Romans 13:3-4 (NAS)
3 For rulers are not a cause of fear for good behavior, but for evil. Do you want to have no fear of authority? Do what is good and you will have praise from the same; 4 for it is a minister of God to you for good. But if you do what is evil, be afraid; for it does not bear the sword for nothing; for it is a minister of God, an avenger who brings wrath on the one who practices evil.
I interpret this passage from Romans to require (at least expect) the governing authorities to "bear the sword" agianst those who practice evil. The authority in this instance is a minister of God - one who has responsibility to act on God's wrath over evil.
There is no doubt that the civil authority bears the sword. (The policeman with the gun; the soldier with the gun.)
Having it, there is no doubt that it is available to use.
In pursuing the criminal who has committed murder is it required that the policeman use his weapon against the offender in capturing him? No....although he can if necessary.
If the murderer is captured the justice system has authority to execute the criminal.
It has the opportunity to view each case separately and to acknowledge differences between them. It also can designate certain classes of murders for automatic execution.
It has an obligation to execute some murderers, in my opinion, to permanently excise the evil from among us so there is no longer any danger from that front. It also should execute some because the affront is so heinous that justice can only be satisfied by the execution of that criminal. Finally, it should execute some so that the value of innocent life is not cheapened and so that a culture of cheap life is not encouraged.