Quantum computers are capable of computing things which aren't classically-computable. For a clear explanation I recommend "Simulating Physics with Computers" b

Quantum computers are capable of computing things which aren't classically-computable. For a clear explanation I recommend "Simulating Physics with Computers" by Richard Feynman. It presents one example of such computation and step-by-step walkthrough. An excerpt: "That's why quantum mechanics can't seem to be imitable by a local classical computer".