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gwern comments on The Kolmogorov complexity of a superintelligence - Less Wrong
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Legg's 2006 "Is There an Elegant Universal Theory of Prediction?" may be relevant.
(The answer, BTW, is 'no'; seems to be in the usual Godelian limit vein of thought: "In this paper, it is shown that although highly powerful algorithms exist, they are necessarily highly complex.")
The paper seems not very quantative. It is not obvious from it whether a human needs a thousand bits, a million bits, a trillion bits - or whatever.
It would be quite impressive if it were able to...
My point was that Legg has shown, as I understand it, that any powerful prediction algorithm which is powerful enough to predict most/all of the universe (as one would expect a fearsome AGI to able to do) will be at least as complex as the universe it's predicting.