Abstract
In this work we report about the fundamental correspondence between the high efficiency of the broadband quantum memory on multifrequency absorbers in the single-mode cavity and the topology of the observed frequency lines. We have found the spectral-topological matching condition by using the multiparametric optimization of the absorber characteristics which makes it possible to improve considerably the spectral efficiency of quantum memory under conditions of a real experiment. The elaborated approach opens the possibility for the creation of the broadband quantum interface consisting of a small number of the absorbers and characterized by the super-high quantum efficiency of more than 99.9%.