[jcranmer]

The essential problem with a quantum computer, as I understand is it, is that you can't actually read out the state you've created. Sure I can create a state which is an equal admixture of all 2^64 basis vectors, but if I try to look at it, I'm going to randomly end up with only one of the basis vectors.

[lmm]

Sure, but you might be able to perform some computation that involves those 2^64 possible states that ends up with some determined state that you can reliably measure. So while you can't store 2^64 classical values in one quantum bit, nor can you necessarily simulate that quantum bit exactly with even 2^64 classical values.

[wyager]

That’s why quantum algorithms try to bring the final result down to (mostly) a combination of only a few standard basis states.