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even I, non-expert in this field, can suggest there may be a couple of problems in this “proof” such as:
(1) Why only the Monte Carlo statistical technique, why not other techniques? Are there other techniques? The article doesn’t say. Here is a book that talks about alternative ideas on solving the Schrodinger equation (http://www.worldscientific.com/worldscibooks/10.1142/p780) so we can guess that there might be other methods

(2) there is an implicit assumption that “memory” requirements are physical and we would “run out of atoms for storage”. What about non-local information? Clearly this is not in the mechanist worldview underpinning this article/”proof”

(3) there is also an assumption about how computers might solve the problem. It seems they assume binary computing type problem solving. What about some of the cryptographic solution methods that have undercut some of these exponentially increasing numbers of calculations? I am sure the maths geniuses will come up with ever more clever ways of busting cryptography methods and hence exponentially might be better addressed

(4) more simply, they built a model and the results are based on the model….. and as we have learnt from “climate models” these are only ever approximations