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Obstacles to Variational Quantum Optimization from Symmetry Protection
Open accessAbstract
The quantum approximate optimization algorithm (QAOA) employs variational states generated by a parameterized quantum circuit to maximize the expected value of a Hamiltonian encoding a classical cost function. Whether or not the QAOA can outperform classical algorithms in some tasks is an actively debated question. Our work exposes fundamental limitations of the QAOA resulting from the symmetry and the locality of variational states. A surprising consequence of our results is that the classical Goemans-Williamson algorithm outperforms the QAOA for certain instances of MaxCut, at any constant level. To overcome these limitations, we propose a nonlocal version of the QAOA and give numerical evidence that it significantly outperforms the standard QAOA for frustrated Ising models.
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“An empirical evaluation of recursive QAOA has demonstrated its superiority compared to the standard version as well as its competitiveness compared to the Newman benchmark algorithm [203] for the Max-Cut problem [23].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [23]
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Vizzuso, M., Passarelli, G., Cantele, G., & Lucignano, P. (2024) · Physical Review A · doi:10.1103/physreva.110.062606 · Cited by 3
Multiscale quantum approximate optimization algorithm
Zou, P. (2025) · Physical Review A · doi:10.1103/physreva.111.012427 · Cited by 9
Eclipse Qrisp QAOA: Description and Preliminary Comparison with Qiskit Counterparts
Osaba, E., Petrič, M., Oregi, I., Seidel, R., Ruiz, A., Bock, S., & Kourtis, M. (2025) · Communications in computer and information science · doi:10.1007/978-3-031-85884-0_12 · Cited by 2
The Better Solution Probability Metric: Optimizing QAOA to Outperform its Warm-Start Solution
Feeney, S., Tate, R., & Eidenbenz, S. (2025) · International Conference on Quantum Communications, Networking, and Computing (QCNC) · doi:10.1109/qcnc64685.2025.00077 · Cited by 2
Alonso, M., Martínez, R., Díez-Valle, P., Garbayo, A., García‐Santiago, X., & Gil, G. B. (2025) · IEEE Access · doi:10.1109/access.2025.3578780 · Cited by 2
Metadata
- Authors
- Bravyi, S., Kliesch, A., Koenig, R., & Tang, E.
- Affiliations
- IBM (United States) (US)
- Technical University of Munich (DE)
- California Institute of Technology (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2020-12-24
- Volume
- 125
- Issue
- 26
- Pages
- 260505-260505
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2980835754
- Cited by
- 278
- References
- 22
- Citations by year
- 2026: 23 · 2025: 50 · 2024: 52 · 2023: 71 · 2022: 42 · 2021: 31 · 2020: 8
- FWCI
- 14.93
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Army Research Office (W911NF-20-1-0014)
- Natural Sciences and Engineering Research Council of Canada
- National Science Foundation (PHY-1733907)
- Deutsche Forschungsgemeinschaft
- IBM Research Frontiers Institute
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum approximate optimization algorithm, variational quantum optimization, symmetry protection, Goemans-Williamson algorithm, MaxCut, frustrated Ising model
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