In this work, we propose a universal (spectral-topological) approach towards the realization of the quantum memory, consisting of a small number of controlled absorbers, providing a super-high quantum efficiency of more than 99.9% required for practical quantum information science. In this way, we have found a series of spectral-topological matching conditions for the spectroscopic parameters of the absorbers which ensure the maximal efficiency in the broadband spectral range due to controlling the relative position (topology) of the eigenfrequencies in the absorbers spectrum. We also discuss the implementation of the proposed approach using the modern microwave and optical technologies.