 This is not to say that quantum computation is no more powerful than classical computation. The key point, of course, is that one does not end a quantum computation with an arbitrary superposition, but aims for a very special, ‘clever’ state—to use Pitowsky’s term. Quantum computations may not always be mimicked with a classical computer because the characterisation of the computational subspace of certain quantum states is difficult, and it seems that these special, ‘clever’, quantum states cannot be classically represented as vectors derivable via a quantum computation in an optimal basis, or at least that one cannot do so in such way that would allow one to calculate the outcome of the final measurement made on these states.