In this paper we propose the first efficient quantum version of key-recovery attacks on block ciphers based on impossible differentials, which was left as an open problem in previous work. These attacks work in two phases. First, a large number of differential pairs are collected, by solving a limited birthday problem with the attacked block cipher considered as a black box. Second, these pairs are filtered with respect to partial key candidates. We show how to translate the pair filtering step into a quantum procedure, and provide a complete analysis of its complexity. If the path of the attack can be properly reoptimized, this procedure can reach a significant speedup with respect to classical attacks. We provide two applications on SKINNY-128-256 and AES-192/256. These results do not threaten the security of these ciphers but allow us to better understand their (post-quantum) security margin.