Is capital punishment cruel and unusual punishment?

This argument is based on the 8th Amendment and I wrote it for my US Government class.
The point of the 8th amendment is to prevent the government from cruel and unusually punishing criminals. A cruel and unusual punishment means that it psychologically and physically tortures the person. Personally, I feel that the idea that I'm going to die some torturous death like a lethal injection, being electrocuted or having some firing squad shot me would make me suffer mentally especially the firing squad… I mean what if I survive the shots but lay there bleeding to death and suffocating. I suppose I deserve it if I killed someone. However, I am a Christian and believe in the teachings of Jesus Christ who said "Turn the other cheek when someone strikes you on one cheek." The idea of an "eye for an eye" is also in the Bible and is in the Old Testament. So does this mean that Christ abolished what it says? No, it doesn't. He reemphasized to us what it means to be compassionate and merciful. The teaching 'eye for an eye" is sort of brought down a bit to a level that we as human beings may judge and try each other for criminal acts to an extent. We do not have the power to take another humans life into our hands. It is at this time that we humbly leave that decision into the Almighty's hands, the One who has the power to Create and to destroy life as He sees fit. We humbly leave this decision of another human beings life into His hands by having the prisoner put in prison for life, with or without parole (depending on how intense the crime is). Then helping that person work out their unsettled soul or their psychological problems or whatever they need. We are called to be compassionate toward each other and to visit those in prison and to love those who hate us and forgive those who have hurt us. These teachings are hard but they make living life a lot easier. Prison used to be a place where a criminal was detained and helped and it's sad to see that that idea has diminished. I hope that one day we can realize that "back then" we actually did something right and we need to get it back. So, yes, the death penalty is cruel and unusual punishment; it's the most intense form.