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Processing information is what all physical systems do. Quantum computation is not just a technological promise, but the most challenging test for the conceptual problems in Quantum Mechanics. We could say that Schrödinger's cat has been tamed and is leading us along the most charming paths of the physical world. Anyway, NP-complete problems appear impregnable even by traditional quantum computing. All that sounds paradoxical considering that the local and classical world emerges from the non-local quantum one, which permeates any aspect of the physical world. Quantum Turing Machines constrain the quantum system to yes/no answers, whereas the real computational vocation of QM would be to use superposition and non-locality to obtain probabilistic oracles beyond Turing barrier performance. In this volume we have tried to provide a panorama of these trends. On one hand the physics of traditional, Turing-based Quantum Computing - crucial to clarify the old foundational problems and surely decisive in the future in nanotechnology and quantum communication -, on the other the possibility of a broader concept of quantum information which will lead to a new pact between quantum dissipative field theory and the concept of computation in physical systems.