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An Improved Quantum Max Cut Approximation via Maximum Matching

Authors Eunou Lee, Ojas Parekh

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Subject Classification

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

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Abstract

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ICALP.2024.105

Author Details

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

Funding

Eunou Lee was supported by Individual Grant No.CG093801 at Korea Institute for Advanced Study. This work is supported by a collaboration between the US DOE and other Agencies. Ojas Parekh was supported by the U.S. Department of Energy (DOE), Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. Additional support is acknowledged from DOE, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing, Fundamental Algorithmic Research in Quantum Computing. 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.

Acknowledgements

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

References

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