  We propose a cascade scheme of a superefficient broadband quantum memory
consisting of four high-Q ring resonators forming a controllable frequency comb
and interacting with long-lived spin systems and with a common waveguide. Using
the transfer function giving extended matching conditions, the optimization of
all spectroscopic parameters of the system for quantum memory in the resonator
is carried out. It was shown that our quantum memory scheme does not impose
large restrictions on the parameters of losses in resonators and allows to
achieve super high efficiency 99.99 % in a wide frequency range.
