I'm just wondering, because it seems like it would. Cryptography as a field may have to start all over from the beginning.
On a slightly different tack, Mike's response addresses the question of "could/can quantum computing destroy" some of our present encryption. This is slightly different than "will they". Basic quantum computers have been built and work. The challenge now lies in increasing the number of qubits.
In a recent breakthrough MIT researchers were able to use a quantum computer to calculate the factors of 15 with 5 qubits. Now 15 is a pretty big number. I can't even count that high without taking off one of my shoes. The world record is calculating the factors of 21. I can't count that high with both of my shoes off!
Kidding aside, the point here is that for a quantum computers to factor a large key, they need a lot of qubits to be in superposition. The thing is that the more qubits you try to keep together in that state, the harder it is to maintain. This is the reason that quantum mechanics is so strange to us because even the tiniest objects we deal with in the natural world are all made up of very large numbers of atoms.
It's kind of like juggling. A lot of people (e.g. me) can juggle three balls. Juggling four is way less common. Not something I can do. Juggling 5 is pretty extraordinary. 6, 7 we are talking amazing. 11 balls is the Guinness world record. Getting 5 qubits working together was a big deal. Getting 1025 in superposition? No one today knows if that's feasible and if it is, who's to say we aren't using 12288 bit encryption at that point?
Don't get me wrong. I'm not saying it won't happen. Perhaps there will be a breakthrough and the increasing difficulty of keeping more qubits in superposition goes away. I think most people who really understand this stuff and being honest will tell you it is still an 'if' and not a 'when' yet.