[piannucci]

You don't get the entire wave-function as output; the wave-function is not observable. Different measurements might reveal information about certain components of the state, at least probabilistically, but those same measurements will always destroy some information. See the No-cloning Theorem.

[samaman]

Right, but you would still get the basis states for all 127 qubits right? And that would be 2^127 output states. Yes, you could do some sort of search maybe to find highest probability outputs only, but if you needed every output value for a follow up algorithmic step (like in VQE for ground state prep wherein you keep using previous results to adjust the wavefunctions until ground is reached), then wouldn't it be a bit tough to use?

[krastanov]

You have 127 qubits that you measure and you end up with a classical string of length 127. Sure, that classical string, the measurement result, could have ended being any of 2^127 possible different values into which the wavefunction collapses. But that is no different from saying that there are 1^1024 possible states that a 1kB of classical RAM can be in. It is not related to the (conjectured) computational advantage that quantum computers have.

[samaman]

Right okay makes sense...guess I am just too used to NISQ and having to run many thousands of shots for high enough fidelity..if all you wanted was one output, then yeah one classical string is easy enough, thanks