Quantum computers are known to solve some problems faster than classical computers. For example, see Shor's Algoroithm (http://en.wikipedia.org/wiki/Shors_algor

Quantum computers are known to solve some problems faster than classical computers. For example, see Shor's Algoroithm (http://en.wikipedia.org/wiki/Shors_algorithm http://en.wikipedia.org/wiki/Shors_algorithm) for factorization, which finds factors of a number in polynomial time on a quantum computer. This alone is an enormous breakthrough. The question is whether Quantum Computer can solve NP problems in Polynomial time, which no one knows yet.