If you want to know exactly what the heck a Controlled NOT gate is (and you have a PhD or better ) visit here, or here.
Hmmm the square root of a not gate. Such intruiging stuff this quantum mechanics is. We had a talk about it by some woman from cambridge. She basically said that normal logic simply does not apply in quantum computing but you simply use what you've got in order to get something useful from it. Basically no one knows why certain stuff happens, but it does and from that they can hopefully make quantum processors. And that factor of primes thing I don't get. I thought primes always only had factors of themselves and 1.
That's because of Heisemberg priciple. On a atomic scale, we can not grasp the velocity and the position of a particle with precision; if we know exactly the velocity, we don't know the position and the other way around, if we know exactly the position we don't know the velocity. What is used in quantum theory is probability. One interesting thing is that if we adopt quantum theory postulates in macroscopic world we obtain the same results of classical physics, that is, classical physics is a special case of the quantum theory