[Dn_Ab]

The short version is, if this is correct (which is exceedingly unlikely) then either quantum mechanics is wrong or whether P=NP has just become irrelevant. This is because, as Scott Aaronson is often forced to tirelessly point out, an inability to build a Quantum Computer must also show Quantum mechanics to somehow be in error. If instead, we can build a Quantum computer and this result is true then the universe has suddenly become an incredibly more interesting place (for one example, building this would also solve AI).

The result also has consequences for quantum computation specifically, in that it also takes care of the negative sign problem, which arises when simulating certain kinds of important quantum many body systems.

And last but certainly not least, all those press releases breathlessly proclaiming Quantum computers work by trying a gazillion possibilities at once (with no worries about the plausibility of actually reading out the correct answer with a non-negligible probability) weren't so far off after all.

All in all, either there is a mistake hidden somewhere in the preprint or this is the greatest scientific achievement since Evolution invented Human Level intelligence.

See here for intuition on why NP-complete problems if at all solvable without brute force, should also be efficiently solvable: http://windowsontheory.org/2013/05/06/reasons-to-care-in-hon...