Where is the information stored?

[Esquilax]

In the picture I've outlined above, the fields contain the dynamics (all the potential), but the concrete state of the universe is a separate mathematical entity called - the state.

Lets call all possible universes the landscape. The fields would contain the information of the landscape. That is a lot of information.

I'm a little leery about what you're talking about here, mainly due to the way you're using the word information. Information isn't a thing that can be "contained" in anything, as it's not an objective phenomenon on its own. Information is a conceptual label that humans place upon descriptions of phenomena; at best, all you can really say is that a given quantity in the physical world contains aspects that humans have imbued meaning onto, sufficient to create a pattern that can be decoded by minds familiar with that meaning, and that the resultant description of what the pattern does is information.

We sometimes get the same kind of language with DNA, this claim that it must be designed because it contains information, which requires a designer, but that misses two different points. The first is that what DNA really contains is a set of predictable patterns (this set of genes expresses predictably in X way, this other set does the same in Y) that, due to their consistent nature, can be "read" as a sort of language, but that the language exists only because of the consistent nature of the expressed genes, and our ability to recognize that. The second is that everything contains information; the position of an object in space, the age of an object, its molecular makeup, that's all information, due to objective facts about the object expressed in terms of human measurements. The point is though, that no matter how thoroughly you crack open any object, information will never spill out of it. You'll never be able to hold information in your hand, or weigh it, or anything.

Objects do not "contain" information. They are information, when viewed by human observers willing to quantify the object. The question in the OP is malformed.