DROPS

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2026.71

The Quantum Smooth Label Cover Problem Is Undecidable

Authors: Eric Culf, Kieran Mastel, Connor Paddock, and Taro Spirig

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract

We show that the quantum smooth label cover problem is undecidable and RE-hard. This sharply contrasts the quantum unique label cover problem, which can be decided efficiently by a result of Kempe, Regev, and Toner (FOCS'08). On the other hand, our result aligns with the RE-hardness of the quantum label cover problem, which follows from the celebrated MIP^* = RE result of Ji, Natarajan, Vidick, Wright, and Yuen (ACM'21). Additionally, we show that the quantum oracularized smooth label cover problem is RE-hard. Our second result fits with the alternative quantum unique games conjecture recently proposed by Mousavi and Spirig (ITCS'25) on the RE-hardness of the quantum oracularized unique label cover problem. Our proof techniques include a quantum version of Feige’s reduction from 3SAT to 3SAT5 (STOC'96) for BCS-MIP^*-protocols, which may be of independent interest.

Cite as

Eric Culf, Kieran Mastel, Connor Paddock, and Taro Spirig. The Quantum Smooth Label Cover Problem Is Undecidable. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 71:1-71:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{culf_et_al:LIPIcs.ICALP.2026.71,
  author =	{Culf, Eric and Mastel, Kieran and Paddock, Connor and Spirig, Taro},
  title =	{{The Quantum Smooth Label Cover Problem Is Undecidable}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{71:1--71:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.71},
  URN =		{urn:nbn:de:0030-drops-264602},
  doi =		{10.4230/LIPIcs.ICALP.2026.71},
  annote =	{Keywords: Complexity Theory, Constraint Satisfaction Problems, Hardness of Approximation, Quantum Computing}
}

Search Results

Documents authored by Mastel, Kieran

The Quantum Smooth Label Cover Problem Is Undecidable

Abstract

Cite as

Thanks for your feedback!

Could not send message