Working quantum computers have already been constructed. In fact the quantum algorithm for prime factorization has already been run on one, although it was only to factor 15 into 3 and 5. https://www.schneier.com/blog/archives/2009/09/quantum_compute.html It is quite likely that a good deal of progress has been made since the first time they did this. Even doing it at all was a big step though as it took Shors algorithm from theoretical to implemented on a quantum computer. Now I am not educated enough to be truly up to date on the latest happenings with quantum computing, but I listen to smart cryptographers and physicists when they talk. And I have seen over the past few years the attitude shift from one of dismissing quantum computers as a viable strategy for attacking vulnerable sorts of asymmetric cryptography, to being one of acceptance that all of the widely used asymmetric algorithms are in serious danger and probably are not going to be secure for much longer. Even with really really big keys. In cryptography literature you can see a new interest in quantum resistant multivariate quadratic polynomial algorithms, and there is a good chance that this sort of asymmetric crypto will replace quantum vulnerable elliptic curve (ECDH) and prime factorization (RSA) sorts of asymmetric cryptography. Nobody knows when they will be able to break the keys we are currently using, but many people predict that there is going to be a rapid and exponential increase in the size of the composite numbers they can factor with their quantum computers.