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New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs

Authors Alkida Balliu , Corinna Coupette , Antonio Cruciani , Francesco d'Amore , Massimo Equi , Henrik Lievonen , Augusto Modanese , Dennis Olivetti , Jukka Suomela

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Quantum computation theory
Keywords
  • linear programming
  • distributed quantum advantage
  • quantum-LOCAL model
  • SLOCAL model
  • online-LOCAL model
  • non-signaling distributions
  • locally checkable labeling problems
  • dequantization

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Abstract

In this work, we give two results that put new limits on distributed quantum advantage in the context of the LOCAL model of distributed computing:  
1) We show that there is no distributed quantum advantage for any linear program. Put otherwise, if there is a quantum-LOCAL algorithm 𝒜 that finds an α-approximation of some linear optimization problem Π in T communication rounds, we can construct a classical, deterministic LOCAL algorithm 𝒜' that finds an α-approximation of Π in T rounds. As a corollary, all classical lower bounds for linear programs, including the KMW bound, hold verbatim in quantum-LOCAL. 
2) Using the above result, we show that there exists a locally checkable labeling problem (LCL) for which quantum-LOCAL is strictly weaker than the classical deterministic SLOCAL model.  Our results extend from quantum-LOCAL to finitely dependent and non-signaling distributions, and one of the corollaries of our work is that the non-signaling model and the SLOCAL model are incomparable in the context of LCL problems: By prior work, there exists an LCL problem for which SLOCAL is strictly weaker than the non-signaling model, and our work provides a separation in the opposite direction.

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Alkida Balliu, Corinna Coupette, Antonio Cruciani, Francesco d'Amore, Massimo Equi, Henrik Lievonen, Augusto Modanese, Dennis Olivetti, and Jukka Suomela. New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.11

Author Details

Alkida Balliu
  • Gran Sasso Science Institute, L’Aquila, Italy
Corinna Coupette
  • Aalto University, Espoo, Finland
  • Max Planck Institute for Informatics, Saarbrücken, Germany
Antonio Cruciani
  • Aalto University, Espoo, Finland
Francesco d'Amore
  • Gran Sasso Science Institute, L’Aquila, Italy
Massimo Equi
  • Aalto University, Espoo, Finland
Henrik Lievonen
  • Aalto University, Espoo, Finland
Augusto Modanese
  • Aalto University, Espoo, Finland
Dennis Olivetti
  • Gran Sasso Science Institute, L’Aquila, Italy
Jukka Suomela
  • Aalto University, Espoo, Finland

Funding

This work was supported in part by the MUR (Italy) Department of Excellence 2023 - 2027 for GSSI, the European Union - NextGenerationEU under the Italian MUR National Innovation Ecosystem grant ECS00000041 - VITALITY – CUP: D13C21000430001, the PNRR MIUR research project GAMING "Graph Algorithms and MinINg for Green agents" (PE0000013, CUP D13C24000430001), and the Research Council of Finland, Grants 363558 and 359104.

Acknowledgements

We thank the anonymous reviewers for their helpful comments and suggestions, which allowed us to improve the quality of this paper.

References

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