updated 2025-08-17
[AGM20] Anurag Anshu, David Gosset, and Karen Morenz. Beyond Product State Approximations for a Quantum Analogue of Max Cut. LIPIcs TQC 2020, Vol. 158 (2020), 7:1–7:15. arXiv:2003.14394 [quant-ph].
[ALMPS25] Anuj Apte, Eunou Lee, Kunal Marwaha, Ojas Parekh, James Sud. Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings. Apr. 2025. European Symposium on Algorithms 2025. arXiv:2504.15276 [quant-ph].
[APS25] Anuj Apte, Ojas Parekh, and James Sud. Conjectured Bounds for 2-Local Hamiltonians via Token Graphs. June 2025. arXiv:2506.03441 [quant-ph].
[BFV10] Jop Briet, Fernando Mario de Oliveira Filho, and Frank Vallentin. The Positive Semidefinite Grothendieck Problem with Rank Constraint. Lecture Notes in Computer Science, Vol. 6198 (2010), pp. 31–42. arXiv:0910.5765 [math].
[BH14] Fernando G. S. L. Brandão and Aram W. Harrow. Product-State Approximations to Quantum Ground States. Dec. 2014. arXiv:1310.0017.
[CM16] Toby Cubitt and Ashley Montanaro. Complexity Classification of Local Hamiltonian Problems. Mar. 2016. arXiv:1311.3161 [quant-ph].
[Edm65] Jack Edmonds. Paths, Trees, and Flowers. Canadian Journal of Mathematics 17 (1965), pp. 449–467. DOI:10.4153/CJM-1965-045-4.
[GP19] Sevag Gharibian and Ojas Parekh. Almost Optimal Classical Approximation Algorithms for a Quantum Generalization of Max-Cut. LIPIcs APPROX/RANDOM 2019, Vol. 145 (2019), 31:1–31:17. arXiv:1909.08846 [quant-ph].
[GSS25] Sander Gribling, Lennart Sinjorgo, and Renata Sotirov. Improved Approximation Ratios for the Quantum Max-Cut Problem on General, Triangle-Free and Bipartite Graphs. Apr. 2025. arXiv:2504.11120 [quant-ph].
[HTPG24] Felix Huber, Kevin Thompson, Ojas Parekh, and Sevag Gharibian. Second Order Cone Relaxations for Quantum Max Cut. Nov. 2024. arXiv:2411.04120 [quant-ph].
[HNPTW22] Yeongwoo Hwang, Joe Neeman, Ojas Parekh, Kevin Thompson, John Wright. Unique Games hardness of Quantum Max-Cut, and a conjectured vector-valued Borell’s inequality. Sep. 2022. arXiv:2411.04120 [quant-ph].
[JN25] Nathan Ju and Ansh Nagda. Improved Approximation Algorithms for the EPR Hamiltonian. Apr. 2025. arXiv:2504.10712 [quant-ph].
[JKKSW24] Zackary Jorquera, Alexandra Kolla, Steven Kordonowy, Juspreet Singh Sandhu, and Stuart Wayland. Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians. Nov. 2024. arXiv:2410.15544 [quant-ph].
[Kin23] Robbie King. An Improved Approximation Algorithm for Quantum Max-Cut. Quantum 7 (Nov. 2023), p. 1180. arXiv:2209.02589 [quant-ph].
[Lee22] Eunou Lee. Optimizing Quantum Circuit Parameters via SDP. Sept. 2022. arXiv:2209.00789 [quant-ph].
[LP24] Eunou Lee and Ojas Parekh. An Improved Quantum Max Cut Approximation via Matching. Feb. 2024. arXiv:2401.03616 [quant-ph].
[NPA08] Miguel Navascues, Stefano Pironio, and Antonio Acin. A Convergent Hierarchy of Semidefinite Programs Characterizing the Set of Quantum Correlations. New Journal of Physics 10.7 (2008), p. 073013. arXiv:0803.4290 [quant-ph].
[PM15] Stephen Piddock and Ashley Montanaro. The Complexity of Antiferromagnetic Interactions and 2D Lattices. Dec. 2015. arXiv:1506.04014.
[PT21] Ojas Parekh and Kevin Thompson. Application of the Level-2 Quantum Lasserre Hierarchy in Quantum Approximation Algorithms. LIPIcs ICALP 2021, Vol. 198 (2021), 102:1–102:20. arXiv:2105.05698 [quant-ph].
[PT22] Ojas Parekh and Kevin Thompson. An Optimal Product-State Approximation for 2-Local Quantum Hamiltonians with Positive Terms. June 2022. arXiv:2206.08342 [quant-ph].
[Tak+23] Jun Takahashi, Chaithanya Rayudu, Cunlu Zhou, Robbie King, Kevin Thompson, and Ojas Parekh. An SU(2)-Symmetric Semidefinite Programming Hierarchy for Quantum Max Cut. Aug. 2023. arXiv:2307.15688 [quant-ph].
[TZ25a] Wenxuan Tao and Fen Zuo. A Refined Algorithm For the EPR Model. June 2025. arXiv:2506.08547 [quant-ph].
[TZ25b] Wenxuan Tao and Fen Zuo. Testing APS Conjecture on Regular Graphs. July 2025. arXiv:2507.10050 [quant-ph].
[WCEHK24] Adam Bene Watts, Anirban Chowdhury, Aidan Epperly, J. William Helton, and Igor Klep. Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators. Quantum 8 (May 2024), p. 1352. arXiv:2307.15661 [math-ph, physics:quant-ph].