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Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings

Authors Anuj Apte , Eunou Lee, Kunal Marwaha , Ojas Parekh , James Sud

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ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Quantum computing
  • Quantum MaxCut
  • Maximum matching

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Abstract

We introduce a 0.611-approximation algorithm for Quantum MaxCut and a (1+√5)/4 ≈ 0.809-approximation algorithm for the EPR Hamiltonian of [King, 2023]. A novel ingredient in both of these algorithms is to partially entangle pairs of qubits associated to edges in a matching, while preserving the direction of their single-qubit Bloch vectors. This allows us to interpolate between product states and matching-based states with a tunable parameter.

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Anuj Apte, Eunou Lee, Kunal Marwaha, Ojas Parekh, and James Sud. Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 101:1-101:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.101

Author Details

Anuj Apte
  • University of Chicago, IL, USA
Eunou Lee
  • Korea Institute for Advanced Study, Seoul, South Korea
Kunal Marwaha
  • University of Chicago, IL, USA
Ojas Parekh
  • Sandia National Laboratories, Albuquerque, NM, USA
James Sud
  • University of Chicago, IL, USA

Funding

K.M and J.S. acknowledge that this material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 2140001.
  • Lee, Eunou: E.L is supported by a KIAS Individual Grant CG093801 at Korea Institute for Advanced Study.
  • Marwaha, Kunal: K.M acknowledges support from AFOSR (FA9550-21-1-0008).
  • Parekh, Ojas: O.P. acknowledges that this material is based upon work supported by the U.S. Department of Energy, Office of Science, Accelerated Research in Quantum Computing, Fundamental Algorithmic Research toward Quantum Utility (FAR-Qu).
  • Sud, James: J.S acknowledges that this work is funded in part by the STAQ project under award NSF Phy-232580; in part by the US Department of Energy Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing Program.

Acknowledgements

This work is supported by a collaboration between the US DOE and other Agencies. The work of A.A is supported by the Data Science Institute at the University of Chicago. This article has been authored by an employee of National Technology & Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The employee owns all right, title and interest in and to the article and is solely responsible for its contents. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this article or allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan https://www.energy.gov/downloads/doe-public-access-plan.

References

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