diff --git a/constants/50a.md b/constants/50a.md index 316ec08..3ffd8d4 100644 --- a/constants/50a.md +++ b/constants/50a.md @@ -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 @@ -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