A Post-Quantum Lower Bound for the Distributed Lovasz Local Lemma

In this work, we study the Lovász local lemma (LLL) problem in the area of distributed quantum computing, which has been the focus of attention of recent advances in quantum computing [STOC’24, STOC’25, STOC’25]. We prove a lower bound of \(2^{\Omega(\log^*n)}\) for the complexity of the distributed LLL in the quantum-LOCAL model. More specifically, we obtain our lower bound already for a very well-studied special case of the LLL, called sinkless orientation, in a stronger model than quantum-LOCAL, called the randomized online-LOCAL model. As a consequence, we obtain the same lower bounds for sinkless orientation and the distributed LLL also in a variety of other models studied across different research communities.