of the Quran, it is unjust and unlawful killings of innocents that is forbidden. However the verses for capital punishment can be found clearly as are the authentic narrations of the Prophet having ordered the death penalty for certain crimes(though forgiveness is encouraged and said to be better than vengeance).
That said it is well known that capital punishment was only applied when the case was clear and the wrongdoer was guilty of the crime without any doubt. And that is how the death penalty should be put to action anywhere if legislated.