Document Open Access Logo

A 0.8395-Approximation Algorithm for the EPR Problem

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

PDF

File

Thumbnail PDF
PDF
LIPIcs.ESA.2026.144.pdf
  • Filesize: 0.74 MB
  • 13 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Quantum computing
  • optimization
  • approximation algorithms

Metrics

Abstract

We give an efficient 0.8395-approximation algorithm for the EPR Hamiltonian. Our improvement comes from a new nonlinear monogamy-of-entanglement bound on star graphs and a refined parameterization of a shallow quantum circuit from previous works. We also prove limitations showing that current methods cannot achieve substantially better approximation ratios, indicating that further progress will require fundamentally new techniques.

Cite As Get BibTex

Anuj Apte, Eunou Lee, Kunal Marwaha, Ojas Parekh, Lennart Sinjorgo, and James Sud. A 0.8395-Approximation Algorithm for the EPR Problem. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 144:1-144:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.144

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
Lennart Sinjorgo
  • CentER, Department of Econometrics and OR, Tilburg University, The Netherlands
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. 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

  1. Anurag Anshu, David Gosset, and Karen Morenz. Beyond product state approximations for a quantum analogue of Max Cut. LIPIcs, Volume 158, TQC 2020, 158:7:1-7:15, 2020. URL: https://doi.org/10.4230/LIPIcs.TQC.2020.7.
  2. Anuj Apte, Eunou Lee, Kunal Marwaha, Ojas Parekh, and James Sud. Improved Algorithms for Quantum MaxCut via Partially Entangled Matchings, April 2025. URL: https://doi.org/10.48550/arXiv.2504.15276.
  3. Anuj Apte, Ojas Parekh, and James Sud. Conjectured Bounds for 2-Local Hamiltonians via Token Graphs, June 2025. URL: https://doi.org/10.48550/arXiv.2506.03441.
  4. Sergey Bravyi, Arvid J Bessen, and Barbara M Terhal. Merlin-arthur games and stoquastic complexity. arXiv preprint quant-ph/0611021, 2006. Google Scholar
  5. Sabine Burgdorf, Igor Klep, and Janez Povh. Optimization of polynomials in non-commuting variables. SpringerBriefs in Mathematics. Springer, 2016. Google Scholar
  6. Sevag Gharibian and Ojas Parekh. Almost optimal classical approximation algorithms for a quantum generalization of Max-Cut. LIPIcs, Volume 145, APPROX/RANDOM 2019, 145:31:1-31:17, 2019. URL: https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.31.
  7. Michel X. Goemans and David P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM, 42(6):1115-1145, November 1995. URL: https://doi.org/10.1145/227683.227684.
  8. Sander Gribling, Lennart Sinjorgo, and Renata Sotirov. Improved approximation ratios for the Quantum Max-Cut problem on general, triangle-free and bipartite graphs, April 2025. URL: https://doi.org/10.48550/arXiv.2504.11120.
  9. Zackary Jorquera, Alexandra Kolla, Steven Kordonowy, Juspreet Singh Sandhu, and Stuart Wayland. Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians, November 2024. URL: https://doi.org/10.48550/arXiv.2410.15544.
  10. Nathan Ju and Ansh Nagda. Improved approximation algorithms for the EPR Hamiltonian, April 2025. URL: https://doi.org/10.48550/arXiv.2504.10712.
  11. Robbie King. An Improved Approximation Algorithm for Quantum Max-Cut. Quantum, 7:1180, November 2023. URL: https://doi.org/10.22331/q-2023-11-09-1180.
  12. A. Kitaev, A. Shen, and M. Vyalyi. Classical and Quantum Computation, volume 47 of Graduate Studies in Mathematics. American Mathematical Society, Providence, Rhode Island, May 2002. URL: https://doi.org/10.1090/gsm/047.
  13. Eunou Lee and Ojas Parekh. An improved Quantum Max Cut approximation via matching, February 2024. URL: https://arxiv.org/abs/2401.03616.
  14. Elliott Lieb and Daniel Mattis. Ordering Energy Levels of Interacting Spin Systems. Journal of Mathematical Physics, 3(4):749-751, July 1962. URL: https://doi.org/10.1063/1.1724276.
  15. Kunal Marwaha and James Sud. Quantum maxcut reference, 2025. URL: https://marwahaha.github.io/quantum-maxcut-reference/.
  16. 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):073013, July 2008. URL: https://doi.org/10.1088/1367-2630/10/7/073013.
  17. Ojas Parekh and Kevin Thompson. Application of the Level-2 Quantum Lasserre Hierarchy in Quantum Approximation Algorithms. LIPIcs, Volume 198, ICALP 2021, 198:102:1-102:20, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.102.
  18. Ojas Parekh and Kevin Thompson. An Optimal Product-State Approximation for 2-Local Quantum Hamiltonians with Positive Terms, June 2022. URL: https://doi.org/10.48550/arXiv.2206.08342.
  19. Jun Takahashi, Chaithanya Rayudu, Cunlu Zhou, Robbie King, Kevin Thompson, and Ojas Parekh. An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut, August 2023. URL: https://doi.org/10.48550/arXiv.2307.15688.
  20. Wenxuan Tao and Fen Zuo. A Refined Algorithm For the EPR model, June 2025. URL: https://doi.org/10.48550/arXiv.2506.08547.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact