  We introduce a general scheme to realize perfect quantum state reconstruction
and storage in systems of interacting qubits. This novel approach is based on
the idea of controlling the residual interactions by suitable external controls
that, acting on the inter-qubit couplings, yield time-periodic inversions in
the dynamical evolution, thus cancelling exactly the effects of quantum state
diffusion. We illustrate the method for spin systems on closed rings with XY
residual interactions, showing that it enables the massive storage of
arbitrarily large numbers of local states, and we demonstrate its robustness
against several realistic sources of noise and imperfections.
