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We provide the first quantum (exact) protocol for the Dining Philosophersproblem (DP), a central problem in distributed algorithms. It is well knownthat the problem cannot be solved exactly in the classical setting. We then useour DP protocol to provide a new quantum protocol for the tightly relatedproblem of exact leader election (LE) on a ring, improving significantly inboth time and memory complexity over the known LE protocol by Tani et. al. Todo this, we show that in some sense the exact DP and exact LE problems areequivalent; interestingly, in the classical non-exact setting they are not.Hopefully, the results will lead to exact quantum protocols for other importantdistributed algorithmic questions; in particular, we discuss interestingconnections to the ring size problem, as well as to a physically motivatedquestion of breaking symmetry in 1D translationally invariant systems.

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