Dining Philosophers, Leader Election and Ring Size problems, in the quantum setting

TL;DR

This paper introduces the first exact quantum protocol for the Dining Philosophers problem, then leverages it to develop improved quantum protocols for leader election and related problems in distributed algorithms.

Contribution

It presents the first exact quantum solution for the Dining Philosophers problem and uses it to enhance quantum leader election protocols, revealing equivalences between these problems.

Findings

First exact quantum protocol for Dining Philosophers

Improved quantum leader election protocol in time and memory

Establishes equivalence between DP and LE in the quantum exact setting

Abstract

We provide the first quantum (exact) protocol for the Dining Philosophers problem (DP), a central problem in distributed algorithms. It is well known that the problem cannot be solved exactly in the classical setting. We then use our DP protocol to provide a new quantum protocol for the tightly related problem of exact leader election (LE) on a ring, improving significantly in both time and memory complexity over the known LE protocol by Tani et. al. To do this, we show that in some sense the exact DP and exact LE problems are equivalent; interestingly, in the classical non-exact setting they are not. Hopefully, the results will lead to exact quantum protocols for other important distributed algorithmic questions; in particular, we discuss interesting connections to the ring size problem, as well as to a physically motivated question of breaking symmetry in 1D translationally invariant systems.