Can quantum computers really compute a vast number of possible solutions simultaneously?

Question

This link says

They are not constrained to stepwise calculations but, rather, can compute a vast number of possible solutions simultaneously—and at a speed that is far beyond anything we can imagine.

Is this really true? AFAIU quantum computers cannot compute a vast number of possible solutions simultaneously. A quantum computer is not a parallel computer. It is true that the wave function will exist in a superposition of states before measurement, but when we make a measurement it will collapse to a definite state. And measurements is all we can do.

From scott aaronson’s blog (https://www.scottaaronson.com/blog/)

If you take just one piece of information from this blog: Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once.

curious to know what experts think

Answer 1

They are not constrained to stepwise calculations

As far as I know, all QC models are stepwise.

Under the laws of nature, the ball spins either to the right or to the left, but never in both directions at the same time. The world of quantum computing is different: Here, the ball can revolve in both directions simultaneously

I think this is the source from which comes all this “QC is a massive parallel computation”.

It is not exactly wrong to think of superposition $\frac{|0\rangle + |1\rangle}{\sqrt{2}}$ as “both $|0\rangle$ and $|1\rangle$ at the same time”, but it’s confusing. It might make you think that both things are simultaneously available for arbitrary processing, which you can fully control. As if preparing a superposition is something like creating clones.

A more precise way to think about superposition is interpreting it as uncertainty. So, less confusing statement would be “neither $|0\rangle$ nor $|1\rangle$, until the setup forces it to be definite”.