Formulating and Solving Routing Problems on Quantum Computers
Open accessAbstract
The determination of vehicle routes fulfilling connectivity, time, and operational constraints is a well-studied combinatorial optimization problem. The NP-hard complexity of vehicle routing problems has fostered the adoption of tailored exact approaches, matheuristics, and metaheuristics on classical computing devices. The ongoing evolution of quantum computing hardware and the recent advances of quantum algorithms (i.e., VQE, QAOA, and ADMM) for mathematical programming make decision-making for routing problems an avenue of research worthwhile to be explored on quantum devices. In this article, we propose several mathematical formulations for inventory routing cast as vehicle routing with time windows and comment on their strengths and weaknesses. The optimization models are compared from a quantum computing perspective, specifically with metrics to evaluate the difficulty in solving the underlying quadratic unconstrained binary optimization problems. Finally, the solutions obtained on simulated quantum devices demonstrate the relative benefits of different algorithms and their robustness when put into practice.
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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 [61]
In “Sequence-Based Formulation With Continuous Time,” the paper says that some inexactness in ADMM is beneficial for overall solution quality and notes that quantum computations are affected by errors and noise. It does not establish that adding noise to the quantum solver itself improves the final solution. (LLM, conf=0.82)
Experimental — accuracy not yet measured
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Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
Integer and Combinatorial Optimization
Williams, H. P., Nemhauser, G. L., & Wolsey, L. A. (1990) · Journal of the Operational Research Society · doi:10.2307/2583737 · Cited by 5,526 · 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 1× · see citing works
“Variational algorithms such as the quantum approximate optimization algorithm (QAOA) [11] and variational quantum eigensolver (VQE) [12] can be implemented on current gate-based devices.”
MethodInteger and Combinatorial Optimization
Nemhauser, G. L., & Wolsey, L. A. (1988) · Wiley eBooks · doi:10.1002/9781118627372 · Cited by 3,180 · see citing works
Conn, A. R., Gould, N. I. M., & Toint, P. L. (2000) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719857 · Cited by 3,023 · see citing works
Hardware-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
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
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
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
Fiacco, A. V., & McCormick, G. P. (1968) · Defense Technical Information Center (DTIC) · Cited by 2,270 · 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
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
Self-citationQiskit: 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
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
A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows
Desrochers, M., Desrosiers, J., & Solomon, M. (1992) · Operations Research · doi:10.1287/opre.40.2.342 · Cited by 1,204 · 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
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
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
A fully programmable 100-spin coherent Ising machine with all-to-all connections
McMahon, P. L., Marandi, A., Haribara, Y., Hamerly, R., Langrock, C., Tamate, S., Inagaki, T., Takesue, H., Utsunomiya, S., Aihara, K., et al. (2016) · Science · doi:10.1126/science.aah5178 · Cited by 700 · see citing works
Baldacci, R., Mingozzi, A., & Roberti, R. (2011) · European Journal of Operational Research · doi:10.1016/j.ejor.2011.07.037 · Cited by 480 · 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
Quantum Supremacy through the Quantum Approximate Optimization Algorithm
Farhi, E., & Harrow, A. W. (2016) · arXiv · doi:10.48550/arxiv.1602.07674 · Cited by 331 · 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
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
Intrinsic optimization using stochastic nanomagnets
Sutton, B., Camsari, K. Y., Behin‐Aein, B., & Datta, S. (2017) · Scientific Reports · doi:10.1038/srep44370 · Cited by 245 · see citing works
A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer
Feld, S., Roch, C., Gabor, T., Seidel, C., Neukart, F., Galter, I. R., Mauerer, W., & Linnhoff–Popien, C. (2019) · Frontiers in ICT · doi:10.3389/fict.2019.00013 · 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
Formulations and exact algorithms for the vehicle routing problem with time windows
Kallehauge, B. (2007) · Computers & Operations Research · doi:10.1016/j.cor.2006.11.006 · Cited by 177 · 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
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
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
Papageorgiou, D. J., Nemhauser, G. L., Sokol, J. S., Cheon, M.-S., & Keha, A. B. (2013) · European Journal of Operational Research · doi:10.1016/j.ejor.2013.12.013 · Cited by 103 · see citing works
An Accelerator Architecture for Combinatorial Optimization Problems
Tsukamoto, S., Motomu, T., Matsubara, S., & Hirotaka, T. (2017) · Fujitsu Scientific and Technical Journal · Cited by 91 · see citing works
Quantum Annealing of Vehicle Routing Problem with Time, State and Capacity
Irie, H., Wongpaisarnsin, G., Terabe, M., Miki, A., & Taguchi, S. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-14082-3_13 · Cited by 81 · see citing works
Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers
Gambella, C., & Simonetto, A. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.3033139 · Cited by 60 · see citing works
Self-citationQuantum 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
Constructing SAT Filters with a Quantum Annealer
Douglass, A., King, A. D., & Raymond, J. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-24318-4_9 · Cited by 40 · see citing works
Efficient Analog Circuits for Boolean Satisfiability
Yin, X., Sedighi, B., Varga, M., Ercsey-Ravasz, M., Toroczkai, Z., & Hu, X. S. (2017) · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · doi:10.1109/tvlsi.2017.2754192 · Cited by 39 · 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
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
Pillay, N., & Qu, R. (2018) · Natural computing series · doi:10.1007/978-3-319-96514-7_7 · Cited by 26 · see citing works
Recent Progress Using Matheuristics for Strategic Maritime Inventory Routing
Papageorgiou, D. J., Cheon, M.-S., Harwood, S. M., Trespalacios, F., & Nemhauser, G. L. (2017) · Intelligent systems reference library · doi:10.1007/978-3-319-61801-2_3 · Cited by 22 · see citing works
Self-citationDesigning Adiabatic Quantum Optimization: A Case Study for the Traveling Salesman ProblemPreprint
Heim, B., Brown, E., Wecker, D., & Troyer, M. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1702.06248 · Cited by 11 · see citing works
Adiabatic quantum optimization
(2018) · Physics Subject Headings (PhySH) · doi:10.29172/f4eda6e0-9440-429d-814e-2e368b9b5f8a · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- United Nations, "Review of maritime transport," United Nations, New York, NY, USA, Tech. Rep. UNCTAD/RMT/2018, 2018.
Cited by
Sorted by citations
Quantum computing challenges in the software industry. A fuzzy AHP-based approach
Awan, U., Hannola, L., Tandon, A., Goyal, R. K., & Dhir, A. (2022) · Information and Software Technology · doi:10.1016/j.infsof.2022.106896 · Cited by 153 · see citing works
Exploring the Advantages of Quantum Generative Adversarial Networks in Generative Chemistry
Kao, P.-Y., Yang, Y.-C., Chiang, W.-Y., Hsiao, J.-Y., Cao, Y., Aliper, A., Ren, F., Aspuru‐Guzik, A., Zhavoronkov, A. A., Hsieh, M.-H., et al. (2023) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.3c00562 · Cited by 101 · see citing works
A Systematic Literature Review of Quantum Computing for Routing Problems
Osaba, E., Villar-Rodríguez, E., & Oregi, I. (2022) · IEEE Access · doi:10.1109/access.2022.3177790 · Cited by 82 · see citing works
Contemporary Quantum Computing Use Cases: Taxonomy, Review and Challenges
Singh, J., & Bhangu, K. S. (2022) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-022-09809-5 · Cited by 53 · see citing works
The MQT Handbook : A Summary of Design Automation Tools and Software for Quantum Computing
Wille, R., Berent, L., Forster, T., Kunasaikaran, J., Mato, K., Peham, T., Quetschlich, N., Rovara, D., Sander, A., Schmid, L., et al. (2024) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw62656.2024.00013 · Cited by 54 · 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
A Survey on Available Tools and Technologies Enabling Quantum Computing
Singh, P., Dasgupta, R., Singh, A., Pandey, H., Hassija, V., Chamola, V., & Sikdar, B. (2024) · IEEE Access · doi:10.1109/access.2024.3388005 · Cited by 51 · see citing works
Quinton, F. A., Myhr, P. A. S., Barani, M., Crespo del Granado, P., & Zhang, H. (2025) · Scientific Reports · doi:10.1038/s41598-025-96220-2 · Cited by 46 · 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
Self-citationApplying quantum approximate optimization to the heterogeneous vehicle routing problem
Fitzek, D., Ghandriz, T., Laine, L., Granath, M., & Kockum, A. F. (2024) · Scientific Reports · doi:10.1038/s41598-024-76967-w · Cited by 49 · see citing works
MQT QMAP: Efficient Quantum Circuit Mapping
Wille, R., & Burgholzer, L. (2023) · Proceedings of the 2023 International Symposium on Physical Design · doi:10.1145/3569052.3578928 · Cited by 41 · see citing works
Quantum Key Distribution Protocol Selector Based on Machine Learning for Next-Generation Networks
Okey, O. D., Maidin, S. S., Rosa, R. L., Toor, W. T., Carrillo, D., Wuttisittikulkij, L., Saadi, M., & Rodríguez, D. Z. (2022) · Sustainability · doi:10.3390/su142315901 · Cited by 41 · see citing works
Quantum Technologies for Beyond 5G and 6G Networks: Applications, Opportunities, and Challenges
Zeydan, E., de Alwis, C., Khan, R., Türk, Y., Aydeger, A., Gadekallu, T. R., & Liyanage, M. (2025) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2025.3591842 · Cited by 49 · see citing works
Mohanty, N., Behera, B. K., & Ferrie, C. (2023) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2023.3303989 · Cited by 37 · 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
New frontiers of quantum computing in chemical engineering
Ajagekar, A., & You, F. (2022) · Korean Journal of Chemical Engineering · doi:10.1007/s11814-021-1027-6 · Cited by 38 · see citing works
Urgelles, H., Picazo-Martínez, P., García‐Roger, D., & Monserrat, J. F. (2022) · Sensors · doi:10.3390/s22197570 · Cited by 36 · see citing works
Quantum Computing in Supply Chain Management State of the Art and Research Directions
Gachnang, P., Ehrenthal, J. C. F., Hanne, T., & Dornberger, R. (2022) · Asian Journal of Logistics Management · doi:10.14710/ajlm.2022.14325 · Cited by 47 · see citing works
Bouchmal, O., Cimoli, B., Stabile, R., Olmos, J. J. V., & Monroy, I. T. (2023) · Frontiers in Communications and Networks · doi:10.3389/frcmn.2023.1220227 · Cited by 37 · see citing works
Predicting Good Quantum Circuit Compilation Options
Quetschlich, N., Burgholzer, L., & Wille, R. (2023) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw59989.2023.00015 · Cited by 30 · see citing works
Variational Quantum Algorithms for the Allocation of Resources in a Cloud/Edge Architecture
Mastroianni, C., Plastina, F., Settino, J., & Vinci, A. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3398410 · Cited by 27 · see citing works
The Quantum Internet: Enhancing Classical Internet Services One Qubit at A Time
Cacciapuoti, A. S., Illiano, J., Koudia, S., Simonov, K., & Caleffi, M. (2022) · IEEE Network · doi:10.1109/mnet.001.2200162 · Cited by 26 · see citing works
An integrated coupled oscillator network to solve optimization problems
Graber, M., & Hofmann, K. (2024) · Communications Engineering · doi:10.1038/s44172-024-00261-w · Cited by 25 · see citing works
A scientometric analysis of quantum driven innovations in intelligent transportation systems
Monika, & Sood, S. K. (2024) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2024.109258 · Cited by 27 · see citing works
Maritime inventory routing: recent trends and future directions
Fagerholt, K., Hvattum, L. M., Papageorgiou, D. J., & Urrutia, S. A. (2023) · International Transactions in Operational Research · doi:10.1111/itor.13313 · 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
“The CO problems that have been studied in this context are the vehicle routing problem with time windows [61] on gate-based devices; the job-shop scheduling problem [156], the maximum k-colorable subgraph problem [113], as well as the 3-SAT problem [80] on quantum annealers; and the graph…”
BackgroundOhyama, T., Kawamoto, Y., & Kato, N. (2022) · IEEE Transactions on Emerging Topics in Computing · doi:10.1109/tetc.2022.3161542 · Cited by 22 · see citing works
Calibrating the role of entanglement in variational quantum circuits
Nakhl, A. C., Quella, T., & Usman, M. (2024) · Physical Review A · doi:10.1103/physreva.109.032413 · Cited by 22 · see citing works
Leonidas, I. D., Dukakis, A., Tan, B. Y. L., & Angelakis, D. G. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202300309 · Cited by 24 · see citing works
Approximate Boltzmann distributions in quantum approximate optimization
Lotshaw, P. C., Siopsis, G., Ostrowski, J., Herrman, R., Alam, R., Powers, S., & Humble, T. S. (2023) · Physical Review A · doi:10.1103/physreva.108.042411 · Cited by 18 · see citing works
Transfer of Logistics Optimizations to Material Flow Resource Optimizations using Quantum Computing
Pfister, R., Schubert, G., & Kröll, M. (2024) · Procedia Computer Science · doi:10.1016/j.procs.2024.01.004 · Cited by 18 · see citing works
A Collaborative Neurodynamic Algorithm for Quadratic Unconstrained Binary Optimization
Li, H., & Wang, J. (2024) · IEEE Transactions on Emerging Topics in Computational Intelligence · doi:10.1109/tetci.2024.3405370 · Cited by 18 · see citing works
Fermionic 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
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
Li, M., Wang, S., Fan, L., & Han, Z. (2025) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2025.3527970 · Cited by 15 · see citing works
Singh, A., Prakash, S., & Singh, S. (2022) · Concurrency and Computation Practice and Experience · doi:10.1002/cpe.6960 · Cited by 15 · 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
Readout error mitigated quantum state tomography tested on superconducting qubits
Aasen, A. S., Giovanni, A. D., Rotzinger, H., Ustinov, A. V., & Gärttner, M. (2024) · Communications Physics · doi:10.1038/s42005-024-01790-8 · Cited by 15 · see citing works
Simulations of frustrated Ising Hamiltonians using quantum approximate optimization
Lotshaw, P. C., Xu, H., Khalid, B., Buchs, G., Humble, T. S., & Banerjee, A. (2022) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2021.0414 · Cited by 15 · see citing works
Using quantum computing to solve the maximal covering location problem
Giraldo-Quintero, A., Pulido, J. G. L., Duque, J. C., & Sierra-Sosa, D. (2022) · Computational Urban Science · doi:10.1007/s43762-022-00070-x · Cited by 13 · see citing works
Utilizing Resource Estimation for the Development of Quantum Computing Applications
Quetschlich, N., Soeken, M., Murali, P., & Wille, R. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00036 · Cited by 16 · see citing works
QOPTLib: A Quantum Computing Oriented Benchmark for Combinatorial Optimization Problems
Osaba, E., & Villar-Rodríguez, E. (2023) · Springer tracts in nature-inspired computing · doi:10.1007/978-981-99-3970-1_4 · Cited by 13 · see citing works
Solving the vehicle routing problem via quantum support vector machines
Mohanty, N., Behera, B. K., & Ferrie, C. (2024) · Quantum Machine Intelligence · doi:10.1007/s42484-024-00161-4 · Cited by 13 · see citing works
Peddada, S. R. T., Zeidner, L., Ilieş, H., James, K. A., & Allison, J. T. (2022) · Journal of Mechanical Design · doi:10.1115/1.4055055 · Cited by 12 · see citing works
The interactive system of Bloch sphere for quantum computing education
Liao, Y.-P., Cheng, Y.-L., Zhang, Y.-T., Wu, H., & Lu, R.-C. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00097 · Cited by 12 · see citing works
Quantum computing for several AGV scheduling models
Tang, L. B., Yang, C., Wen, K., Wu, W., & Guo, Y. (2024) · Scientific Reports · doi:10.1038/s41598-024-62821-6 · Cited by 12 · see citing works
Quantum Speedup for Index Modulation
Ishikawa, N. (2021) · IEEE Access · doi:10.1109/access.2021.3103207 · Cited by 12 · see citing works
Quantum Approximate Optimization Algorithm for Routing Optimization in 6G Optical Networks
Bouchmal, O., Cimoli, B., Stabile, R., Olmos, J. J. V., & Monroy, I. T. (2024) · International Conference on Optical Network Design and Modeling (ONDM) · doi:10.23919/ondm61578.2024.10582687 · Cited by 10 · see citing works
Hybrid Quantum Tabu Search for Solving the Vehicle Routing Problem
Holliday, J. B., Morgan, B., Churchill, H., & Luu, K. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.10305 · Cited by 10 · see citing works
Review of quantum algorithms for medicine, finance and logistics
Ciacco, A., Guerriero, F., & Macrina, G. (2025) · Soft Computing · doi:10.1007/s00500-025-10540-z · Cited by 12 · see citing works
Review of the application of quantum annealing-related technologies in transportation optimization
Mohammed, M. Q., Meeß, H., & Otte, M. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04870-y · Cited by 10 · see citing works
How to Approximate any Objective Function via Quadratic Unconstrained Binary Optimization
Gabor, T., Lingsch-Rosenfeld, M., Linnhoff–Popien, C., & Feld, S. (2022) · IEEE International Conference on Software Analysis, Evolution and Reengineering (SANER) · doi:10.1109/saner53432.2022.00149 · Cited by 12 · see citing works
Hybrid Quantum-Classical Heuristic to Solve Large-Scale Integer Linear Programs
Svensson, M., Andersson, M., Grönkvist, M., Vikstål, P., Dubhashi, D., Ferrini, G., & Johansson, G. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.20.034062 · Cited by 15 · see citing works
Quantum Game Theory-Based Cloud Resource Allocation: A Novel Approach
Bandyopadhyay, A., Choudhary, U., Tiwari, V., Mukherjee, K., Turjya, S. M., Ahmad, N., Haleem, A., & Mallik, S. (2025) · Mathematics · doi:10.3390/math13091392 · Cited by 9 · see citing works
Quantum-inspired optimization for wavelength assignment
Boev, A. S., Usmanov, S. R., Semenov, A. M., Ushakova, M. M., Salahov, G. V., Mastiukova, A. S., Kiktenko, E. O., & Fedorov, A. K. (2023) · Frontiers in Physics · doi:10.3389/fphy.2022.1092065 · Cited by 11 · see citing works
Quantum Computing in Transportation Engineering: A Survey
Somvanshi, S., Islam, M. M., Polock, S. B. B., Chhetri, G., Anderson, D., Anandi, D., & Das, S. (2026) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2026.3662626 · Cited by 8 · see citing works
Oscillator-based optimization: design, emulation, and implementation
Beattie, B. A., Noll, M., Kohlstedt, H., & Ochs, K. (2024) · The European Physical Journal B · doi:10.1140/epjb/s10051-023-00644-6 · Cited by 8 · see citing works
Cadeliña, A. R., Cuevas, M. A., Kallos, M., Montemayor, M. J., Uy, R. J., Rodriguez, J. B., & Tubola, O. D. (2024) · ECTI Transactions on Computer and Information Technology (ECTI-CIT) · doi:10.37936/ecti-cit.2024181.253577 · Cited by 8 · see citing works
Solving Logistic-Oriented Bin Packing Problems Through a Hybrid Quantum-Classical Approach
Romero, S. V., Osaba, E., Villar-Rodríguez, E., & Asla, A. (2023) · IEEE International Conference on Intelligent Transportation Systems (ITSC) · doi:10.1109/itsc57777.2023.10422581 · Cited by 9 · see citing works
Exponential qubit reduction in optimization for financial transaction settlement
Huber, E. X., Tan, B. Y. L., Griffin, P., & Angelakis, D. G. (2024) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-024-00262-w · Cited by 9 · see citing works
Alleviating the quantum Big-M problem
Alessandroni, E., Ramos-Calderer, S., Roth, I., Traversi, E., & Aolita, L. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01067-0 · Cited by 11 · 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
Soleimani, A., Dolatabadi, S. H. H., Heidari, M., Khorrami, B. M., & Luo, Y. (2023) · Preprints.org · doi:10.20944/preprints202310.0415.v1 · Cited by 8 · see citing works
Quantum computing approach for multi-objective routing and spectrum assignment optimization
Bouchmal, O., Cimoli, B., Stabile, R., Olmos, J. J. V., Hernández-Chulde, C., Martínez, R., Casellas, R., & Monroy, I. T. (2025) · Journal of Optical Communications and Networking · doi:10.1364/jocn.552061 · Cited by 7 · see citing works
Application of Grover’s Algorithm in Route Optimization
Bogatyrev, V. A., & Moskvin, V. S. (2023) · Intelligent Technologies and Electronic Devices in Vehicle and Road Transport Complex (TIRVED) · doi:10.1109/tirved58506.2023.10332621 · Cited by 7 · see citing works
Quantum Computing in Civil Engineering: Potentials and Limitations
Ploennigs, J., Berger, M., Mevissen, M., & Smarsly, K. (2025) · Lecture Notes in Civil Engineering · doi:10.1007/978-3-031-87364-5_2 · Cited by 7 · see citing works
A Multifaceted Analysis of Intelligent Vehicle Route Optimization
Pooja, & Sood, S. K. (2025) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2025.3528961 · Cited by 6 · see citing works
Pham, V., Huynh, D. V., Ak, E., Nguyen, L. D., Canberk, B., Dobre, O. A., & Duong, T. Q. (2025) · IEEE Internet of Things Journal · doi:10.1109/jiot.2025.3592874 · Cited by 6 · see citing works
Applications of quantum computing to optimization
Sotelo, R. (2021) · IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON) · doi:10.1109/chilecon54041.2021.9703081 · Cited by 6 · see citing works
Quantum Technologies for Space and Aerial Vehicles
Landers, V. S. (2024) · Space Law and Policy · doi:10.1007/978-3-031-62228-1_4 · Cited by 7 · see citing works
Exploring the Versatility of QAOA: A Comprehensive Review
Kashapogu, R., Hasib, S., & Rasool, A. (2024) · International Conference on Computing, Communication and Networking Technologies (ICCCNT) · doi:10.1109/icccnt61001.2024.10725610 · Cited by 6 · see citing works
Quantum 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
Solving the Element Detecting Problem in Graphs via Quantum Walk Search Algorithm (QWSA)
Gill, S. K., Kaur, G., Shankar, G., & Veeramanickam (2023) · Lecture notes in networks and systems · doi:10.1007/978-981-19-7982-8_36 · Cited by 6 · see citing works
Utilizing modern computer architectures to solve mathematical optimization problems: A survey
Bernal, D. E., Laird, C. D., Lueg, L. R., Harwood, S. M., Trenev, D., & Venturelli, D. (2024) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2024.108627 · Cited by 6 · see citing works
Self-citationPedagogical Approach for Quantum Computing in Engineering Education
Orts, F. J. (2025) · Computer Applications in Engineering Education · doi:10.1002/cae.70004 · Cited by 5 · see citing works
Goel, M., Singh, J., & Bairwa, A. K. (2025) · IEEE Access · doi:10.1109/access.2025.3606531 · Cited by 5 · see citing works
Multi-Objective Routing Optimization Using Coherent Ising Machine in Wireless Multihop Networks
Lin, Y., Xu, C., & Wang, C. X. (2025) · International Conference on Communications · doi:10.1109/icc52391.2025.11162085 · Cited by 5 · see citing works
Towards Equivalence Checking of Classical Circuits Using Quantum Computing
Quetschlich, N., Forster, T. V., Osterwind, A., Helms, D., & Wille, R. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00040 · Cited by 5 · see citing works
Resource Optimization of SFC Embedding for IoT Networks Using Quantum Computing
Emu, M., Choudhury, S., & Salomaa, K. (2022) · IEEE International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD) · doi:10.1109/camad55695.2022.9966892 · Cited by 5 · see citing works
Quantum Computing Empowered Metaverse: An Approach for Resource Optimization
Emu, M., Choudhury, S., & Salomaa, K. (2023) · International Conference on Communications · doi:10.1109/icc45041.2023.10278858 · Cited by 5 · see citing works
Reducing the Compilation Time of Quantum Circuits Using Pre-Compilation on the Gate Level
Quetschlich, N., Burgholzer, L., & Wille, R. (2023) · International Conference on Quantum Computing and Engineering · doi:10.1109/qce57702.2023.00091 · Cited by 10 · see citing works
Quantum computing in the automotive industry: survey, challenges, and perspectives
Arshad, M. W., & Lodi, S. (2025) · The Journal of Supercomputing · doi:10.1007/s11227-025-07573-4 · Cited by 4 · see citing works
Stade, Y., Burgholzer, L., & Wille, R. (2025) · International Conference for High Performance Computing, Networking, Storage and Analysis (SC) · doi:10.1145/3731599.3767546 · Cited by 6 · see citing works
Abdel‐Aty, A., Omri, M., Mohamed, A. ‐. A., & Rmili, H. (2023) · Alexandria Engineering Journal · doi:10.1016/j.aej.2023.05.013 · Cited by 4 · see citing works
Case-Based and Quantum Classification for ERP-Based Brain–Computer Interfaces
Cattan, G., & Quemy, A. (2023) · Brain Sciences · doi:10.3390/brainsci13020303 · Cited by 5 · see citing works
Warm and Cold Start Quantum Annealing for Metaverse Resource Optimization
Emu, M., Choudhury, S., & Salomaa, K. (2024) · IEEE Open Journal of the Communications Society · doi:10.1109/ojcoms.2024.3359188 · 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
The Second Quantum Revolution: Unexplored Facts and Latest News
Intonti, K., Viscardi, L., Lamberti, V., Matteucci, A., Micciola, B., Modestino, M. R., & Noce, C. (2024) · Encyclopedia · doi:10.3390/encyclopedia4020040 · Cited by 8 · see citing works
Osaba, E., Villar-Rodriguez, E., Miranda-Rodríguez, P., & Asla, A. (2025) · International Conference on Quantum Computing and Engineering · doi:10.1109/qce65121.2025.00228 · Cited by 2 · see citing works
Research on Qubit Mapping Technique Based on Batch SWAP Optimization
Li, H., Lü, K., Han, Z., Qin, H., Ju, M., & Liu, S. (2023) · International Journal of Advanced Computer Science and Applications · doi:10.14569/ijacsa.2023.0141217 · Cited by 3 · see citing works
Emu, M., Rahman, T., Choudhury, S., & Salomaa, K. (2024) · IEEE Open Journal of the Computer Society · doi:10.1109/ojcs.2024.3513237 · Cited by 3 · see citing works
Joint Optimal Design for Speed and Routing in Maritime Logistics with Quantum Optimization
Pham, V., Huynh, D. V., McNiven, B. D. E., Canberk, B., Dobre, O. A., & Duong, T. Q. (2025) · International Conference on Quantum Communications, Networking, and Computing (QCNC) · doi:10.1109/qcnc64685.2025.00053 · Cited by 3 · see citing works
Scaling Vehicle Routing Problem Solvers with QUBO-based Specialized Hardware
Xu, H., Ushijima‐Mwesigwa, H., & Ghosh, I. (2022) · IEEE/ACM Symposium on Edge Computing (SEC) · doi:10.1109/sec54971.2022.00056 · Cited by 3 · see citing works
Experimental Demonstration of Fermionic QAOA with One-Dimensional Cyclic Driver Hamiltonian
Yoshioka, T., Sasada, K., Nakano, Y., & Fujii, K. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00041 · Cited by 3 · see citing works
Accelerating Continuous Variable Coherent Ising Machines via Momentum
Brown, R., Venturelli, D., Pavone, M., & Bernal, D. E. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-60597-0_8 · Cited by 5 · see citing works
Banerjee, A., Bej, P., Mukherjee, A., Naik, S. G., Alimuddin, M., & Banik, M. (2024) · APL Quantum · doi:10.1063/5.0204288 · Cited by 3 · see citing works
Quantum Approaches to Sustainable Resource Management in Supply Chains
Thiyagarajan, S., Thangadurai, J. S., Mohana Priya, T., & Rajendran, R. K. (2024) · Advances in logistics, operations, and management science book series · doi:10.4018/979-8-3693-4107-0.ch013 · Cited by 3 · see citing works
Applying analog quantum computing to solve optimisation problems: case studies on Max-Cut and CVRP
Deleplanque, S., Yaagoubi, A. E., Gras, T., Descamps, F., Mourrier, J., & Lefebvre, I. (2025) · International Journal of Systems Science Operations & Logistics · doi:10.1080/23302674.2025.2463530 · Cited by 3 · see citing works
Svensson, M., Andersson, M., Grönkvist, M., Vikstål, P., Dubhashi, D., Ferrini, G., & Johansson, G. (2021) · arXiv (Cornell University) · Cited by 3 · see citing works
- Authors
- Harwood, S., Gambella, C., Trenev, D., Simonetto, A., Bernal Neira, D., & Greenberg, D.
- Affiliations
- ExxonMobil (United States) (US)
- IBM (Ireland) (IE)
- Quantum Computing Group, Carnegie Mellon University, Pittsburgh, PA, USA
- IBM (United States) (US)
- Venue
- IEEE Transactions on Quantum Engineering
- Published
- 2021
- Volume
- 2
- Pages
- 1-17
- ISSN
- 2689-1808 (ISSN-L)
- OpenAlex
- W3124206520
- Cited by
- 145
- References
- 42
- Citations by year
- 2026: 17 · 2025: 34 · 2024: 37 · 2023: 31 · 2022: 21 · 2021: 5
- FWCI
- 12.15
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- IEEE Transactions on Quantum Engineering (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- International Business Machines Corporation
- Topics
- Physical Sciences › Engineering › Industrial and Manufacturing Engineering › Vehicle Routing Optimization Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Keywords
- vehicle routing, inventory routing problem, vehicle routing problem with time windows, quantum computing, QUBO, variational quantum eigensolver, alternating direction method of multipliers, combinatorial optimization, mathematical programming formulation
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