 This feature of the quantum circuit model supports the conjecture that the power of quantum computers, if any, lies not in quantum dynamics (i.e., in the Schrödinger equation), but rather in the quantum state, or the wave function. Another argument in favour of this conjecture is that the Hilbert subspace “visited” during a quantum computational process is, at any moment, a linear space spanned by all of the vectors in the total Hilbert space which have been created by the computational process up to that moment. But this Hilbert subspace is thus a subspace spanned by a polynomial number of vectors and is thus at most a polynomial subspace of the total Hilbert space. A classical simulation of the quantum evolution on a Hilbert space with polynomial number of dimensions (that is, a Hilbert space spanned by a number of basis vectors which is polynomial in the number of qubits involved in the computation), however, can be carried out in a polynomial number of classical computations. Were quantum dynamics the sole ingredient responsible to the efficiency of quantum computing, the latter could be mimicked in a polynomial number of steps with a classical computer (see, e.g. Vidal 2003).