The death penalty is not simply a state-by-state issue.
Besides the existence of a federal and military death penalty, the federal court system, including the US Supreme Court, deals with Constitutional issues related to the death penalty in states constantly, and has imposed various restrictions on its usage. SCOTUS has also been on an excruciatingly slow but clear path towards total nationwide abolishment.
There is very little in the US that can be treated as purely state-by-state, and so long as the 8th and 14th amendments exist, capital punishment definitely isn't one of them.