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A Quantum Unique Games Conjecture

Authors Hamoon Mousavi, Taro Spirig

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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
  • Theory of computation → Quantum complexity theory
Keywords
  • hardness of approximation
  • quantum computing
  • noncommutative constraint satisfaction problems
  • Fourier analysis

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Abstract

After the NP-hardness of computational problems such as 3SAT and MaxCut was established, a natural next step was to explore whether these problems remain hard to approximate. While the quantum nonlocal games extensions of some of these problems are known to be hard - indeed undecidable - their inapproximability remains largely unresolved. In this work, we introduce definitions for the quantum extensions of Label-Cover and Unique-Label-Cover. We show that these problems play a similarly crucial role in studying the inapproximability of quantum constraint satisfaction problems as they do in the classical setting.

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Hamoon Mousavi and Taro Spirig. A Quantum Unique Games Conjecture. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 76:1-76:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.76

Author Details

Hamoon Mousavi
  • Simons Institute for Theoretical Computer Science, University of California, Berkeley, CA, USA
Taro Spirig
  • QMATH, Department of Mathematical Sciences, University of Copenhagen, Denmark

Funding

  • Mousavi, Hamoon: Supported by a Simons-CIQC postdoctoral fellowship through NSF QLCI Grant No. 2016245.
  • Spirig, Taro: Supported by the European Union under the Grant Agreement No 101078107, QInteract and VILLUM FONDEN via Villum Young Investigator grant (No 37532) and the QMATH Centre of Excellence (Grant No 10059).

Acknowledgements

We thank Henry Yuen for valuable discussions on the topics explored in this paper. We thank Eric Culf and Michael Chapman for helpful discussions.

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