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We introduce a general scheme to realize perfect quantum state reconstructionand storage in systems of interacting qubits. This novel approach is based onthe idea of controlling the residual interactions by suitable external controlsthat, acting on the inter-qubit couplings, yield time-periodic inversions inthe dynamical evolution, thus cancelling exactly the effects of quantum statediffusion. We illustrate the method for spin systems on closed rings with XYresidual interactions, showing that it enables the massive storage ofarbitrarily large numbers of local states, and we demonstrate its robustnessagainst several realistic sources of noise and imperfections.Comment: 10 pages, 3 figures. Contribution to the Proceedings of the Workshop  on "Quantum entanglement in physical and information sciences", held in Pisa,  December 14-18, 200

MASSIVE QUANTUM MEMORIES BY PERIODICALLY INVERTED DYNAMIC EVOLUTIONS