Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms.
In theory this kind of computing power will be unbelievably powerful and be able to achieve much greater "solving power" which could crack algorithm behind bitcoin (commonly referred as: public key cryptography).
For more information visit: http://en.wikipedia.org/wiki/Quantum_computing
Bitcoin is designed to last for over a 100 years. Obviously we don't have this kind of computers yet.
But we will be, maybe in 10 maybe in 20 years, but definitely sooner that we may think - and then, at that time bitcoin may be world currency...
So do you think quantum computers would break Bitcoin's security?
Bitcoin is SHA256, SHA2 hasn't even been broken yet, once 256 will be broken, the bitcoin algo can change to SHA512 for another 40/50 years