There are two very good quotes about quantum physics. The first is from Richard Feynman, in 1965: "I think I can safely say that nobody understands quantum mechanics." The second is from Niels Bohr, who said, "Those who are not shocked when they first come across quantum theory cannot possibly have understood it."
What makes quantum computers so terribly impossible is that they are really, really, really hard to understand. The basis of them is the idea that unlike a binary bit, a quantum bit or qubit can have more than two 'positions'. In binary computers a bit is given a value of either 1 or 0; in a quantum computer a bit can be either 1, 0 or a superposition of both.
Understand? No, that's fine, no one else does either. But trust us when we say, this is some next-level stuff. In theory, a quantum computer could be many times more efficient than a standard computer. For example, cracking encryption could be achieved in minutes or seconds, rather than many years in a traditional computer. What does that mean? Well, as the only people who'll have quantum computers for quite some time to come are governments and universities, it means your encrypted stuff isn't safe any more and physics students will be able to break into porn sites with incredible ease.
It gets even more mind-bending when you consider the principle of quantum entanglement, which suggests that it's possible to manipulate two separate electrons, separated by considerable space, as long as they were created at the same time. Entanglement suggests that if you do one thing to one electron, its 'pair' will be subjected to the same action, even if they are separated by a considerable gap. The implications for this in computing are vast, and instantaneous communication could make very powerful computers that could quite easily take over the world and enslave the human race in nanoseconds. It would also be really good for pirating movies.
