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arXiv · 2212.02768

Non-trivial lower bound for 3-coloring the ring in the quantum LOCAL model

François Le Gall·Ansis Rosmanis
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Abstract

We consider the LOCAL model of distributed computing, where in a single round of communication each node can send to each of its neighbors a message of an arbitrary size. It is know that, classically, the round complexity of 3-coloring an $n$-node ring is $Θ(\log^*\!n)$. In the case where communication is quantum, only trivial bounds were known: at least some communication must take place. We study distributed algorithms for coloring the ring that perform only a single round of one-way communication. Classically, such limited communication is already known to reduce the number of required colors from $Θ(n)$, when there is no communication, to $Θ(\log n)$. In this work, we show that the probability of any quantum single-round one-way distributed algorithm to output a proper $3$-coloring is exponentially small in $n$.

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François Le Gall, Ansis Rosmanis. 2022-12-06. Non-trivial lower bound for 3-coloring the ring in the quantum LOCAL model. https://arxiv.org/abs/2212.02768

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