"Quantum computation happens in parallel worlds simultaneously" is a lazy take trotted out by people who want to believe in parallel worlds. It is a bad mental image, because it gives the misleading impression that a quantum computer could speed up anything. But all the indications from the actual math are that quantum computers would be better at some tasks than at others. (If you want to use the names that CS people have invented for complexity classes, this imagery would lead you to think that quantum computers could whack any problem in EXPSPACE. But the actual complexity class for "problems efficiently solvable on a quantum computer", BQP, is known to be contained in PSPACE, which is strictly smaller than EXPSPACE.) It also completely obscures the very important point that some tasks look like they'd need a quantum computer — the program is written in quantum circuit language and all that — but a classical computer can actually do the job efficiently. Accepting the goofy pop-science/science-fiction imagery as truth would mean you'd never imagine the Gottesman–Knill theorem could be true.

To quote a paper by Andy Steane, one of the early contributors to quantum error correction:

The answer to the question ‘where does a quantum computer manage to perform its amazing computations?’ is, we conclude, ‘in the region of spacetime occupied by the quantum computer’.