Infinite CPU capability does not automatically imply infinite storage, but it does imply that you can compress any storage to an information-theoretic minimum size, by writing a search for an arbitrary program to generate the same data.
And that's some absurdly good compression, given the universe simulator assumed in the story: anything that will ever occur as a state of the universe can be compressed to a set of space-time coordinates and an extraction algorithm.
With some additional assumptions about the nature of the pseudo-causal loop demonstrated in the story, that compression can also include any arbitrary search parameters you can conceive of, without you having to express them as a program: just search for the data that will be on your hard drive in the future after having executed the search you're currently thinking of.
And that's some absurdly good compression, given the universe simulator assumed in the story: anything that will ever occur as a state of the universe can be compressed to a set of space-time coordinates and an extraction algorithm.
With some additional assumptions about the nature of the pseudo-causal loop demonstrated in the story, that compression can also include any arbitrary search parameters you can conceive of, without you having to express them as a program: just search for the data that will be on your hard drive in the future after having executed the search you're currently thinking of.