Any point of the space is a source with different intensity of waves that transport information in all the space where are superposed in a complex way to generate the wave field. while finding one for integer factorization wouldn't have such wide-ranging implications on other problems (though it might have implications for other not-yet-known-to-be-in-P problems, if the technique were transferable).Neural network and quantum computer have the same conceptual structure similar to Huygens sources in the wave field generation. But in a sense it'd be more surprising if one were found for traveling salesman, because that would imply P = NP. On regular computers, no polynomial algorithm is known for either problem. But on quantum computers, the fastest known integer factorization algorithm is polynomial, while the only way we could do that for traveling salesman is if QBP = NP. So it's not provably known that integer factorization is easier than traveling salesman on any kind of computer. However, since integer factorization isn't NP-complete, this doesn't have any implications for whether QBP = NP or not. Shor's algorithm (the subject of this article) is a polynomial-time algorithm for quantum computers, so integer factorization is in QBP. Therefore, a polynomial-time algorithm on regular computers could exist without P = NP- but we don't know of one.
Integer factorization is in NP, but not known to be either NP-complete or in P. If we found a polynomial-time algorithm on quantum computers, QBP = NP. Therefore, if we found a polynomial-time algorithm on regular computers, P = NP. NP-complete, which are problems in NP to which all other NP problems can be reduced (provably!) in polynomial time. However, the possibilities are constrained by, It is not known whether any of these classes are equivalent. QBP problems are those solvable in polynomial time on a quantum computer. That is, if you gave the answer to the problem, in polynomial time I could tell you if it was the correct one. NP problems are (one definition) those verifiable in polynomial time on regular computers. P problems are those solvable in polynomial time on a regular computer. You're right, it isn't currently known either way. It looks like their technique does not employ error checking, making large numbers of qbits near impossible to work with.
So yeah, fear it, but in terms of cracking larger numbers this is not even a proverbial "smoke in the building" scenario. I know that there are some proposed algorithms that only allow for a polynomial speedup in quantum computers, but I couldn't find them between when I posted initially and now. Any time you need to exchange secure data without having previously encountered the far end securely first, game over. SSH is no longer secure, SSL is trash, the list goes on. The short of it is this: you can no longer trust any key exchange system that relies on public keys. I'm a bit of a crypto nerd (more of a fan, not exactly up to sratch on designing the algorithms, but I've read EXTENSIVELY on their proper use) and if you get a large quantum computer working, things go titsup for any of our currently viable public key crypto schemes. As far as being terrified by it, that's fairly easy.