Grover Adaptive Search for Constrained Polynomial Binary Optimization
1JPMorgan Chase
2IBM Quantum, IBM Research – Zurich
| Published: | 2021-04-08, volume 5, page 428 |
| Eprint: | arXiv:1912.04088v3 |
| Doi: | https://doi.org/10.22331/q-2021-04-08-428 |
| Citation: | Quantum 5, 428 (2021). |
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Abstract
In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a quadratic speed-up for combinatorial optimization problems compared to brute force search. However, this requires the development of efficient oracles to represent problems and flag states that satisfy certain search criteria. In general, this can be achieved using quantum arithmetic, however, this is expensive in terms of Toffoli gates as well as required ancilla qubits, which can be prohibitive in the near-term. Within this work, we develop a way to construct efficient oracles to solve CPBO problems using GAS algorithms. We demonstrate this approach and the potential speed-up for the portfolio optimization problem, i.e. a QUBO, using simulation and experimental results obtained on real quantum hardware. However, our approach applies to higher-degree polynomial objective functions as well as constrained optimization problems.
Featured image: The output probabilities of GAS for two iterations run on real quantum hardware, with respective thresholds $y$ and $r$ applications of the Grover operator. The valid measurement outcomes are shown in blue, while the invalid measurement outcomes are shown in grey.
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[1] Lov K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, STOC '96, pages 212–219, New York, NY, USA, 1996. ACM. ISBN 0-89791-785-5. 10.1145/237814.237866.
https://doi.org/10.1145/237814.237866
[2] Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26 (5): 1484–1509, Oct 1997. ISSN 1095-7111. 10.1137/s0097539795293172.
https://doi.org/10.1137/s0097539795293172
[3] B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, and et al. Towards quantum chemistry on a quantum computer. Nature Chemistry, 2 (2): 106–111, Jan 2010. ISSN 1755-4349. 10.1038/nchem.483.
https://doi.org/10.1038/nchem.483
[4] Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations. Physical Review Letters, 103 (15), Oct 2009. ISSN 1079-7114. 10.1103/physrevlett.103.150502.
https://doi.org/10.1103/physrevlett.103.150502
[5] Carlos Bravo-Prieto, Ryan LaRose, M. Cerezo, Yigit Subasi, Lukasz Cincio, and Patrick J. Coles. Variational quantum linear solver, 2020. URL https://arxiv.org/abs/1909.05820.
arXiv:1909.05820
[6] Patrick Rebentrost, Brajesh Gupt, and Thomas R. Bromley. Quantum computational finance: Monte carlo pricing of financial derivatives. Phys. Rev. A, 98: 022321, Aug 2018. 10.1103/PhysRevA.98.022321.
https://doi.org/10.1103/PhysRevA.98.022321
[7] Stefan Woerner and Daniel J. Egger. Quantum risk analysis. npj Quantum Information, 5: 15, 2019. 10.1038/s41534-019-0130-6.
https://doi.org/10.1038/s41534-019-0130-6
[8] D. J. Egger, R. Garcia Gutierrez, J. Cahue Mestre, and S. Woerner. Credit risk analysis using quantum computers. IEEE Transactions on Computers, pages 1–1, 2020. 10.1109/TC.2020.3038063.
https://doi.org/10.1109/TC.2020.3038063
[9] Nikitas Stamatopoulos, Daniel J. Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, and Stefan Woerner. Option pricing using quantum computers. Quantum, 4: 291, Jul 2020. ISSN 2521-327X. 10.22331/q-2020-07-06-291.
https://doi.org/10.22331/q-2020-07-06-291
[10] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A Quantum Approximate Optimization Algorithm, 2014. URL https://arxiv.org/abs/1411.4028.
arXiv:1411.4028
[11] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man Hong Yung, Xiao Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O'Brien. A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5: 4213, 2014. ISSN 20411723. 10.1038/ncomms5213.
https://doi.org/10.1038/ncomms5213
[12] Giacomo Nannicini. Performance of hybrid quantum-classical variational heuristics for combinatorial optimization. Physical Review E, 99: 013304, Jan 2019. 10.1103/PhysRevE.99.013304.
https://doi.org/10.1103/PhysRevE.99.013304
[13] Panagiotis Kl. Barkoutsos, Giacomo Nannicini, Anton Robert, Ivano Tavernelli, and Stefan Woerner. Improving variational quantum optimization using cvar. Quantum, 4: 256, Apr 2020. ISSN 2521-327X. 10.22331/q-2020-04-20-256.
https://doi.org/10.22331/q-2020-04-20-256
[14] L. Braine, D. J. Egger, J. Glick, and S. Woerner. Quantum algorithms for mixed binary optimization applied to transaction settlement. IEEE Transactions on Quantum Engineering, 2: 1–8, 2021. 10.1109/TQE.2021.3063635.
https://doi.org/10.1109/TQE.2021.3063635
[15] Andrew M Childs, Edward Farhi, and John Preskill. Robustness of adiabatic quantum computation. Physical Review A, 65 (1): 012322, 2001. 10.1103/PhysRevA.65.012322.
https://doi.org/10.1103/PhysRevA.65.012322
[16] Mark W Johnson, Mohammad HS Amin, Suzanne Gildert, Trevor Lanting, Firas Hamze, Neil Dickson, Richard Harris, Andrew J Berkley, Jan Johansson, Paul Bunyk, et al. Quantum annealing with manufactured spins. Nature, 473 (7346): 194–198, 2011. 10.1038/nature10012.
https://doi.org/10.1038/nature10012
[17] Christoph Dürr and Peter Høyer. A quantum algorithm for finding the minimum, 1996. URL https://arxiv.org/abs/quant-ph/9607014.
arXiv:quant-ph/9607014
[18] D. Bulger, W. P. Baritompa, and G. R. Wood. Implementing pure adaptive search with grover's quantum algorithm. Journal of Optimization Theory and Applications, 116 (3): 517–529, Mar 2003. ISSN 1573-2878. 10.1023/A:1023061218864.
https://doi.org/10.1023/A:1023061218864
[19] W. P. Baritompa, D. W. Bulger, and G. R. Wood. Grover's quantum algorithm applied to global optimization. SIAM J. on Optimization, 15 (4): 1170–1184, April 2005. ISSN 1052-6234. 10.1137/040605072.
https://doi.org/10.1137/040605072
[20] Austin Gilliam, Charlene Venci, Sreraman Muralidharan, Vitaliy Dorum, Eric May, Rajesh Narasimhan, and Constantin Gonciulea. Foundational patterns for efficient quantum computing, 2019. URL https://arxiv.org/abs/1907.11513.
arXiv:1907.11513
[21] Thomas G. Draper. Addition on a quantum computer, 2000. URL https://arxiv.org/abs/quant-ph/0008033.
arXiv:quant-ph/0008033
[22] Román Orús, Samuel Mugel, and Enrique Lizaso. Quantum computing for finance: Overview and prospects. Reviews in Physics, 4: 100028, Nov 2019. ISSN 2405-4283. 10.1016/j.revip.2019.100028.
https://doi.org/10.1016/j.revip.2019.100028
[23] Daniel J. Egger, Claudio Gambella, Jakub Marecek, Scott McFaddin, Martin Mevissen, Rudy Raymond, Andrea Simonetto, Stefan Woerner, and Elena Yndurain. Quantum computing for finance: State-of-the-art and future prospects. IEEE Transactions on Quantum Engineering, 1: 1–24, 2020a. ISSN 2689-1808. 10.1109/tqe.2020.3030314.
https://doi.org/10.1109/tqe.2020.3030314
[24] Patrick Rebentrost and Seth Lloyd. Quantum computational finance: quantum algorithm for portfolio optimization, 2018. URL https://arxiv.org/abs/1811.03975.
arXiv:1811.03975
[25] Davide Venturelli and Alexei Kondratyev. Reverse Quantum Annealing Approach to Portfolio Optimization Problems. Quantum Machine Intelligence, 1, 2019. 10.1007/s42484-019-00001-w.
https://doi.org/10.1007/s42484-019-00001-w
[26] Daniel J. Egger, Jakub Marecek, and Stefan Woerner. Warm-starting quantum optimization, 2020b. URL https://arxiv.org/abs/2009.10095.
arXiv:2009.10095
[27] Héctor Abraham et. al. Qiskit: An open-source framework for quantum computing. 2019. 10.5281/zenodo.2562110.
https://doi.org/10.5281/zenodo.2562110
[28] Michele Mosca. Quantum searching, counting and amplitude amplification by eigenvector analysis. In Proceedings of Randomized Algorithms, Workshop of Mathematical Foundations of Computer Science, pages 90–100, 1998. URL https://eccc.weizmann.ac.il//resources/pdf/moscafi.pdf.
https://eccc.weizmann.ac.il//resources/pdf/moscafi.pdf
[29] Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp. Quantum Amplitude Amplification and Estimation. Contemporary Mathematics, 305, 2002. 10.1090/conm/305.
https://doi.org/10.1090/conm/305
[30] Yohichi Suzuki, Shumpei Uno, Rudy Raymond, Tomoki Tanaka, Tamiya Onodera, and Naoki Yamamoto. Amplitude estimation without phase estimation. Quantum Information Processing, 19 (2), Jan 2020. ISSN 1573-1332. 10.1007/s11128-019-2565-2.
https://doi.org/10.1007/s11128-019-2565-2
[31] Scott Aaronson and Patrick Rall. Quantum approximate counting, simplified. Symposium on Simplicity in Algorithms, page 24–32, Jan 2020. 10.1137/1.9781611976014.5.
https://doi.org/10.1137/1.9781611976014.5
[32] Michel Boyer, Gilles Brassard, Peter Høyer, and Alain Tapp. Tight bounds on quantum searching. Fortschritte der Physik, 46 (4-5): 493–505, Jun 1998. ISSN 1521-3978. 10.1002/(SICI)1521-3978(199806)46:4/5<493::AID-PROP493>3.0.CO;2-P.
https://doi.org/10.1002/(SICI)1521-3978(199806)46:4/5<493::AID-PROP493>3.0.CO;2-P
[33] Benjamín Barán and Marcos Villagra. Multiobjective Optimization Grover Adaptive Search, pages 191–211. Springer International Publishing, Cham, 2019. ISBN 978-3-319-99648-6. 10.1007/978-3-319-99648-6_11.
https://doi.org/10.1007/978-3-319-99648-6_11
[34] Yunseong Nam, Yuan Su, and Dmitri Maslov. Approximate quantum fourier transform with o(n log(n)) t gates. npj Quantum Information, 6 (1), Mar 2020. ISSN 2056-6387. 10.1038/s41534-020-0257-5.
https://doi.org/10.1038/s41534-020-0257-5
[35] Steven A. Cuccaro, Thomas G. Draper, Samuel A. Kutin, and David Petrie Moulton. A new quantum ripple-carry addition circuit, 2004. URL https://arxiv.org/abs/quant-ph/0410184.
arXiv:quant-ph/0410184
[36] Thomas G. Draper, Samuel A. Kutin, Eric M. Rains, and Krysta M. Svore. A logarithmic-depth quantum carry-lookahead adder. Quantum Info. Comput., 6 (4): 351–369, July 2006. ISSN 1533-7146. 10.26421/QIC6.4-5-4.
https://doi.org/10.26421/QIC6.4-5-4
[37] Craig Gidney. Halving the cost of quantum addition. Quantum, 2: 74, Jun 2018. ISSN 2521-327X. 10.22331/q-2018-06-18-74.
https://doi.org/10.22331/q-2018-06-18-74
[38] Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, and Jay M. Gambetta. Validating quantum computers using randomized model circuits. Physical Review A, 100 (3), Sep 2019. ISSN 2469-9934. 10.1103/physreva.100.032328.
https://doi.org/10.1103/physreva.100.032328
[39] A. Dewes, F. R. Ong, V. Schmitt, R. Lauro, N. Boulant, P. Bertet, D. Vion, and D. Esteve. Characterization of a two-transmon processor with individual single-shot qubit readout. Phys. Rev. Lett., 108: 057002, Feb 2012. 10.1103/PhysRevLett.108.057002.
https://doi.org/10.1103/PhysRevLett.108.057002
[40] Svante Janson. Moments of gamma type and the brownian supremum process area. Probab. Surveys, 7: 1–52, 2010. 10.1214/10-PS160.
https://doi.org/10.1214/10-PS160
[41] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, New York, NY, USA, 10th edition, 2011. ISBN 1107002176, 9781107002173. 10.1017/CBO9780511976667.
https://doi.org/10.1017/CBO9780511976667
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[1] Alexis Ralli, Tim Weaving, Peter V. Coveney, and Peter J. Love, "Bridging Quantum Chemistry and MaxCut: Classical Performance Guarantees and Quantum Algorithms for the Hartree–Fock Method", Journal of Chemical Theory and Computation 21 19, 9511 (2025).
[2] M. R. Perelshtein, A. I. Pakhomchik, Ar. A. Melnikov, M. Podobrii, A. Termanova, I. Kreidich, B. Nuriev, S. Iudin, C. W. Mansell, and V. M. Vinokur, "NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization", Quantum 7, 1186 (2023).
[3] Fang Gao, Rongzhao Hu, Linfei Yin, Huibin Cao, Jun Yu, and Feng Shuang, "Quantum Grover Search-Inspired Global Maximum Power Point Tracking for Photovoltaic Systems Under Partial Shading Conditions", IEEE Transactions on Sustainable Energy 15 3, 1601 (2024).
[4] Yidong Liao, Min-Hsiu Hsieh, and Chris Ferrie, "Quantum optimization for training quantum neural networks", Quantum Machine Intelligence 6 1, 33 (2024).
[5] Yaswitha Gujju, Atsushi Matsuo, and Rudy Raymond, "Quantum machine learning on near-term quantum devices: Current state of supervised and unsupervised techniques for real-world applications", Physical Review Applied 21 6, 067001 (2024).
[7] Bence Bakó, Adam Glos, Özlem Salehi, and Zoltán Zimborás, "Prog-QAOA: Framework for resource-efficient quantum optimization through classical programs", Quantum 9, 1663 (2025).
[8] Hiroshi Ohno, "Grover’s search with learning oracle for constrained binary optimization problems", Quantum Machine Intelligence 6 1, 12 (2024).
[9] Yilun Zhao, Yanan Guo, Yuan Yao, Amanda Dumi, Devin M Mulvey, Shiv Upadhyay, Youtao Zhang, Kenneth D Jordan, Jun Yang, and Xulong Tang, 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA) 726 (2022) ISBN:978-1-6654-2027-3.
[10] Romain Piron, Muhammad Idham Habibie, and Claire Goursaud, "Mixed Grover: A Hybrid Version to Improve Grover's Algorithm for Unstructured Database Search", IEEE Transactions on Quantum Engineering 6, 1 (2025).
[11] Hyeon Seok Rou, Kein Yukiyoshi, Taku Mikuriya, Giuseppe Thadeu Freitas De Abreu, and Naoki Ishikawa, 2024 58th Asilomar Conference on Signals, Systems, and Computers 817 (2024) ISBN:979-8-3503-5405-8.
[12] Mohammadreza Soltaninia and Junpeng Zhan, "Quantum global minimum finder based on variational quantum search", Scientific Reports 15 1, 13880 (2025).
[13] Si-Qi Zhou, Hai Jin, Jin-Min Liang, Shao-Ming Fei, Yunlong Xiao, and Zhihao Ma, "Coherence fraction in Grover's search algorithm", Physical Review A 110 6, 062429 (2024).
[14] Massimiliano Cutugno, Annarita Giani, Paul Alsing, Laura Wessing, and Austar Schnore, "Quantum Computing Approaches for Mission Covering Optimization", Algorithms 15 7, 224 (2022).
[15] Rhonda Au-Yeung, Nicholas Chancellor, and Pascal Halffmann, "NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems", Frontiers in Quantum Science and Technology 2, 1128576 (2023).
[16] Hyeon Seok Rou and Giuseppe Thadeu Freitas de Abreu, "Chirp-Permuted AFDM for Quantum-Resilient Physical-Layer Secure Communications", IEEE Wireless Communications Letters 14 8, 2376 (2025).
[17] Sabri Gündüz and İhsan Yılmaz, "Leveraging qudits: high-dimensional Grover adaptive search algorithm for solving quadratic and higher-order unconstrained binary optimization problems", The European Physical Journal Plus 141 4, 368 (2026).
[18] Anna M. Krol, Marvin Erdmann, Ewan Munro, Andre Luckow, and Zaid Al-Ars, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 211 (2024) ISBN:979-8-3315-4137-8.
[19] Yuki Sano, Kosuke Mitarai, Naoki Yamamoto, and Naoki Ishikawa, "Accelerating Grover Adaptive Search: Qubit and Gate Count Reduction Strategies With Higher Order Formulations", IEEE Transactions on Quantum Engineering 5, 1 (2024).
[20] Irsa Sajjad, Huda M. Alshanbari, Mohammed M. A. Almazah, Hanen Louati, and Sana Rauf, "Adaptive Grover-driven optimization for quantum-inspired deep learning: A gradient-free training framework", AIMS Mathematics 10 11, 26568 (2025).
[21] Thorsten Koch, David E. Bernal Neira, Ying Chen, Giorgio Cortiana, Daniel J. Egger, Raoul Heese, Narendra N. Hegade, Alejandro Gomez Cadavid, Rhea Huang, Toshinari Itoko, Thomas Kleinert, Pedro Maciel Xavier, Naeimeh Mohseni, Jhon A. Montanez-Barrera, Koji Nakano, Giacomo Nannicini, Corey O’Meara, Justin Pauckert, Manuel Proissl, Anurag Ramesh, Maximilian Schicker, Noriaki Shimada, Mitsuharu Takeori, Víctor Valls, David Van Bulck, Stefan Woerner, and Christa Zoufal, "The Quantum Optimization Benchmarking Library", Nature Computational Science 6 6, 653 (2026).
[22] Qifan Jiang, Liqiang Lu, Debin Xiang, Tianyao Chu, Tianze Zhu, Jingwen Leng, Yun Liang, Xiaoming Sun, and Jianwei Yin, Proceedings of the 58th IEEE/ACM International Symposium on Microarchitecture 764 (2025) ISBN:9798400715730.
[23] Yuki Sano, Masaya Norimoto, and Naoki Ishikawa, "Qubit Reduction and Quantum Speedup for Wireless Channel Assignment Problem", IEEE Transactions on Quantum Engineering 4, 1 (2023).
[24] Masaya Norimoto, Taku Mikuriya, and Naoki Ishikawa, "Quantum Speedup for Multiuser Detection With Optimized Parameters in Grover Adaptive Search", IEEE Access 12, 83810 (2024).
[25] T. Muser, E. Zapusek, V. Belis, and F. Reiter, "Provable advantages of kernel-based quantum learners and quantum preprocessing based on Grover's algorithm", Physical Review A 110 3, 032434 (2024).
[26] Kein Yukiyoshi and Naoki Ishikawa, "Quantum search algorithm for binary constant weight codes", Quantum Information Processing 23 10, 360 (2024).
[27] Friedrich Wagner and Frauke Liers, "Quantum Subroutines in Branch-Price-and-Cut for Vehicle Routing", IEEE Transactions on Quantum Engineering 7, 3103116 (2026).
[28] Jehn-Ruey Jiang and Yu-Jie Wang, "Using a Simplified Quantum Counter to Implement Quantum Circuits Based on Grover’s Algorithm to Tackle the Exact Cover Problem", Mathematics 13 1, 90 (2024).
[29] Qing-Guo Zeng, Xiao-Peng Cui, Xian-Zhe Tao, Jia-Qi Hu, Shi-Jie Pan, Wei E.I. Sha, and Man-Hong Yung, "High-order-modulation large MIMO detector based on physics-inspired methods", Physical Review Applied 24 3, 034027 (2025).
[30] Naphan Benchasattabuse, Andreas Bärtschi, Luis Pedro García-Pintos, John Golden, Nathan Lemons, and Stephan Eidenbenz, "Lower bounds on the number of rounds of the quantum approximate optimization algorithm required for guaranteed approximation ratios", Physical Review A 111 6, 062411 (2025).
[31] Kip Nieman, Helen Durand, Saahil Patel, Daniel Koch, and Paul M. Alsing, "Parallelizing process model integration for model predictive control through oracle design and analysis for a Grover’s algorithm-inspired optimization strategy", Digital Chemical Engineering 13, 100179 (2024).
[32] Ahmad Alomari and Sathish A. P. Kumar, "GPA: Grover Policy Agent for Generating Optimal Quantum Sensor Circuits", IEEE Transactions on Artificial Intelligence 6 10, 2722 (2025).
[33] Hiroyuki Tezuka, Kouhei Nakaji, Takahiko Satoh, and Naoki Yamamoto, "Grover search revisited: Application to image pattern matching", Physical Review A 105 3, 032440 (2022).
[34] Mohamed Salah Dahassa and Nadjet Zioui, "Optimal Control-Based Grover’s Algorithm for a Six-Jointed Articulated Robotic Arm", Electronics 14 13, 2503 (2025).
[35] Amir Pourabdollah, Giovanni Acampora, and Roberto Schiattarella, "Fuzzy Logic on Quantum Annealers", IEEE Transactions on Fuzzy Systems 30 8, 3389 (2022).
[36] Kornélia Sára Szatmáry, 2024 IEEE 18th International Symposium on Applied Computational Intelligence and Informatics (SACI) 1 (2024) ISBN:979-8-3503-2952-0.
[37] Engin Zeydan, Josep Mangues-Bafalluy, Yekta Turk, Abdullah Aydeger, and Madhusanka Liyanage, 2025 IEEE International Mediterranean Conference on Communications and Networking (MeditCom) 1 (2025) ISBN:979-8-3315-2965-9.
[38] Masaya Norimoto, Ryuhei Mori, and Naoki Ishikawa, "Quantum Algorithm for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection", IEEE Transactions on Communications 71 4, 1926 (2023).
[39] Francisco Orts, Gloria Ortega, Elías F. Combarro, Ignacio F. Rúa, Antonio M. Puertas, and Ester M. Garzón, "Efficient design of a quantum absolute-value circuit using Clifford+T gates", The Journal of Supercomputing 79 11, 12656 (2023).
[40] Dylan Herman, Cody Googin, Xiaoyuan Liu, Yue Sun, Alexey Galda, Ilya Safro, Marco Pistoia, and Yuri Alexeev, "Quantum computing for finance", Nature Reviews Physics 5 8, 450 (2023).
[41] Lu Liu, Xingyu Wu, and Chuan Wang, 2023 International Conference on Intelligent Computing and Next Generation Networks（ICNGN) 1 (2023) ISBN:979-8-3503-2907-0.
[42] Ahmad Alomari and Sathish A. P. Kumar, "ReLAQA: Reinforcement Learning-Based Autonomous Quantum Agent for Quantum Applications", IEEE Transactions on Artificial Intelligence 6 3, 549 (2025).
[43] J. Prado, I. Rojas, and M.P. Cuéllar, 2026 IEEE Conference on Artificial Intelligence (CAI) 1829 (2026) ISBN:979-8-3315-6039-3.
[44] Manqoba Q. Hlatshwayo, Manav Babel, Dalila Islas-Sanchez, and Konstantinos Georgopoulos, "A Technical Review of Quantum Computing Use Cases for Finance and Economics", Quantum Reports 8 1, 26 (2026).
[45] Ahmad Alomari and Sathish A.P. Kumar, "Securing IoT systems in a post-quantum environment: Vulnerabilities, attacks, and possible solutions", Internet of Things 25, 101132 (2024).
[46] R. Au-Yeung, A.J. Williams, V.M. Kendon, and S.J. Lind, "Quantum algorithm for smoothed particle hydrodynamics", Computer Physics Communications 294, 108909 (2024).
[47] Marika Svensson, Martin Andersson, Mattias Grönkvist, Pontus Vikstål, Devdatt Dubhashi, Giulia Ferrini, and Göran Johansson, "Hybrid Quantum-Classical Heuristic to Solve Large-Scale Integer Linear Programs", Physical Review Applied 20 3, 034062 (2023).
[48] Giacomo Orlandi, Deborah Volpe, Mariagrazia Graziano, and Giovanna Turvani, "Qoolchain: A QUBO Preprocessing Toolchain for Enhancing Quantum Optimization", Advanced Quantum Technologies 8 5, 2400384 (2025).
[49] Stuart Harwood, Claudio Gambella, Dimitar Trenev, Andrea Simonetto, David Bernal Neira, and Donny Greenberg, "Formulating and Solving Routing Problems on Quantum Computers", IEEE Transactions on Quantum Engineering 2, 1 (2021).
[50] Shih-Cheng Horng, Shieh-Shing Lin, and Wei-Hao Huang, 2023 International Automatic Control Conference (CACS) 1 (2023) ISBN:979-8-3503-0635-4.
[51] Taku Mikuriya, Kengo Ando, Kein Yukiyoshi, Giuseppe Thadeu Freitas de Abreu, Koji Ishibashi, and Naoki Ishikawa, 2025 IEEE 101st Vehicular Technology Conference (VTC2025-Spring) 1 (2025) ISBN:979-8-3315-3147-8.
[52] Nima Nikmehr, Peng Zhang, and Mikhail A. Bragin, "Quantum Distributed Unit Commitment: An Application in Microgrids", IEEE Transactions on Power Systems 37 5, 3592 (2022).
[53] Abdullah Ash Saki, Rasit Onur Topaloglu, and Swaroop Ghosh, 2022 Design, Automation & Test in Europe Conference & Exhibition (DATE) 322 (2022) ISBN:978-3-9819263-6-1.
[54] Ahmad Alomari and Sathish A. P. Kumar, 2025 IEEE Conference on Artificial Intelligence (CAI) 1375 (2025) ISBN:979-8-3315-2400-5.
[55] Felix Gemeinhardt, Antonio Garmendia, Manuel Wimmer, and Robert Wille, "A Model-Driven Framework for Composition-Based Quantum Circuit Design", ACM Transactions on Quantum Computing 5 4, 1 (2024).
[56] Hiroshi Ohno, "Quantum greedy algorithms for multi-armed bandits", Quantum Information Processing 22 2, 101 (2023).
[57] Toshiki Matsumine, Hideki Ochiai, and Junji Shikata, "Quantum Algorithms for the Physical Layer: Potential Applications to Physical Layer Security", IEEE Access 13, 13988 (2025).
[58] Natchapol Patamawisut, Naphan Benchasattabuse, Michal Hajdušek, and Rodney Van Meter, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 291 (2025) ISBN:979-8-3315-5736-2.
[59] Nikolaos G. Paterakis, "Hybrid quantum-classical multi-cut Benders approach with a power system application", Computers & Chemical Engineering 172, 108161 (2023).
[60] Francisco Orts, Gloria Ortega, Elías F. Combarro, Ignacio F. Rúa, Antonio M. Puertas, and Ester M. Garzón, "Efficient design of a quantum absolute-value circuit using Clifford+T gates", (2022).
[61] Fei Feng, Peng Zhang, Mikhail A. Bragin, and Yifan Zhou, "Novel Resolution of Unit Commitment Problems Through Quantum Surrogate Lagrangian Relaxation", IEEE Transactions on Power Systems 38 3, 2460 (2023).
[62] Hiroaki Ominato, Takahiro Ohyama, and Koichiro Yamaguchi, "Grover Adaptive Search With Fewer Queries", IEEE Access 12, 74619 (2024).
[63] Takuya Yoshioka, Keita Sasada, Yuichiro Nakano, and Keisuke Fujii, "Fermionic quantum approximate optimization algorithm", Physical Review Research 5 2, 023071 (2023).
[64] Harishankar Mishra, Asvija Balasubramanyam, and Gudapati Naresh Raghava, "Deterministic quantum search for arbitrary initial success probabilities", Quantum Information Processing 25 7, 222 (2026).
[65] Ioannis Liliopoulos, Georgios D. Varsamis, and Ioannis G. Karafyllidis, "Discrete-time quantum walk-based optimization algorithm", Quantum Information Processing 23 1, 23 (2024).
[66] Shintaro Fujiwara and Naoki Ishikawa, "Grover Adaptive Search With Spin Variables", IEEE Transactions on Quantum Engineering 6, 1 (2025).
[67] David Bucher, Jonas Stein, Sebastian Feld, and Claudia Linnhoff-Popien, "Penalty-free approach to accelerating constrained quantum optimization", Physical Review A 112 6, 062605 (2025).
[68] Rei Sato, Cui Gordon, Kazuhiro Saito, Hideyuki Kawashima, Tetsuro Nikuni, and Shohei Watabe, "Two-Step Quantum Search Algorithm for Solving Traveling Salesman Problems", IEEE Transactions on Quantum Engineering 6, 1 (2025).
[69] Deborah Volpe, Giacomo Orlandi, and Giovanna Turvani, "Improving the Solving of Optimization Problems: A Comprehensive Review of Quantum Approaches", Quantum Reports 7 1, 3 (2025).
[70] Xiaodong Zheng, Ding Lin, and Haoyong Chen, "Grover Adaptive Search-Based Hybrid Benders Decomposition for Mixed-Integer Linear Programs", IEEE Transactions on Quantum Engineering 7, 1 (2026).
[71] Xujun Bai and Yun Shang, "A quantum speedup algorithm for TSP based on quantum dynamic programming with very few qubits", Theoretical Computer Science 1052, 115423 (2025).
[72] Daniel Koch, Massimiliano Cutugno, Saahil Patel, Laura Wessing, and Paul M. Alsing, "Variational Amplitude Amplification for Solving QUBO Problems", Quantum Reports 5 4, 625 (2023).
[73] Hyoga Iizumi, Naoki Ishikawa, Shunsuke Uehashi, Kota Nakamura, Akira Kurita, and Masao Oga, 2025 IEEE 102nd Vehicular Technology Conference (VTC2025-Fall) 1 (2025) ISBN:979-8-3315-0320-8.
[74] Jungin E. Kim and Yan Wang, "Quantum Approximate Bayesian Optimization Algorithms With Two Mixers and Uncertainty Quantification", IEEE Transactions on Quantum Engineering 4, 1 (2023).
[75] Naoki Ishikawa, "Quantum Speedup for Index Modulation", IEEE Access 9, 111114 (2021).
[76] Amir Pourabdollah, Giovanni Acampora, and Roberto Schiattarella, 2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) 1 (2022) ISBN:978-1-6654-6710-0.
[77] Lu Liu, Ling Qian, Xing-Yu Wu, Chen-Rui Fan, Lu-Fan Zhang, Dun-Bo Cai, Hui-Jun Lu, Tie-Jun Wang, and Chuan Wang, "Solving Vehicle Routing Problem Using Grover Adaptive Search Algorithm", IEEE Transactions on Intelligent Transportation Systems 26 7, 9682 (2025).
[78] Charles Ross, Gabriele Gradoni, Qi Jian Lim, and Zhen Peng, "Engineering Reflective Metasurfaces With Ising Hamiltonian and Quantum Annealing", IEEE Transactions on Antennas and Propagation 70 4, 2841 (2022).
[79] Ginés Carrascal, Paula Hernamperez, Guillermo Botella, and Alberto del Barrio, "Backtesting Quantum Computing Algorithms for Portfolio Optimization", IEEE Transactions on Quantum Engineering 5, 1 (2024).
[80] Xiaodong Zheng, Jianhui Wang, and Meng Yue, "A Fast Quantum Algorithm for Searching the Quasi-Optimal Solutions of Unit Commitment", IEEE Transactions on Power Systems 39 2, 4755 (2024).
[81] Eldar Sultanow, Madjid Tehrani, Siddhant Dutta, William J. Buchanan, and Muhammad Shahbaz Khan, "Defining Quantum Agents: Formal Foundations, Architectures, and NISQ-Era Prototypes", Quantum Reports 8 1, 24 (2026).
[82] Deborah Volpe, Nils Quetschlich, Mariagrazia Graziano, Giovanna Turvani, and Robert Wille, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 1014 (2024) ISBN:979-8-3315-4137-8.
[83] Prathyush P. Poduval, Zhuowen Zou, and Mohsen Imani, "Approximate quantum search", Physics Letters A 585, 131626 (2026).
[84] Kein Yukiyoshi, Taku Mikuriya, Hyeon Seok Rou, Giuseppe Thadeu Freitas de Abreu, and Naoki Ishikawa, "Quantum Speedup of the Dispersion and Codebook Design Problems", IEEE Transactions on Quantum Engineering 5, 1 (2024).
[85] Francesco Calcagno, Delmar G. A. Cabral, Ivan Rivalta, and Victor S. Batista, "The quantum ensemble variational optimization algorithm: Applications to molecular inverse design", Proceedings of the National Academy of Sciences 123 30, e2531186123 (2026).
[86] Zhijian Wang, Yuchen He, Tian Luan, and Yong Long, "An Improved GAS Algorithm", Entropy 27 3, 240 (2025).
[87] Li-Yi Hsu and Ching-Hsu Chen, "Conservation Laws in Quantum Database Search", Foundations of Physics 54 5, 70 (2024).
[88] Guilherme Adamatti Bridi and Franklin de Lima Marquezino, "Analytical results for the quantum alternating operator ansatz with Grover mixer", Physical Review A 110 5, 052409 (2024).
[89] Sandeep Kumar Sood, Manmohan Singh, and Munish Bhatia, "Industrial progress with quantum algorithms: an in-depth review", The Journal of Supercomputing 81 9, 1064 (2025).
[90] Felix Gemeinhardt, Martin Eisenberg, Stefan Klikovits, and Manuel Wimmer, 2023 ACM/IEEE International Conference on Model Driven Engineering Languages and Systems Companion (MODELS-C) 614 (2023) ISBN:979-8-3503-2498-3.
[91] Yifan Sun and Lian-Ao Wu, "Quantum search algorithm on weighted databases", Scientific Reports 14 1, 30169 (2024).
[92] Deborah Volpe, Giacomo Orlandi, Mattia Boggio, Carlo Novara, Lorenzo Zino, and Giovanna Turvani, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 2258 (2025) ISBN:979-8-3315-5736-2.
[93] Dylan Herman, Ruslan Shaydulin, Yue Sun, Shouvanik Chakrabarti, Shaohan Hu, Pierre Minssen, Arthur Rattew, Romina Yalovetzky, and Marco Pistoia, "Constrained optimization via quantum Zeno dynamics", Communications Physics 6 1, 219 (2023).
[94] Hyakka Nakada, Kotaro Tanahashi, and Shu Tanaka, "Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization", IEEE Access 13, 73096 (2025).
[95] Robin Ollive and Stephane Louise, 2025 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) 519 (2025) ISBN:979-8-3315-2643-6.
[96] Diego García-Vega, Fernando Plou Llorente, Alejandro Leal Castaño, Elías F. Combarro, and José Ranilla, "pLazyQML: A parallel package for efficient execution of QML models on classical computers", (2025).
[97] Vinicius Marchioli, Mattia Boggio, Deborah Volpe, Luca Massotti, and Carlo Novara, "Quantum Optimization for Closed-Loop Scheduling of Earth Observation Satellite Formation", SN Computer Science 6 6, 739 (2025).
[98] Takuya Yoshioka, Keita Sasada, Yuichiro Nakano, and Keisuke Fujii, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 300 (2023) ISBN:979-8-3503-4323-6.
[99] Damian Rovara, Nils Quetschlich, and Robert Wille, 2026 IEEE 56th International Symposium on Multiple-Valued Logic (ISMVL) 158 (2026) ISBN:979-8-3315-5956-4.
[100] Masaya Norimoto and Naoki Ishikawa, 2023 IEEE 97th Vehicular Technology Conference (VTC2023-Spring) 1 (2023) ISBN:979-8-3503-1114-3.
[101] Pedro C. S. Costa, Mauro E. S. Morales, Dong An, and Yuval R. Sanders, "Assessing quantum and classical approaches to combinatorial optimization: Testing quadratic speed-ups for heuristic algorithms", Physical Review A 112 2, 022429 (2025).
[102] Robin OLLIVE and Stephane LOUISE, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 256 (2024) ISBN:979-8-3315-4137-8.
[103] Deborah Volpe, Nils Quetschlich, Mariagrazia Graziano, Giovanna Turvani, and Robert Wille, 2024 IEEE International Conference on Quantum Software (QSW) 46 (2024) ISBN:979-8-3503-6847-5.
[104] Allan Wing-Bocanegra, Carlos E. Quintero-Narvaez, and Salvador E. Venegas-Andraca, "Circuit implementation and analysis of a quantum-walk based search complement algorithm", Scientific Reports 15 1, 4865 (2025).
[105] Raphael Seidel, Nikolay Tcholtchev, Sebastian Bock, Colin Kai-Uwe Becker, and Manfred Hauswirth, "Efficient Floating Point Arithmetic for Quantum Computers", IEEE Access 10, 72400 (2022).
[106] Raphael Seidel, Colin Kai-Uwe Becker, Sebastian Bock, Nikolay Tcholtchev, Ilie-Daniel Gheorghe-Pop, and Manfred Hauswirth, "Automatic generation of Grover quantum oracles for arbitrary data structures", Quantum Science and Technology 8 2, 025003 (2023).
[107] Naoki Ishikawa, Giuseppe Thadeu Freitas de Abreu, Petar Popovski, and Robert W. Heath, "Quantum-Accelerated Wireless Communications: Concepts, Connections, and Implications", IEEE Communications Magazine 64 3, 156 (2026).
[108] Naphan Benchasattabuse, Takahiko Satoh, Michal Hajdusek, and Rodney Van Meter, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 22 (2022) ISBN:978-1-6654-9113-6.
[109] Tristan Zaborniak, Juan Giraldo, Hausi Muller, Hosna Jabbari, and Ulrike Stege, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 174 (2022) ISBN:978-1-6654-9113-6.
[110] Amira Abbas, Andris Ambainis, Brandon Augustino, Andreas Bärtschi, Harry Buhrman, Carleton Coffrin, Giorgio Cortiana, Vedran Dunjko, Daniel J. Egger, Bruce G. Elmegreen, Nicola Franco, Filippo Fratini, Bryce Fuller, Julien Gacon, Constantin Gonciulea, Sander Gribling, Swati Gupta, Stuart Hadfield, Raoul Heese, Gerhard Kircher, Thomas Kleinert, Thorsten Koch, Georgios Korpas, Steve Lenk, Jakub Marecek, Vanio Markov, Guglielmo Mazzola, Stefano Mensa, Naeimeh Mohseni, Giacomo Nannicini, Corey O’Meara, Elena Peña Tapia, Sebastian Pokutta, Manuel Proissl, Patrick Rebentrost, Emre Sahin, Benjamin C. B. Symons, Sabine Tornow, Víctor Valls, Stefan Woerner, Mira L. Wolf-Bauwens, Jon Yard, Sheir Yarkoni, Dirk Zechiel, Sergiy Zhuk, and Christa Zoufal, "Challenges and opportunities in quantum optimization", Nature Reviews Physics 6 12, 718 (2024).
[111] Takuto Moriya, Masashi Tawada, and Nozomu Togawa, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 488 (2025) ISBN:979-8-3315-5736-2.
[112] Maryam Tariq, Raneem Abdelrahim, Omar Alhussein, and Sami Muhaidat, 2025 IEEE Globecom Workshops (GC Wkshps) 466 (2025) ISBN:979-8-3315-6741-5.
[113] Sayan Mukherjee, "A Grover Search-Based Algorithm for the List Coloring Problem", IEEE Transactions on Quantum Engineering 3, 1 (2022).
[114] Julien Gacon, Christa Zoufal, Giuseppe Carleo, and Stefan Woerner, "Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information", Quantum 5, 567 (2021).
[115] Dan Li and Guoliang Ju, "Non-convex optimization algorithm based on alternating quantum walk with potentials", Quantum Information Processing 25 3, 88 (2026).
[116] Debin Xiang, Qifan Jiang, Liqiang Lu, Siwei Tan, and Jianwei Yin, 2025 IEEE International Symposium on High Performance Computer Architecture (HPCA) 275 (2025) ISBN:979-8-3315-0647-6.
[117] Thomas Beck, Alessandro Baroni, Ryan Bennink, Gilles Buchs, Eduardo Antonio Coello Pérez, Markus Eisenbach, Rafael Ferreira da Silva, Muralikrishnan Gopalakrishnan Meena, Kalyan Gottiparthi, Peter Groszkowski, Travis S. Humble, Ryan Landfield, Ketan Maheshwari, Sarp Oral, Michael A. Sandoval, Amir Shehata, In-Saeng Suh, and Christopher Zimmer, "Integrating quantum computing resources into scientific HPC ecosystems", Future Generation Computer Systems 161, 11 (2024).
[118] Tung-Yeh Wu and Ting-Chi Wang, Proceedings of the 2026 International Symposium on Physical Design 173 (2026) ISBN:9798400723148.
[119] Zhan Li, Yusen Wu, Run-Qing Zhang, Jing-Wei Wen, Tie-Jun Wang, and Chuan Wang, "Studies of quantum combinatorial optimization algorithms: <?A3B2 pi6?>a review", Chinese Science Bulletin 71 21, 5109 (2026).
[120] Ramaraj S, Jaiganesh M, Mercy S, Bodla. Ashwin Kumar, Senthur Balaji K, and Lathika M, 2026 8th International Conference on Devices, Circuits, and Systems (ICDCS) 1 (2026) ISBN:979-8-3195-0595-8.
[121] Taku Mikuriya, Hyeon Seok Rou, Giuseppe Thadeu Freitas De Abreu, Koji Ishibashi, and Naoki Ishikawa, 2025 IEEE 102nd Vehicular Technology Conference (VTC2025-Fall) 1 (2025) ISBN:979-8-3315-0320-8.
[122] J. M. Hernández Cáceres and I. F. Rúa, "On finding PUBO problems on Diophantine equations", Quantum Information Processing 25 4, 113 (2026).
[123] Arul Rhik Mazumder and Sridhar Tayur, Tutorials in Operations Research: Advances in Analytics and Operations Research: Improving Decisions to Secure the Future 145 (2025) ISBN:979-8-9882856-3-2.
[124] Felix Gemeinhardt, Antonio Garmendia, Manuel Wimmer, Benjamin Weder, and Frank Leymann, "Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study", ACM Computing Surveys 56 3, 1 (2024).
[125] Ankit Khandelwal, Handy Kurniawan, Shraddha Aangiras, Özlem Salehi, and Adam Glos, "Classification and transformations of quantum circuit decompositions for permutation operations", Quantum Information Processing 23 9, 322 (2024).
[126] Mei Ian Sam, Tzu-Ling Kuo, and Tai-Yue Li, ICASSP 2026 - 2026 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 22042 (2026) ISBN:979-8-3315-6701-9.
[127] Luigi Giuffrida, Deborah Volpe, Giovanni Amedeo Cirillo, Maurizio Zamboni, and Giovanna Turvani, "Engineering Grover Adaptive Search: Exploring the Degrees of Freedom for Efficient QUBO Solving", IEEE Journal on Emerging and Selected Topics in Circuits and Systems 12 3, 614 (2022).
[128] Titos Matsakos and Adrian Lomas, "A quantum unstructured search algorithm for discrete optimisation: the use case of portfolio optimisation", arXiv:2505.14645, (2025).
[129] Natchapol Patamawisut, Naphan Benchasattabuse, Michal Hajdušek, and Rodney Van Meter, "Quantum Circuit Design for Decoded Quantum Interferometry", arXiv:2504.18334, (2025).
[130] Daniel J. Egger, Claudio Gambella, Jakub Marecek, Scott McFaddin, Martin Mevissen, Rudy Raymond, Andrea Simonetto, Stefan Woerner, and Elena Yndurain, "Quantum Computing for Finance: State-of-the-Art and Future Prospects", IEEE Transactions on Quantum Engineering 1, TQE.2020.3030314 (2020).
[131] Takuya Yoshioka, Keita Sasada, Yuichiro Nakano, and Keisuke Fujii, "Experimental Demonstration of Fermionic QAOA with One-Dimensional Cyclic Driver Hamiltonian", arXiv:2312.04710, (2023).
[132] Arul Mazumder and Sridhar Tayur, "Five Starter Problems: Solving Quadratic Unconstrained Binary Optimization Models on Quantum Computers", arXiv:2401.08989, (2024).
[133] Yudai Suzuki, Marek Gluza, Jeongrak Son, Bi Hong Tiang, Nelly H. Y. Ng, and Zoë Holmes, "Grover's algorithm is an approximation of imaginary-time evolution", arXiv:2507.15065, (2025).
[134] Su Yeon Chang, Steven Herbert, Sofia Vallecorsa, Elías F. Combarro, and Ross Duncan, "Dual-Parameterized Quantum Circuit GAN Model in High Energy Physics", European Physical Journal Web of Conferences 251, 03050 (2021).
[135] Bai Xujun and Shang Yun, "A quantum speedup algorithm for TSP based on quantum dynamic programming with very few qubits", arXiv:2502.08853, (2025).
[136] Naphan Benchasattabuse, "Resource Management in Heterogeneous Quantum Repeater Networks", arXiv:2605.25132, (2026).
[137] Thomas Beck, Alessandro Baroni, Ryan Bennink, Gilles Buchs, Eduardo Antonio Coello Perez, Markus Eisenbach, Rafael Ferreira da Silva, Muralikrishnan Gopalakrishnan Meena, Kalyan Gottiparthi, Peter Groszkowski, Travis S. Humble, Ryan Landfield, Ketan Maheshwari, Sarp Oral, Michael A. Sandoval, Amir Shehata, In-Saeng Suh, and Christopher Zimmer, "Integrating Quantum Computing Resources into Scientific HPC Ecosystems", arXiv:2408.16159, (2024).
[138] Claudio Gambella and Andrea Simonetto, "Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers", IEEE Transactions on Quantum Engineering 1, TQE.2020.3033139 (2020).
[139] Deborah Volpe, Nils Quetschlich, Mariagrazia Graziano, Giovanna Turvani, and Robert Wille, "A Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem", arXiv:2408.03613, (2024).
[140] A. Ege Yilmaz, Stefan Stettler, Thomas Ankenbrand, and Urs Rhyner, "Grover Search for Portfolio Selection", arXiv:2308.13063, (2023).
[141] Yidong Liao, Min-Hsiu Hsieh, and Chris Ferrie, "Quantum Optimization for Training Quantum Neural Networks", arXiv:2103.17047, (2021).
[142] Megan C. Giron, Georgios Korpas, Waqas Parvaiz, Prashant Malik, and Johannes Aspman, "Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing (May 2023)", IEEE Transactions on Quantum Engineering 4, TQE.2023 (2023).
[143] Mathew Vanherreweghe, Lirandë Pira, and Patrick Rebentrost, "Degree-Optimized Cumulative Polynomial Kolmogorov-Arnold Networks", arXiv:2505.15228, (2025).
[144] Ahmad Alomari and Sathish A. P. Kumar, "GPA: Grover Policy Agent for Generating Optimal Quantum Sensor Circuits", arXiv:2502.13755, (2025).
[145] Dekuan Dong, Yingzhou Li, and Jiaxin Ma, "Random Grover Search", arXiv:2606.11759, (2026).
[146] kos Nagy, Jaime Park, Cindy Zhang, Atithi Acharya, and Alex Khan, "Fixed-Point Grover Adaptive Search for Quadratic Binary Optimization Problems", IEEE Transactions on Quantum Engineering 5, TQE.2024 (2024).
[147] Damian Rovara, Nils Quetschlich, and Robert Wille, "A Framework to Formulate Pathfinding Problems for Quantum Computing", arXiv:2404.10820, (2024).
[148] Sayantan Pramanik, M Girish Chandra, Shampa Sarkar, and Manoj Nambiar, "Approximate Phase Search and Eigen Estimation using Modified Grover's Algorithm", arXiv:2012.11497, (2020).
[149] Austin Gilliam, Marco Pistoia, and Constantin Gonciulea, "Optimizing Quantum Search with a Binomial Version of Grover's Algorithm", arXiv:2007.10894, (2020).
[150] Deborah Volpe, Nils Quetschlich, Mariagrazia Graziano, Giovanna Turvani, and Robert Wille, "Towards an Automatic Framework for Solving Optimization Problems with Quantum Computers", arXiv:2406.12840, (2024).
[151] Deborah Volpe, Giacomo Orlandi, Mattia Boggio, Carlo Novara, Lorenzo Zino, and Giovanna Turvani, "A Quantum Approach for Optimal Transient Control in Network-Based Epidemic Models", arXiv:2507.15989, (2025).
[152] Austin Gilliam, Marco Pistoia, and Constantin Gonciulea, "Canonical Construction of Quantum Oracles", arXiv:2006.10656, (2020).
[153] José Miguel Monzón-Verona, Santiago García-Alonso, and Francisco Jorge Santana-Martín, "Quantum Variational vs. Quantum Kernel Machine Learning Models for Partial Discharge Classification in Dielectric Oils", Sensors 25 4, 1277 (2025).
[154] Chien-Hung Cho, Chih-Yu Chen, Kuo-Chin Chen, Tsung-Wei Huang, Ming-Chien Hsu, Ning-Ping Cao, Bei Zeng, Seng-Ghee Tan, and Ching-Ray Chang, "Quantum computation: Algorithms and Applications", Chinese Journal of Physics 72, 248 (2021).
[155] Austin Gilliam, Marco Pistoia, and Constantin Gonciulea, "Optimizing Quantum Search Using a Generalized Version of Grover's Algorithm", arXiv:2005.06468, (2020).
[156] Anna M. Krol, Marvin Erdmann, Ewan Munro, Andre Luckow, and Zaid Al-Ars, "Assessing the Requirements for Industry Relevant Quantum Computation", arXiv:2408.02587, (2024).
[157] Yilun Zhao, Yu Chen, Kaiyan Chang, He Li, Bing Li, Yinhe Han, and Ying Wang, "A System Architecture for Low Latency Multiprogramming Quantum Computing", arXiv:2601.01158, (2026).
[158] Hefeng Wang and Hua Xiang, "Quantum optimization algorithm based on multistep quantum computation", New Journal of Physics 26 7, 073031 (2024).
[159] Felix G. Gemeinhardt, Robert Wille, and Manuel Wimmer, "Quantum k-community detection: algorithm proposals and cross-architectural evaluation", Quantum Information Processing 20 9, 302 (2021).
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