I have heard some people say that quantum computers imply that P = NP, although the fact that this isn't breaking news seems to indicate that perhaps the people researching quantum computers are full of shit. None of them seem to directly make such a claim, but some people take the claims they make to imply it. In computer science quantum computers are actually kind of controversial it seems to me. Traditional computer scientists seem to dismiss them in many cases, but perhaps it is just because they don't know enough about them. Even cryptographers used to dismiss them, but they seem to be more and more accepting of the fact that they are real now. I think that quantum computers kind of go beyond traditional computer science and more into the realm of advanced physics applied to computation. Certainly that is the case with quantum cryptography, which is very different from traditional cryptography and has a very physics oriented slant to it. (IE: Traditional cryptography you may scramble a plaintext and transmit it on the line, such that if it is intercepted it cannot be deciphered between location A and B. With quantum cryptography, you may use quantum teleportation to transfer a plaintext from point A to point B such that it does not exist at any point between A and B to be intercepted in the first place.) On the other hand, I don't think it has ever been proven that prime factorization is NP-complete, so perhaps quantum computers theoretic ability to trivially factor massive numbers into primes doesn't imply that P = NP, but rather implies that prime factorization was never NP-complete to begin with. So just because a quantum computer can factor huge numbers into primes doesn't mean that there has been an answer to P vs NP, but is more likely to imply that some problems thought to be, but never proven to be, NP-complete, were actually never NP-complete to begin with. A true quantum computer with enough stabilized qubits is allegedly able to trivially break RSA and ECC and DH and most public key encryption. It is also allegedly able to cut the bit strength of a symmetric algorithm in half. It is true that right now it looks primarily like the NSA has subverted cryptography via influence over the standards as well as releasing some backdoored things, such as the PRNG dual_ec_drbg. However, the NSA is also very likely at the cutting edge of quantum computing, and that is a risk to take into account as well. On the other hand, the NSA is also at the cutting edge of traditional computing, and it is possible that their super computers are merely trying to brute force passwords and crack smaller traditional encryption keys (like RSA or DH 1,024). Sounds right, nice source I have never been able to find exact numbers for how many qubits are required to break an X bit RSA key. On the other hand we should be a bit worried, because over the past few years the number of qubits in quantum computers has grown by two orders of magnitude already. If they keep up at this rate, and they only need 1.5 times as many qubits as RSA key has bits, they may be able to break even 4,096 bit RSA keys in the next couple of years. Shors algorithm can decrypt things in nearly real time. If a quantum computer exists that can crack RSA-X, it can crack RSA-X almost instantly.