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Updates on quantum Max Cut bounds + alphabetically sorted references #76

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ed4ace9
add [JKKSW24] value
huberfe Feb 11, 2026
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Merge branch 'teorth:main' into main
huberfe Feb 11, 2026
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Merge branch 'teorth:main' into main
huberfe May 19, 2026
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update quantum max cut bounds and references
huberfe May 19, 2026
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Merge branch 'main' of https://github.com/huberfe/optimizationproblems
huberfe May 19, 2026
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25 changes: 15 additions & 10 deletions constants/50a.md
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Original file line number Diff line number Diff line change
Expand Up @@ -31,9 +31,11 @@ $$C_{50} = \sup_f \min_G
| 0.531 | [AGM20] |
| 0.533 | [PT21] |
| 0.562 | [L22] |
| 0.595 | [LP24] |
| 0.595 | [LP24] |
| 0.599 | [JKKSW24] |
| 0.603 | [GSS25] |
| 0.611 | [ALMPS25] |
| 0.614 | [BBKL26] | Proves monogamy conjecture from [ALMPS25]


## Additional comments
Expand All @@ -48,20 +50,23 @@ Marwaha and Sud, [webpage](https://marwahaha.github.io/quantum-maxcut-reference/


## References
- **[P25]** S. Piddock, *Quantum Max-Cut is NP-hard to approximate*, [arXiv:2510.07995v1](https://arxiv.org/abs/2510.07995)


- **[AGM20]** A. Anshu, D. Gosset, K. Morenz, *Beyond product state approximations for a quantum analogue of Max Cut*, In proceedings of 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020), [arXiv:2003.14394](https://arxiv.org/abs/2003.14394)
- **[ALMPS25]** A. Apte, A. Lee, K. Marwaha, O. Parekh, J. Sud. *Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings*, [arXiv:2504.15276](https://arxiv.org/abs/2504.15276)
- **[BBKL26]** Ainesh Bakshi, Arpon Basu, Pravesh Kothari, Anqi Li, *Sharp Bounds on the Eigenvalues of Kikuchi Graphs and Applications to Quantum Max Cut* [arXiv:2605.14994](https://arxiv.org/abs/2605.14994)
- **[GP19]** S. Gharibian and O. Parekh. *Almost Optimal Classical Approximation Algorithms for a Quantum Generalization of Max-Cut*.
In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019), volume 145 of Leibniz International Proceedings in Informatics (LIPIcs), pages 31:1–31:17, 2019, [arXiv:1909.08846](https://arxiv.org/abs/1909.08846)
- **[HTPG24]** F. Huber, K. Thompson, O. Parekh, S. Gharibian. *Second order cone relaxations for quantum Max Cut*, [arXiv:2411.04120](https://arxiv.org/abs/2411.04120)
- **[AGM20]** A. Anshu, D. Gosset, K. Morenz, *Beyond product state approximations for a quantum analogue of Max Cut*, In proceedings of 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020), [arXiv:2003.14394](https://arxiv.org/abs/2003.14394)
- **[PT21]** O. Parekh, K. Thompson, *Application of the Level-2 Quantum Lasserre Hierarchy in Quantum Approximation Algorithms*, Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP), 2021, arXiv:2105.05698
- **[L22]** E. Lee. *Optimizing Quantum Circuit Parameters via SDP*. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ISAAC.2022.48, arXiv:2209.00789
- **[K22]** R. King, *An Improved Approximation Algorithm for Quantum Max-Cut*, Quantum 7, 1180 (2023), [arXiv:2209.02589](https://arxiv.org/abs/2209.02589)
- **[LP24]** E. Lee, O. Parekh. *An improved Quantum Max Cut approximation via maximum matching*, In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 105:1-105:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICALP.2024.105, [arXiv:2401.03616](https://arxiv.org/abs/2401.03616)
- **[GSS25]** S. Gribling, L. Sinjorgo, R. Sotirov. *Improved approximation ratios for the Quantum Max-Cut problem on general, triangle-free and bipartite graphs*, [arXiv:2504.11120](https://arxiv.org/abs/2504.11120)
- **[ALMPS25]** A. Apte, A. Lee, K. Marwaha, O. Parekh, J. Sud. *Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings*, [arXiv:2504.15276](https://arxiv.org/abs/2504.15276)
- **[H25]** F. Huber, *A Lovász theta lower bound on Quantum Max Cut*, [arXiv:2512.20326](https://arxiv.org/abs/2512.20326).
- **[HTPG24]** F. Huber, K. Thompson, O. Parekh, S. Gharibian. *Second order cone relaxations for quantum Max Cut*, [arXiv:2411.04120](https://arxiv.org/abs/2411.04120)
- **[JN25]**, N. Ju, A. Nagda, *Improved approximation algorithms for the EPR Hamiltonian*, [arXiv:2504.10712](https://arxiv.org/abs/2504.10712)

- **[JKKSW24]**, Z. Jorquera, A. Kolla, S. Kordonowy, S. S. Sandhu, and S. Wayland. *Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians*. Nov. 2024. [arXiv:2410.15544](https://arxiv.org/abs/2410.15544)
- **[K22]** R. King, *An Improved Approximation Algorithm for Quantum Max-Cut*, Quantum 7, 1180 (2023), [arXiv:2209.02589](https://arxiv.org/abs/2209.02589)
- **[L22]** E. Lee. *Optimizing Quantum Circuit Parameters via SDP*. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ISAAC.2022.48, arXiv:2209.00789
- **[LP24]** E. Lee, O. Parekh. *An improved Quantum Max Cut approximation via maximum matching*, In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 105:1-105:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICALP.2024.105, [arXiv:2401.03616](https://arxiv.org/abs/2401.03616)
- **[P25]** S. Piddock, *Quantum Max-Cut is NP-hard to approximate*, [arXiv:2510.07995v1](https://arxiv.org/abs/2510.07995)
- **[PT21]** O. Parekh, K. Thompson, *Application of the Level-2 Quantum Lasserre Hierarchy in Quantum Approximation Algorithms*, Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP), 2021, arXiv:2105.05698

## Contribution notes

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