In The Fabric of Reality, David Deutsch argues the following:
To those who still cling to a single-universe world-view, I issue this challenge: explain how Shor's algorithm works. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor's algorithm has factorized a number, using $10^{500}$ or so times the computational resources that can be seen to be present, where was the number factorized? There are only about $10^{80}$ atoms in the entire visible universe, an utterly minuscule number compared with $10^{500}$. So if the visible universe where the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed?
Doesn't this imply the existence of the multiverse? How/where could the number be factorized otherwise?
This thread does not answer this question, as 1. the fact that there are still some unknowns doesn't necessarily mean the multiverse theory is wrong, and 2. it doesn't explain how/where the number could be factorized otherwise if not in the so-called "parallel universes".