Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.
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?

Here's the one-minute introduction: "Imagine that it's fifteen years from now. Somebody announces that he's built a large quantum computer. RSA is dead. DSA is dead. Elliptic curves, hyperelliptic curves, class groups, whatever, dead, dead, dead. So users are going to run around screaming and say 'Oh my God, what do we do?' Well, we still have secret-key cryptography, and we still have some public-key systems. There's hash trees. There's NTRU. There's McEliece. There's multivariate-quadratic systems.