It was to my understanding that some NP-complete problems - like factorization - are (theoretically) solvable in P time using quantum computing, all within (and

It was to my understanding that some NP-complete problems - like factorization - are (theoretically) solvable in P time using quantum computing, all within (and indeed as a result of) the constraints of quantum mechanics, perhaps utilizing Shor's algorithm. And that this fact does not imply P=NP, but rather that we'd have a computer that could perform some exponential functions as if some logarithm were applied to them. I'm no expert, but at the very least I believe it's recognized that some subset of NP problems, perhaps not NP-hard, should be solvable as if they were polynomial, using quantum computers. That said, my knowledge of this subject starts and ends with things I've read on the internet, so I could be mistaken. Either way, this[1] was a very interesting introduction to some of the implications/concepts that are involved with this. 1: http://www.scottaaronson.com/papers/philos.pdf http://www.scottaaronson.com/papers/philos.pdf