The DOI matches its Crossref record; 49 of the 49 references it cites were found in a registry or an index.
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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Cites
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
Probing many-body dynamics on a 51-atom quantum simulator
Bernien, H., Schwartz, S., Keesling, A., Levine, H., Omran, A., Pichler, H., Choi, S., Zibrov, A. S., Endres, M., Greiner, M., et al. (2017) · Nature · doi:10.1038/nature24622 · Cited by 2,460
A Quantum Approximate Optimization Algorithm
Farhi, E., Goldstone, J., & Gutmann, S. (2014) · arXiv · doi:10.48550/arxiv.1411.4028 · Cited by 1,789
Quantum computation and quantum-state engineering driven by dissipation
Verstraete, F., Wolf, M. M., & Ignacio Cirac, J. (2009) · Nature Physics · doi:10.1038/nphys1342 · Cited by 1,570
Control of quantum phenomena: past, present and future
Brif, C., Chakrabarti, R., & Rabitz, H. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/7/075008 · Cited by 950
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
Quantum approximate optimization of non-planar graph problems on a planar superconducting processor
Harrigan, M. P., Sung, K. J., Neeley, M., Satzinger, K. J., Arute, F., Arya, K., Atalaya, J., Bardin, J. C., Barends, R., Boixo, S., et al. (2021) · Nature Physics · doi:10.1038/s41567-020-01105-y · Cited by 564
Control of quantum phenomena: past, present and futurePreprint
Brif, C., Chakrabarti, R., & RABITZ, H. A. (2010) · Cited by 548
QAOA for Max-Cut requires hundreds of qubits for quantum speed-up
Guerreschi, G. G., & Matsuura, A. Y. (2019) · Scientific Reports · doi:10.1038/s41598-019-43176-9 · Cited by 337
Quantum Supremacy through the Quantum Approximate Optimization Algorithm
Farhi, E., & Harrow, A. W. (2016) · arXiv · doi:10.48550/arxiv.1602.07674 · Cited by 331
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Yu, S.-L., Wu, Y.-E., Ramam, K., Hsu, T.-E., Ho, M.-K., Li, T.-Y., Hsieh, S., Manjunatha, K., & Wu, S. Y. (2026) · Journal of Energy Storage · doi:10.1016/j.est.2026.124552
Gök, M., Genç, S., CENGİZ, E., & Muhammed, T. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7593754
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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