A Quantum Unique Games Conjecture

Authors Hamoon Mousavi, Taro Spirig



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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

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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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

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.

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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