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Parameter concentrations in quantum approximate optimization
Open accessAbstract
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. In QAOA, a quantum circuit is trained---by repeatedly adjusting circuit parameters---to solve a problem instance. Several recent findings have reported parameter concentration effects in QAOA and their presence has become one of folklore: while empirically observed, the concentrations have not been defined and analytical approaches remain scarce, focusing on limiting system sizes while neglecting parameter scaling as system size increases. We found that optimal QAOA circuit parameters concentrate as an inverse polynomial in the problem size, providing an optimistic result for improving circuit training. Our results are analytically demonstrated for QAOA at $p=1,2$ (corresponding to 2 and 4 tunable parameters, respectively). The technique is also applicable for higher depths wherein the concentration effect is cross verified numerically. Parameter concentrations allow for training on a fraction $w
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“On the other hand, there is increasing evidence that classes of problems exhibit pronounced parameter concentration of the optimal or near optimal angles [19], [51], [1], [6], [61], [17], [48], [41]”
From High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices (2023) · cites this paper as [1]
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Matsuyama, H., & Yamashiro, Y. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00253
Jiang, L., Zhang, C., & Chen, F. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00167 · Cited by 5
Approximating Ground States of Quantum Hamiltonians with Snapshot-QAOA
Tate, R., Langfitt, Q., Pelofske, E., Kirmani, A. A., Bärtschi, A., Golden, J. K., & Eidenbenz, S. (2025) · IEEE International Conference on Quantum Artificial Intelligence (QAI) · doi:10.1109/qai63978.2025.00035
Quantum optimization for the Physician Scheduling Problem
Mlaouhi, B., Ahabchane, C., & Benslimen, I. (2025) · International Conference on Embedded Systems and Artificial Intelligence (ESAI) · doi:10.1109/esai67033.2025.11438759
Performance evaluation and control improvements for solving optimization problems on NISQ platforms
Gilbert, V. (2024) · theses.fr (ABES) · doi:10.70675/81f9c638z5867z40e4zaed8ze9824ff5a163
Implementation of the Quantum Approximate Optimization Algorithm for Max-Cut
J., S., J., G., P., V., Oswal, B., Kumawat, T. S., & Pandey, S. (2026) · 2026 International Conference on Next-Gen Quantum and Advanced Computing: Algorithms, Security, and Beyond (NQComp) · doi:10.1109/nqcomp68334.2026.11497732
Role of overparametrization in quantum approximate optimization
Rabinovich, D., Kardashin, A., & Adhikary, S. (2026) · Physical Review A · doi:10.1103/m1d6-1v47 · Cited by 3
Self-citationAnalytical Dimensions and Performance Evaluation of the Quantum Approximate Optimization Algorithm
Trigueros, B., Roig, P., Alcaraz, S., & Gilly, K. (2026) · 2026 International Conference on Integrated Intelligence and Cognitive Engineering (ICIICE) · doi:10.1109/iciice69672.2026.11565281
Metadata
- Authors
- Akshay, V., Rabinovich, D., Campos, E., & Biamonte, J.
- Affiliations
- Skolkovo Institute of Science and Technology (RU)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2021-07-07
- Volume
- 104
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W3139223064
- Cited by
- 103
- References
- 47
- Citations by year
- 2026: 10 · 2025: 25 · 2024: 23 · 2023: 25 · 2022: 17 · 2021: 3
- FWCI
- 6.01
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Funders
- Leading Research Center on Quantum Computing (014/20)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- quantum approximate optimization algorithm, variational quantum algorithms, circuit depth
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