[samaman]

Also another problem: you now have 2^127 output values leaving the quantum processor. If you're using a hybrid quantum algorithm that requires classical processing as well (which are most algos used today), you'd need more than a yottabyte of RAM. We can get around this problem by storing all 2^127 pieces of output data into other data types that compress the total size, but if you genuinely are trying to use all 2^127 outputs, you'd still need to do some pretty intensive searching to even find meaningful outputs. I guess this is where Grovers search could come really handy, right?

[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?