Rational quantum mechanics: Testing quantum theory with quantum computers

I know more about Quantum Chemistry than Quantum Computers. Both use the same Physics theory, the only difference are the goals and implementation details :)

Usually you have a molecule and the most stable state is a sum of products of orbitals (Slate determinant). You can write it using a base of orbitals, that mathematically is just an ortonormal base. In a Quantum Computer the support of the emplacements of the bases are far away (in atomic scales) to protect them against noise. In Quantum Chemistry, they are all overlapped and it's a mess that is impossible to separate, but that is what real molecules have.

The real physical properties does not depend on the ortonormal base you choose. A usual trick in Quantum Chemistry is to pick a ortonormal base were the solution looks almost like only one product of orbital, so you have a simple representation in a simulation in a Classical Computer and you can do the calculations very fast.

But you can also pick a nasty base, where the most stable state looks like a "maximal N-qubit superposition/entanglement". It's stupid because the calculations are slower. But in some calculations you first pick the base and then try to get the most stable state and then perhaps try to get a new ortonormal base that is nice for the calculations.

So, I can't see how is it possible that there are surprising restrictions that appear in the nasty base and don't change the results in the nice base.