An Improved Quantum Max Cut Approximation via Maximum Matching

Authors Eunou Lee, Ojas Parekh

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Author Details

Eunou Lee
  • Korea Institute for Advanced Study, Seoul, South Korea
Ojas Parekh
  • Sandia National Laboratories, Albuquerque, NM, USA


Eunou Lee appreciates helpful comments on the write-up by Andrus Giraldo.

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Eunou Lee and Ojas 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)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rounding techniques
  • approximation
  • optimization
  • local Hamiltonian
  • rounding
  • SDP
  • matching


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