Quantum computation - fault-tolerance, resources and foundations

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Powerful quantum algorithms such as Shor's celebrated factoring algorithm and Grover's data base search illustrate that quantum computation can become a large technological asset for modern society. Also, and from the scientific perspective first and foremost, it shows that the theory of computation needs to be unified with the theory of quantum mechanics. This has to date not been fully accomplished. For example, What is the cause for the quantum speedup? We have no precise answer to this question, despite the fact that 'entanglement', 'superposition and interference', 'largeness of Hilbert space' and other candidates have received their fair share of attention.