The primary difference between a classic computer and a quantum computer is that a quantum computer's QBITS, "quantum bits" can be in many different states simultaneously whereas a classic computer's bits can only be in one state at a time.

It is therefore possible to solve very complex mathematical equations almost instantaneously using a QBIT system whereas a similar calculation with a classic computer could potentially take longer than the lifetime of the observable universe.

One class of those calculations relates to the cryptographic systems used on the internet and modern computing. Using a quantum computer, these cryptographic schemes can be defeated in reasonably short periods of time rendering the protection afforded by those schemes moot.