Coiteux-Roy, X and D'Amore, F and Gajjala, R and Kuhn, F and Le Gall, F and Lievonen, H and Modanese, A and Renou, M-O and Schmid, G and Suomela, J (2024) No Distributed Quantum Advantage for Approximate Graph Coloring. In: 56th Annual ACM Symposium on Theory of Computing, STOC 2024, 24 June 2024through 28 June 2024, Vancouver, Canada, pp. 1901-1910.
|
PDF
STOC_2024.pdf - Published Version Download (283kB) | Preview |
Abstract
We give an almost complete characterization of the hardness of c-coloring �-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: We give a new distributed algorithm that finds a c-coloring in �-chromatic graphs in �(n1/α) rounds, with α = �c-1/� - 1�. We prove that any distributed algorithm for this problem requires �(n1/α) 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. © 2024 Owner/Author.
| Item Type: | Conference Paper |
|---|---|
| Publication: | Proceedings of the Annual ACM Symposium on Theory of Computing |
| Publisher: | Association for Computing Machinery |
| Additional Information: | The copyright for this article belongs to Authors. |
| Keywords: | Coloring; Computation theory; Distributed computer systems; Information theory; Quantum optics, Chromatic graphs; Deterministics; Distributed graph algorithms; Graph colorings; Low bound; Matchings; Non-signaling model; Quantum advantage; Quantum state; Upper Bound, Graph theory |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 30 Jul 2024 10:27 |
| Last Modified: | 30 Jul 2024 10:27 |
| URI: | http://eprints.iisc.ac.in/id/eprint/85607 |
Actions (login required)
 |
View Item |
