Communication Dans Un Congrès Année : 2024

No distributed quantum advantage for approximate graph coloring

Résumé

We give an almost complete characterization of the hardness of $c$-coloring $\chi$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit any distributed quantum advantage. To do that: 1. We give a new distributed algorithm that finds a $c$-coloring in $\chi$-chromatic graphs in $\tilde{\mathcal{O}}(n^{\frac{1}{\alpha}})$ rounds, with $\alpha = \bigl\lfloor\frac{c-1}{\chi - 1}\bigr\rfloor$. 2. We prove that any distributed algorithm for this problem requires $\Omega(n^{\frac{1}{\alpha}})$ rounds. Our upper bound holds in the classical, deterministic LOCAL model, while the near-matching lower bound holds in the non-signaling model. This model, introduced by Arfaoui and Fraigniaud in 2014, captures all models of distributed graph algorithms that obey physical causality; this includes not only classical deterministic LOCAL and randomized LOCAL but also quantum-LOCAL, even with a pre-shared quantum state. We also show that similar arguments can be used to prove that, e.g., 3-coloring 2-dimensional grids or $c$-coloring trees remain hard problems even for the non-signaling model, and in particular do not admit any quantum advantage. Our lower-bound arguments are purely graph-theoretic at heart; no background on quantum information theory is needed to establish the proofs.

Fichier principal
Vignette du fichier
quantum-coloring.pdf (1.16 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04169010 , version 1 (23-07-2023)
hal-04169010 , version 2 (14-11-2023)

Licence

Identifiants

Citer

Xavier Coiteux-Roy, Francesco d'Amore, Rishikesh Gajjala, Fabian Kuhn, François Le Gall, et al.. No distributed quantum advantage for approximate graph coloring. STOC '24: 56th Annual ACM Symposium on Theory of Computing, Jun 2024, Vancouver BC Canada, Canada. pp.1901-1910, ⟨10.1145/3618260.3649679⟩. ⟨hal-04169010v2⟩
282 Consultations
382 Téléchargements

Altmetric

Partager

  • More