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Summary form only given. Complete and effective control of quantum systems is a challenging task even for systems of moderate complexity, due to the high dimensionality of their Hilbert spaces. It promises, however, adequately rewarding benefits: coherent control of chemical reactions, quantum communication, quantum cryptography, and quantum computation are some of its potential applications. We show that quantum devices with exponentially large Hilbert space dimension can be efficiently controlled, provided they are assembled from completely controllable unit cells in an architecture that is optimized for the specific function they should perform. The unit cell can be constructed from simple quantum objects of arbitrary physical nature, such as two-level atoms, nuclear spins, rotating molecules, quantum dots, etc. This allows to optimize critical properties such as coherence time and control precision for practical realizations. The only requirement is that the unit cell should be non-harmonic, i.e., that it could be sufficiently perturbed to have unconstrained dynamics. This ensures that the cell can be fully controlled and made perform any desired operation.