What gives the State the power to kill?

Killing certain criminals is still allowed in civilized countries, like the USA. I am not interested in a debate about whether or not certain degenerates deserve to die. Many of them do. But exactly where does the notion that the political State, and certainly the governments in the enlightened states of the USA, has the legitimate moral power to kill a criminal, come from? The government constantly reveals itself as incompetent and corrupt. And we give these losers the power to kill based on a justice system that is adequate, but certainly fallible? How did these idiots get the power to kill?