 Even if we could rule out the MWQC, the problem of finding the physical resource(s) responsible for quantum “speed-up” would remain a difficult one. Consider a solution of a decision problem, say satisfiability, with a quantum algorithm based on the circuit model. What we are given here as input is a proposition in the propositional calculus and we have to decide whether it has a satisfying truth assignment. As Pitowsky (2002) shows, the quantum algorithm appears to solve this problem by testing all \(2^{n}\) assignments “at once” as suggested by (2), yet this quantum ‘miracle’ helps us very little since, as previously mentioned, any measurement performed on the output state collapses it, and if there is one possible truth assignment that solves this decision problem, the probability of retrieving it is \(2^{-n}\), just as in the case of a classical probabilistic Turing machine which guesses the solution and then checks it. Pitowsky’s conclusion (echoed, as we saw, by Steane (2003) and Duwell (2007)) is that in order to enhance computation with quantum mechanics we must construct ‘clever’ superpositions that increase the probability of successfully retrieving the result far more than that of a pure guess. Shor’s algorithm and the class of algorithms that evaluate a global property of a function (this class is known as the hidden subgroup class of algorithms) are (so far) a unique example of both a construction of such ‘clever’ superpositions and a retrieval of the solution in polynomial time. The quantum adiabatic algorithm may give us similar results, contingent upon the existence of an energy gap that decreases polynomially with the input.