We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial graph problem with an inherently global definition [Le Gall et al. 2019]. We present a problem that we call iterated GHZ, which is defined using only local constraints. Formally, it is a family of locally checkable labeling problems [Naor and Stockmeyer 1995]; in particular, solutions can be verified with a constant-round distributed algorithm. We show that in graphs of maximum degree $\Delta$, any classical (deterministic or randomized) LOCAL model algorithm will require $\Omega(\Delta)$ rounds to solve the iterated GHZ problem, while the problem can be solved in $1$ round in quantum-LOCAL. We use the round elimination technique to prove that the iterated GHZ problem requires $\Omega(\Delta)$ rounds for classical algorithms. This is the first work that shows that round elimination is indeed able to separate the two models, and this also demonstrates that round elimination cannot be used to prove lower bounds for quantum-LOCAL. To apply round elimination, we introduce a new technique that allows us to discover appropriate problem relaxations in a mechanical way; it turns out that this new technique extends beyond the scope of the iterated GHZ problem and can be used to e.g. reproduce prior results on maximal matchings [FOCS 2019, PODC 2020] in a systematic manner.

翻译：我们提出了首个展现经典随机化LOCAL分布式计算模型与其量子对应模型之间存在超常数分离的局部问题。根据先前的研究，这种分离仅在一个具有内在全局定义的人工图问题上已知[Le Gall等人，2019]。我们提出了一个称为迭代GHZ的问题，该问题仅使用局部约束定义。形式上，它是一个局部可检查标记问题族[Naor和Stockmeyer，1995]；特别地，其解可通过常数轮分布式算法验证。我们证明在最大度为$\Delta$的图中，任何经典（确定性或随机化）LOCAL模型算法需要$\Omega(\Delta)$轮来解决迭代GHZ问题，而该问题在量子LOCAL模型中可在$1$轮内解决。我们使用轮消除技术证明迭代GHZ问题对经典算法需要$\Omega(\Delta)$轮。这是首次证明轮消除技术确实能够区分这两种模型，同时也表明轮消除不能用于证明量子LOCAL模型的下界。为应用轮消除，我们引入了一种新技术，允许以机械方式发现适当的问题松弛；结果表明，这种新技术超出了迭代GHZ问题的范围，可用于以系统化方式重现先前关于最大匹配的研究成果[FOCS 2019, PODC 2020]。