2026-07-25T06:06:31Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20248 2024-07-02T07:52:53Z ddc:004 open_access

An Improved Quantum Max Cut Approximation via Maximum Matching Lee, Eunou Parekh, Ojas approximation optimization local Hamiltonian rounding SDP matching Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state of a given antiferromagnetic Heisenberg Hamiltonian. In this work, we present a classical approximation algorithm for Quantum Max Cut that achieves an approximation ratio of 0.595, outperforming the previous best algorithms of Lee [Eunou Lee, 2022] (0.562, generic input graph) and King [King, 2023] (0.582, triangle-free input graph). The algorithm is based on finding the maximum weighted matching of an input graph and outputs a product of at most 2-qubit states, which is simpler than the fully entangled output states of the previous best algorithms. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eunou Lee and Ojas Parekh 2024 Is Part Of LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2024.105 urn:nbn:de:0030-drops-202482 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.105 eng https://creativecommons.org/licenses/by/4.0/legalcode