Quantum Advantage for the LOCAL Model in Distributed Computing

TL;DR

This paper demonstrates that quantum distributed computing can solve certain problems in the LOCAL model significantly faster than classical methods, achieving constant rounds versus linear rounds in network size.

Contribution

It proves the first quantum advantage in the LOCAL model by identifying a task solvable in constant rounds quantumly but requiring linear rounds classically.

Findings

Quantum advantage in the LOCAL model established

Constant-round quantum solution for a specific task

Classical solution requires linear rounds

Abstract

There are two central models considered in (fault-free synchronous) distributed computing: the CONGEST model, in which communication channels have limited bandwidth, and the LOCAL model, in which communication channels have unlimited bandwidth. Very recently, Le Gall and Magniez (PODC 2018) showed the superiority of quantum distributed computing over classical distributed computing in the CONGEST model. In this work we show the superiority of quantum distributed computing in the LOCAL model: we exhibit a computational task that can be solved in a constant number of rounds in the quantum setting but requires $\Omega(n)$ rounds in the classical setting, where $n$ denotes the size of the network.