[eigenket]

For individual states I think what you're saying is correct, but I think thinking about individual states is not the right way to go about classical simulation or thinking about complexity.

For example imagine we have a big, complicated quantum circuit, which doesn't look "nice" in any way, but at every time it happens that the state may be expressed as a superposition of only 2 (or a few) stabilzer states. Even though the states are simple in this sense, we wouldn't expect to be able to efficiently classically simulate this circuit.

This is because even though there is an efficient classical description of the state of the quantum computer at every timestep (the efficient description is as a superposition of a few stabilizer states), there isn't an efficient way to find these efficient classical descriptions, or even notice that they exist.

[dabeddabed]

Right that is nice point I wouldn't have think about if you hadn't draw my attention there, well that was all I will be not taking more of your time, thank you very much for answering all my doubts it was very productive for me as I learned a lot =), all the best.