsson, P., & Boyd, S. (2016) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2016.2564160 · Cited by 229 · see citing works
Convergence Rate Analysis of Several Splitting Schemes
Davis, D., & Yin, W. (2016) · Scientific computation · doi:10.1007/978-3-319-41589-5_4 · Cited by 223 · see citing works
Sur la géométrie semi- et sous- analytique
Łojasiewicz, S. (1993) · Annales de l’institut Fourier · doi:10.5802/aif.1384 · Cited by 208 · 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
Performance 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
A feasibility pump heuristic for general mixed-integer problems
Bertacco, L., Fischetti, M., & Lodi, A. (2006) · Discrete Optimization · doi:10.1016/j.disopt.2006.10.001 · Cited by 154 · 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
Hong, M., Luo, Z.-Q. T., & Razaviyayn, M. (2015) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2015.7178689 · Cited by 152 · see citing works
A simple effective heuristic for embedded mixed-integer quadratic programming
Takapoui, R., Moehle, N., Boyd, S., & Bemporad, A. (2017) · International Journal of Control · doi:10.1080/00207179.2017.1316016 · Cited by 146 · see citing works
Performance of hybrid quantum-classical variational heuristics for combinatorial optimization
Nannicini, G. (2019) · Physical Review E · doi:10.1103/physreve.99.013304 · Cited by 138 · see citing works
Discrete optimization using quantum annealing on sparse Ising models
Bian, Z., Chudak, F. A., Israel, R. B., Lackey, B., Macready, W. G., & Roy, A. (2014) · Frontiers in Physics · doi:10.3389/fphy.2014.00056 · Cited by 129 · see citing works
Structured nonconvex and nonsmooth optimization: algorithms and iteration complexity analysis
Jiang, B., Lin, T., Ma, S., & Zhang, S. (2018) · Computational Optimization and Applications · doi:10.1007/s10589-018-0034-y · Cited by 128 · see citing works
p-Box ADMM: A Versatile Framework for Integer Programming
Wu, B., & Ghanem, B. (2018) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2018.2845842 · Cited by 125 · 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
A general system for heuristic minimization of convex functions over non-convex sets
Diamond, S., Takapoui, R., & Boyd, S. (2017) · Optimization methods & software · doi:10.1080/10556788.2017.1304548 · Cited by 109 · see citing works
Douglas--Rachford Splitting and ADMM for Nonconvex Optimization: Tight Convergence Results
Themelis, A., & Patrinos, P. (2020) · SIAM Journal on Optimization · doi:10.1137/18m1163993 · Cited by 104 · 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
A Bibliographical Survey On Some Well-Known Non-Standard Knapsack Problems
Lin, E. Y. H. (1998) · INFOR Information Systems and Operational Research · doi:10.1080/03155986.1998.11732364 · Cited by 88 · 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
A Hybrid Approach for Solving Optimization Problems on Small Quantum Computers
Shaydulin, R., Ushijima‐Mwesigwa, H., Negre, C. F. A., Safro, I., Mniszewski, S. M., & Alexeev, Y. (2019) · Computer · doi:10.1109/mc.2019.2908942 · Cited by 67 · 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
A stochastic programming model for a tactical solid waste management problem
Gambella, C., Maggioni, F., & Vigo, D. (2018) · European Journal of Operational Research · doi:10.1016/j.ejor.2018.08.005 · Cited by 64 · see citing works
Self-citationA note on the convergence of ADMM for linearly constrained convex optimization problems
Chen, L., Sun, D., & Toh, K.-C. (2016) · Computational Optimization and Applications · doi:10.1007/s10589-016-9864-7 · Cited by 57 · 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
Building an iterative heuristic solver for a quantum annealer
Rosenberg, G., Vazifeh, M. M., Woods, B., & Haber, E. (2016) · Computational Optimization and Applications · doi:10.1007/s10589-016-9844-y · Cited by 49 · see citing works
qTorch: The quantum tensor contraction handler
Fried, E., Sawaya, N. P. D., Cao, Y., Kivlichan, I., Romero, J., & Aspuru‐Guzik, A. (2018) · PLoS ONE · doi:10.1371/journal.pone.0208510 · Cited by 48 · see citing works
Tao, M., & Yuan, X. (2012) · SIAM Journal on Optimization · doi:10.1137/110847639 · Cited by 45 · see citing works
The distance constrained multiple vehicle traveling purchaser problem
Bianchessi, N., Mansini, R., & Speranza, M. G. (2013) · European Journal of Operational Research · doi:10.1016/j.ejor.2013.10.018 · Cited by 45 · see citing works
Karimi, H., Rosenberg, G., & Katzgraber, H. G. (2017) · Physical review. E · doi:10.1103/physreve.96.043312 · Cited by 37 · see citing works
C.A. Floudas, Nonlinear and Mixed-Integer Optimization. Fundamentals and Applications
Pistikopoulos, E. N. (1998) · Journal of Global Optimization · doi:10.1023/a:1008256302713 · Cited by 36 · see citing works
Unified theory of augmented Lagrangian methods for constrained global optimization
Wang, C., & Li, D. (2008) · Journal of Global Optimization · doi:10.1007/s10898-008-9347-1 · Cited by 36 · see citing works
Embedding Inequality Constraints for Quantum Annealing Optimization
Vyskočil, T., Pakin, S., & Djidjev, H. N. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-14082-3_2 · Cited by 36 · see citing works
Solving the asymmetric traveling purchaser problem
Riera‐Ledesma, J., & Salazar‐González, J. (2006) · Annals of Operations Research · doi:10.1007/s10479-006-0014-y · Cited by 34 · see citing works
Faster quantum and classical SDP approximations for quadratic binary optimization
Brandão, F. G. S. L., Kueng, R., & França, D. S. (2022) · Quantum · doi:10.22331/q-2022-01-20-625 · Cited by 32 · see citing works
Solving a class of continuous global optimization problems using quantum algorithms
Protopopescu, V., & Barhen, J. (2002) · Physics Letters A · doi:10.1016/s0375-9601(02)00187-1 · Cited by 29 · see citing works
Combinatorial Optimization on Gate Model Quantum Computers: A Survey
Zahedinejad, E., & Zaribafiyan, A. (2017) · arXiv · doi:10.48550/arxiv.1708.05294 · Cited by 29 · see citing works
Osogami, T., & Okano, H. (2003) · Journal of Heuristics · doi:10.1023/a:1021837611236 · Cited by 23 · see citing works
Alibaba Cloud Quantum Development Platform: Applications to Quantum Algorithm DesignPreprint
Huang, C., Szegedy, M., Zhang, F., Gao, X., Chen, J., & Shi, Y. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.02559 · Cited by 20 · see citing works
Exact and heuristic solution approaches for the mixed integer setup knapsack problem
Altay, N., Robinson, P., & Bretthauer, K. M. (2007) · European Journal of Operational Research · doi:10.1016/j.ejor.2007.07.003 · Cited by 17 · see citing works
Sun, K., & Sun, X. A. (2019) · arXiv (Cornell University) · Cited by 15 · see citing works
Multi-convex Inequality-constrained Alternating Direction Method of MultipliersPreprint
Wang, J., Zhao, L., & Wu, L. (2019) · arXiv (Cornell University) · Cited by 9 · see citing works
Performance Ratios for the Karmarkar-Karp Differencing Method
Michiels, W., Korst, J., Aarts, E., & Leeuwen, J. V. (2003) · Electronic Notes in Discrete Mathematics · doi:10.1016/s1571-0653(04)00442-1 · Cited by 7 · see citing works
Melo, J. G., & Monteiro, R. D. C. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1705.07229 · Cited by 6 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- R. Glowinski and A. Marrocco, "Sur l'approximation, par elements finis d'ordre un, et la resolution, par penalisation-dualité, d'une classe de problems de Dirichlet non lineares," Revue Francaise d'Automatique, Informatique, et Recherche Opérationelle, vol. 9, pp. 41-76, 1975.
- R. Nishihara, L. Lessard, B. Recht, A. Packard, and M. I. Jordan, "A general analysis of the convergence of ADMM," in Proc. Int. Conf. Mach. Learn., 2015, pp. 343-352, doi: 10.5555/3045118.3045156. · DOI
- H. Attouch, J. Bolte, and B. Svaiter, "Convergence of descent methods for semi-algebraic and tame problems: Proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods," Math. Program., vol. 137, nos. 1/2, pp. 91-129, 2013, doi: 10.1007/s10107-011-0484-9. · DOI
- S. Martello, Knapsack Problems: Algorithms and Computer Implementa- tions (Discrete Mathematics, Optimization). Hoboken, NJ, USA: Wiley, 1990, doi: 10.5555/98124. · DOI
Cited by
Sorted by citations
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-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
“Similarly, decomposition algorithms (such as splitting, or the alternating direction method of multipliers) for MIP often solve the QUBO subproblem using a quantum computer 125,126 , while solving the continuous subproblem classically.”
Ajagekar, A., & You, F. (2022) · Renewable and Sustainable Energy Reviews · doi:10.1016/j.rser.2022.112493 · Cited by 155 · see citing works
Formulating and Solving Routing Problems on Quantum Computers
Harwood, S., Gambella, C., Trenev, D., Simonetto, A., Bernal Neira, D., & Greenberg, D. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3049230 · Cited by 145 · see citing works
Self-citationQuantum computing for smart grid applications
Ullah, M. H., Eskandarpour, R., Zheng, H., & Khodaei, A. (2022) · IET Generation Transmission & Distribution · doi:10.1049/gtd2.12602 · Cited by 107 · see citing works
Novel Resolution of Unit Commitment Problems Through Quantum Surrogate Lagrangian Relaxation
Feng, F., Zhang, P., Bragin, M. A., & Zhou, Y. (2022) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2022.3181221 · 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
Adapting Quantum Approximation Optimization Algorithm (QAOA) for Unit Commitment
Koretsky, S., Gokhale, P., Baker, J. M., Viszlai, J., Zheng, H., Gurung, N., Burg, R., Paaso, E. A., Khodaei, A., Eskandarpour, R., et al. (2021) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00035 · Cited by 45 · see citing works
Perspectives of quantum computing for chemical engineering
Bernal, D. E., Ajagekar, A., Harwood, S. M., Stober, S. T., Trenev, D., & You, F. (2022) · AIChE Journal · doi:10.1002/aic.17651 · Cited by 46 · see citing works
Said, D., Bagaa, M., Oukaira, A., & Lakhssassi, A. (2024) · IEEE Access · doi:10.1109/access.2024.3441931 · Cited by 43 · see citing works
Exploring Potential Applications of Quantum Computing in Transportation Modelling
Cooper, C. (2021) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2021.3132161 · Cited by 34 · see citing works
Fu, W., Xie, H., Zhu, H., Wang, H., Jiang, L., Chen, C., & Bie, Z. (2023) · Energy · doi:10.1016/j.energy.2023.129314 · Cited by 31 · see citing works
NGENI, F. C., Mwakalonge, J., & Siuhi, S. (2024) · Journal of Traffic and Transportation Engineering (English Edition) · doi:10.1016/j.jtte.2023.05.006 · Cited by 25 · see citing works
Quantum Robustness Verification: A Hybrid Quantum-Classical Neural Network Certification Algorithm
Franco, N., Wollschläger, T., Gao, N., Lorenz, J. M., & Günnemann, S. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00033 · Cited by 23 · 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
“Similarly, Alternating Direction Method of Multipliers (ADMM) heuristics [169] have been utilized for such extensions to MBO problems, where the constraints are treated classically [50].”
BackgroundMethodInfluentialMahroo, R., & Kargarian, A. (2023) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2023.3320872 · Cited by 22 · see citing works
A hybrid quantum–classical algorithm for mixed-integer optimization in power systems
Ellinas, P., Chevalier, S. C., & Chatzivasileiadis, S. (2024) · Electric Power Systems Research · doi:10.1016/j.epsr.2024.110835 · Cited by 20 · see citing works
Hybrid Quantum-Classical Unit Commitment
Mahroo, R., & Kargarian, A. (2022) · IEEE Texas Power and Energy Conference (TPEC) · doi:10.1109/tpec54980.2022.9750763 · Cited by 19 · see citing works
Robust Dynamic TEP With an Security Criterion: A Computationally Efficient Model
Mahroo, R., Kargarian, A., Mehrtash, M., & Conejo, A. J. (2022) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2022.3163961 · Cited by 18 · see citing works
Quantum Path Integral Approach for Vehicle Routing Optimization With Limited Qubit
Gautam, K., & Ahn, C. W. (2023) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2023.3327157 · Cited by 19 · see citing works
Solving constrained optimization problems via the variational quantum eigensolver with constraints
Le, T. V., & Kekatos, V. (2024) · Physical Review A · doi:10.1103/physreva.110.022430 · Cited by 15 · see citing works
Quantum Computing Through the Lens of Control: A Tutorial Introduction
Berberich, J., & Fink, D. (2024) · IEEE Control Systems · doi:10.1109/mcs.2024.3466448 · Cited by 18 · see citing works
Operation of distribution network: Challenges and opportunities in the era of peer-to-peer trading
Razavi, S.-M., Haghifam, M., Arefizadeh, S., Larimi, S. M. M., & Shafie‐khah, M. (2024) · Energy Reports · doi:10.1016/j.egyr.2024.04.053 · Cited by 13 · see citing works
Quantum Computing for Stochastic Economic Dispatch in Renewables-Rich Power Systems
Han, X., Li, Z., Gu, W., & Shahidehpour, M. (2025) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2025.3573395 · Cited by 12 · see citing works
Quantum-Embedded Robust Optimization for Resilience-Constrained Unit Commitment
Fu, W., Xie, H., Chen, C., & Bie, Z. (2025) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2025.3534156 · Cited by 12 · see citing works
Variational Algorithms for Workflow Scheduling Problem in Gate-Based Quantum Devices
Plewa, J., Sieńko, J., & Rycerz, K. (2021) · Computing and Informatics · doi:10.31577/cai_2021_4_897 · Cited by 12 · see citing works
Quantum computing for software engineering: prospects
Miranskyy, A. V., Khan, M., Faye, J. P. L., & Mendes, U. C. (2022) · doi:10.1145/3549036.3562060 · Cited by 11 · see citing works
Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness
Franco, N., Wollschläger, T., Poggel, B., Günnemann, S., & Lorenz, J. M. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00066 · Cited by 10 · see citing works
Incentivizing Demand-Side Response Through Discount Scheduling Using Hybrid Quantum Optimization
Bucher, D., Nüßlein, J., O’Meara, C., Angelov, I. B., Wimmer, B., Ghosh, K., Cortiana, G., & Linnhoff–Popien, C. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3407236 · Cited by 12 · see citing works
Investigating an amplitude amplification-based optimization algorithm for model predictive control
Nieman, K., Durand, H., Patel, S., Koch, D., & Alsing, P. M. (2023) · Digital Chemical Engineering · doi:10.1016/j.dche.2023.100134 · Cited by 8 · see citing works
Quantum Annealing for Complex Optimization in Satellite Communication Systems
Dinh, T. Q., Dau, S. H., Lagunas, E., Chatzinotas, S., Nguyen, D. N., & Hoang, D. T. (2024) · IEEE Internet of Things Journal · doi:10.1109/jiot.2024.3481373 · Cited by 7 · see citing works
Optimizing Variational Circuits for Higher-Order Binary Optimization
Verchère, Z., Elloumi, S., & Simonetto, A. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00011 · Cited by 6 · see citing works
Self-citationQuantum Combinatorial Optimization Algorithms for Network Reconfiguration: QRAO vs. QAOA
Ngo, A. P., & Nguyen, H. T. (2024) · North American Power Symposium (NAPS) · doi:10.1109/naps61145.2024.10741660 · Cited by 6 · see citing works
Hybrid quantum-classical multi-cut Benders approach with a power system application
Paterakis, N. G. (2023) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2023.108161 · Cited by 6 · see citing works
A Quantum-aided Algorithm for Unit Commitment Problems
Yang, M., Gao, F., Wu, G., Gong, B., Cao, H., & Shuang, F. (2023) · Chinese Control Conference (CCC) · doi:10.23919/ccc58697.2023.10240915 · Cited by 6 · see citing works
On Quantum Computing for Mixed-Integer ProgrammingPreprint
Chang, C.-Y., Jones, E. B., & Graf, P. A. (2020) · arXiv (Cornell University) · Cited by 6 · see citing works
DC Optimal Power Flow in Unit Commitment Using Quantum Computing: An ADMM Approach
Magar, M. R., Pandit, D., Nguyen, D., & Nguyen, N. (2024) · North American Power Symposium (NAPS) · doi:10.1109/naps61145.2024.10741684 · Cited by 5 · see citing works
Atchade-Adelomou, P., Golobardes-Ribé, E., & Vilasis-Cardona, X. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.05863 · Cited by 6 · see citing works
Penalty-free approach to accelerating constrained quantum optimization
Bucher, D., Stein, J., Feld, S., & Linnhoff–Popien, C. (2025) · Physical Review A · doi:10.1103/fb5m-cl9m · Cited by 4 · see citing works
A Quantum Approach for Stochastic Constrained Binary Optimization
Gupta, S., & Kekatos, V. (2023) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp49357.2023.10097179 · Cited by 4 · see citing works
A Copositive Framework for Analysis of Hybrid Ising-Classical Algorithms
Brown, R., Bernal, D. E., Venturelli, D., & Pavone, M. (2024) · SIAM Journal on Optimization · doi:10.1137/22m1514581 · Cited by 9 · see citing works
Li, J., Mikada, H., & Takekawa, J. (2024) · Pure and Applied Geophysics · doi:10.1007/s00024-024-03449-5 · Cited by 3 · see citing works
Skills Required for Quantum Computing: A Comprehensive Review of Recent Studies
Juárez‐Ramírez, R., Jiménez, S., Cota, C. X. N., García, C. A. G., Pérez‐González, H. G., Fernández-y-Fernández, C. A., Ortiz-Hernández, J., & Villatoro, K. C. (2024) · Programming and Computer Software · doi:10.1134/s0361768824700804 · Cited by 4 · see citing works
A Constraint Programming Approach for QUBO Solving and Quantum Annealing
Codognet, P. (2024) · International Conference on Art, Science, and Engineering of Programming (<Programming>) · doi:10.1145/3660829.3660850 · Cited by 2 · see citing works
A Distributed Variational Quantum Eigensolver Algorithm for Unit Commitment
Hasanzadeh, M., Rajabi, A., & Kargarian, A. (2026) · 2026 IEEE Texas Power and Energy Conference (TPEC) · doi:10.1109/tpec67884.2026.11513141 · Cited by 7 · see citing works
Quantum-based Distributed Algorithms for Edge Node Placement and Workload Allocation
Do, D., Trieu, N., & Nguyen, D. T. (2023) · IEEE Cloud Summit · doi:10.1109/cloudsummit57601.2023.00015 · Cited by 2 · see citing works
Alonso, M., Martínez, R., Díez-Valle, P., Garbayo, A., García‐Santiago, X., & Gil, G. B. (2025) · IEEE Access · doi:10.1109/access.2025.3578780 · Cited by 2 · see citing works
Evaluate Quantum Combinatorial Optimization for Distribution Network Reconfiguration
Ngo, A. P., Thomas, C., Nguyen, H. T., Eroglu, A., & Oikonomou, K. (2022) · North American Power Symposium (NAPS) · doi:10.1109/naps56150.2022.10012259 · Cited by 2 · see citing works
Quantum Computing: A Bubble Ready to Burst or a Looming Breakthrough?Preprint
Bruno, G. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4462929 · Cited by 2 · see citing works
Graph Coarsening Approach to the Vehicle Routing Problem: An Approximation Strategy
Nałęcz-Charkiewicz, K., Das, A., Chatterjee, T., Keene, J., Góra, P., & Kuhn, C. C. N. (2025) · IEEE Access · doi:10.1109/access.2025.3534677 · Cited by 1 · see citing works
Yu, X. W., Xie, H., & Fu, W. (2025) · iEnergy · doi:10.23919/ien.2025.0009 · Cited by 1 · see citing works
Benchmarking the Maritime Inventory Routing Problem on a Quantum Annealing-Hybrid System
Szal, O., Rubbert, S., & Rizvanolli, A. (2025) · TransNav the International Journal on Marine Navigation and Safety of Sea Transportation · doi:10.12716/1001.19.01.14 · Cited by 1 · see citing works
Power-Aware Orchestration for Geo-Distributed LLM Inference via Quantum Optimization
Zheng, X., Min, J., Luo, L., Yu, H., & Li, Z. (2026) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2026.3704855 · Cited by 1 · see citing works
ADMM-Based Distributed Routing and Rebalancing for Autonomous Mobility on Demand Systems
Kim, H., Jeong, H.-M., & Han-lim Choi, A. (2021) · IEEE International Conference on Automation Science and Engineering (CASE) · doi:10.1109/case49439.2021.9551505 · Cited by 1 · see citing works
Pooja, H. M., Nayana, M. G., & Triveni, C. L. (2021) · IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT) · doi:10.1109/conecct52877.2021.9622719 · Cited by 1 · see citing works
Design and Implementation of a Quantum Computing-Based Financial Portfolio Optimization SystemPreprint
Jose, S., Prasad, A. B., Laxmi, K. V., Joshi, P. V., & Kumar, V. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5086647 · Cited by 1 · see citing works
QAOA-based Day-ahead Clearing Model for Electricity Spot Market
Pan, D., Yang, N., Wang, B., Jia, J., Cao, Z., & Zhang, D. (2024) · International Conference on Energy, Power and Grid (ICEPG) · doi:10.1109/icepg63230.2024.10775663
An Efficient Hybrid Classical Quantum Algorithm for Mixed-Integer Constrained Optimization
Surana, A. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.10385
Gholami, A., Nezamoddini, N., & Khasawneh, M. T. (2026) · Analytics · doi:10.3390/analytics5010013
Yang, X., Zhou, F., & Xu, R. (2026) · Journal of Physics Conference Series · doi:10.1088/1742-6596/3236/1/012022
- Authors
- Gambella, C., & Simonetto, A.
- Affiliations
- IBM Research - Ireland (IE)
- Venue
- IEEE Transactions on Quantum Engineering
- Published
- 2020
- Volume
- 1
- Pages
- 1-22
- ISSN
- 2689-1808 (ISSN-L)
- OpenAlex
- W3000028936
- Cited by
- 60
- References
- 79
- Citations by year
- 2026: 4 · 2025: 9 · 2024: 16 · 2023: 13 · 2022: 9 · 2021: 6 · 2020: 3
- FWCI
- 3.04
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- IEEE Transactions on Quantum Engineering (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- alternating direction method of multipliers, variational quantum eigensolver, quantum approximate optimization algorithm, decomposition-based optimization, noisy quantum devices, combinatorial optimization, Qiskit
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
