The likely impossibility of getting infinite comutational power is a problem, but quantum nondeterminism or quantum branching don't prevent using the trick described in the story, they just make it more difficult. You don't have to identify one unique universe that you're in, just a set of universes that includes it. Given an infinitely fast, infinite storage computer, and source code to the universe which follows quantum branching rules, you can get root powers by the following procedure:

Write a function to detect a particular arrangement of atoms with very high information content - enough that it probably doesn't appear by accident anywhere in the universe. A few terabytes encoded as iron atoms present or absent at spots on a substrate, for example. Construct that same arrangement of atoms in the physical world. Then run a program that implements the regular laws of physics, except that wherever it detects that exact arrangement of atoms, it deletes them and puts a magical item, written into the modified laws of physics, in their place.

The only caveat to this method (other than requiring an impossible computer) is that it also modifies other worlds, and other places within the same world, in the same way. If the magical item created is programmable (as it should be), then every possible program will be run on it somewhere, including programs that destroy everything in range, so there will need to be some range limit.