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Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation
Open accessAbstract
We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA works on any NP optimization problem for which it is possible to efficiently prepare an equal superposition of all feasible solutions; it is designed to perform particularly well for constraint optimization problems, where not all possible variable assignments are feasible solutions. GM-QAOA has the following features: (i) It is not susceptible to Hamiltonian Simulation error (such as Trotterization errors) as its operators can be implemented exactly using standard gate sets and (ii) Solutions with the same objective value are always sampled with the same amplitude. We illustrate the potential of GM-QAOA on several optimization problem classes: for permutation-based optimization problems such as the Traveling Salesperson Problem, we present an efficient algorithm to prepare a superposition of all possible permutations of$n$numbers, defined on O (n2) qubits; for the hard constraint k-Vertex-Cover problem, and for an application to Discrete Portfolio Rebalancing, we show that GM-QAOA outperforms existing QAOA approaches.
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“Besides the mentioned ansatz search, as the driving force behind ansatz adaptation, there is also the possibility of having these adaptations as a byproduct, like it happens, e.g., within the Quantum Alternating Operator Ansatz where the primary goal is to find a mixing Hamiltonian that ensures to stay in the feasible subspace [11, 58, 95, 112, 116, 117, 120, 127].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [11]
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“Another possibility is to shift the complexity to the generation of the initial state [11], where the idea is to further utilize the state preparation circuit, which creates an equal superposition of all feasible states, for the design of the mixing Hamiltonian.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [11]
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Qian, W., Basili, R., Eshaghian‐Wilner, M. M., Khokhar, A., Luecke, G. R., & Vary, J. P. (2023) · IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum · doi:10.1109/ipdpsw59300.2023.00094 · Cited by 3
Predict and Conquer: Navigating Algorithm Trade-Offs with Quantum Design Automation
Thelen, S., & Mauerer, W. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00071 · Cited by 4
Quantifying the advantages of applying quantum approximate algorithms to portfolio optimisation
Yuan, H., Long, C. K., Lepage, H. V., & Barnes, C. H. W. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae4a48 · Cited by 2
Solving the Kemeny ranking aggregation problem with quantum optimization algorithms
Combarro, E. F., Pérez‐Fernández, R., Ranilla, J., & Bernard De Baets, C. (2023) · Mathematical Methods in the Applied Sciences · doi:10.1002/mma.9489 · Cited by 2
A Quantum Q-Learning Model for the Capacitated Vehicle Routing Problem
Xu, J., Xie, N., Lee, X., Saito, Y., Asai, N., & Cai, D. (2024) · IEEE International Symposium on Embedded Multicore/Many-core Systems-on-Chip (MCSoC) · doi:10.1109/mcsoc64144.2024.00086 · Cited by 2
CUAOA: A Novel CUDA-Accelerated Simulation Framework for the QAOA
Stein, J., Blenninger, J., Bucher, D., Eder, P. J., Çetiner, E., Zorn, M., & Linnhoff–Popien, C. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.10292 · Cited by 2
Non-Variational Quantum Combinatorial Optimisation
Bennett, T., Noakes, L., & Wang, J. B. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00014 · Cited by 2
Quick design of feasible tensor networks for constrained combinatorial optimization
Nakada, H., Tanahashi, K., & Tanaka, S. (2025) · Quantum · doi:10.22331/q-2025-07-21-1799 · Cited by 2
Learning to Learn With Quantum Optimization Via Quantum Neural Networks
Chen, K., Matsuyama, H., & Huang, W. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00172 · Cited by 3
Complement Grover's Search Algorithm: An Amplitude Suppression Implementation
Vlasic, A., Certo, S., & Pham, A. T. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.10277 · Cited by 2
QAOA-based Fair Sampling on NISQ Devices.Preprint
Golden, J. K., Bärtschi, A., O’Malley, D., & Eidenbenz, S. (2021) · arXiv (Cornell University) · Cited by 2
Self-citationCompact Genetic Algorithm with Quantum-Assisted Feasibility Enforcement
Suksen, K., Benchasattabuse, N., & Chongstitvatana, P. (2022) · ECTI Transactions on Computer and Information Technology (ECTI-CIT) · doi:10.37936/ecti-cit.2022164.247821 · Cited by 1
Li, G., Wang, S., Xiumei, Z., Gao, F., Qin, S., Guo, F.-Z., & Jin, Z. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04783-w · Cited by 1
Multiclass portfolio optimization via variational quantum Eigensolver with Dicke state ansatz
Scursulim, J. V. S., Langeloh, G. M., Beltran, V. L., & Brito, S. (2026) · Scientific Reports · doi:10.1038/s41598-026-36333-4 · Cited by 4
An Adaptive Weighted Qite-Vqe Algorithm for Combinatorial Optimization Problems
Xie, N., Lee, X., Chen, T., Saito, Y., Asai, N., & Cail, D. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00032 · Cited by 1
Implementing Slack-Free Custom Penalty Function for QUBO on Gate-Based Quantum Computers
Lee, X., & Lau, H. C. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00231 · Cited by 1
Efficient QAOA Architecture for Solving Multi-Constrained Optimization Problems
Bucher, D., Porawski, D., Janetschek, M., Stein, J., O’Meara, C., Cortiana, G., & Linnhoff–Popien, C. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00048 · Cited by 1
Software Aided Approach for Constrained Optimization Based on QAOA Modifications
Lamża, T., Zawalska, J., Sterzel, M., & Rycerz, K. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-36030-5_10 · Cited by 1
Solving Quadratic Knapsack Problem with Biased Quantum State Optimization Algorithm
Ha, H. P. N., Nguyễn, V. H., & Ta, A. S. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-62912-9_26 · Cited by 1
Solving the Product Breakdown Structure Problem with constrained QAOA
Zander, R., Seidel, R., Inajetovic, M. A., Steinmann, N., & Petrič, M. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.10356 · Cited by 1
Metadata
- Authors
- Bartschi, A., & Eidenbenz, S.
- Affiliations
- Los Alamos National Laboratory (US)
- ORCID
- Eidenbenz, Stephan
- Venue
- 2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
- Publisher
- IEEE
- Published
- 2020-10
- Pages
- 72-82
- OpenAlex
- W3029819693
- Cited by
- 122
- References
- 21
- Citations by year
- 2026: 11 · 2025: 27 · 2024: 25 · 2023: 29 · 2022: 17 · 2021: 10 · 2020: 3
- FWCI
- 5.55
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE International Conference on Quantum Computing and Engineering (QCE) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- Quantum Alternating Operator Ansatz, mixer design, quantum state preparation, constraint optimization, traveling salesman problem
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