When I opened this page, I was going to be the third comment, then I got caught up trying to explain why their linked paper [1] (proving P=NP) is non-sense. Unfourtuantly, my habit of assuming that my not understanding something just means that I need to re-read it or play with that segment of the proof myself costed me more time than I thought (even after I wrote in my partially completed reply that the introduction alone was sufficient to dismiss the paper as nonsense). Anyway, here is my overkill analysis:
I would be highly skeptical of their claim. First of all, if they did prove P=NP (and long enough ago to write another paper), then I cannot imagine why this is the first I am hearing about it, as solving this problem would likely get a prominent spot in mainstream news, and definitively its own article on HN.
Beyond that, the paper proving P=NP, even to my amateur eye, looks like garbage.
From the P=NP paper:
"What is the powerful ingredient which allows a dramatic speed-up of quantum computation over classical computation ? We propose that this ingredient is an implicit use of the Bayesian probability theory. Furthermore, we argue that both classical and quantum computation are special cases of probability reasoning. On these grounds, introducing Bayesian probability theory in classical computation as well, we reduce a typical NP problem, namely 3-SAT, to a linear programming problem. According to algorithmic complexity theory, this proves that P=NP."
"Any logical algorithm can be formulated as a linear programming problem. Specially, a basic question of logical satisfiability with n variables, namely 3-SAT, is equivalent to a linear programming problem with O(n^3) unknowns and even in general with O(n) unknowns. According to algorithmic complexity theory, this proves that P=NP."
"Again, the main reasons of the supposedly quantum efficiency are basically unknown,
but the common wisdom is that entanglement should be the key ingredient. Indeed, in the
quantum community, it is ‘widely believed that classical systems cannot simulate highly
entangled quantum systems’ [13]. By contrast, we have nevertheless argued [14] that
the concept of entanglement is actually a quite classical attribute of contextual systems.
Furthermore, any classical computer can be regarded as a highly entangled system as far
as the entanglement is measured between the binary digits of the processed data during
the computation. In addition, we shall argue that the crucial ingredient is not in the least
a Hilbert space with its full quantum machinery but only a flexible randomization, or to
be exact, the implicit use of Bayes probabilities. This is like a grin without a cat in Alice
and Bob adventures in Quantum Land."
They devote two pages to history and what should be common knowledge to anyone interested in this paper.
The actual proof is mathametical gibberish, however there are surprisingly large contiguous sections of the proof that, by themselves, work.
[1] http://arxiv.org/pdf/1205.6658v2.pdf