  We introduce a general scheme to realize perfect storage of quantum
information in systems of interacting qubits. This novel approach is based on
{\it global} external controls of the Hamiltonian, that yield time-periodic
inversions in the dynamical evolution, allowing a perfect periodic quantum
state recontruction. We illustrate the method in the particularly interesting
and simple case of spin systems affected by XY residual interactions with or
without static imperfections. The global control is achieved by step
time-inversions of an overall topological phase of the Aharonov-Bohm type. Such
a scheme holds both at finite size and in the thermodynamic limit, thus
enabling the massive storage of arbitrarily large numbers of local states, and
is stable against several realistic sources of noise and imperfections.
