Not all treason conviction require the death penalty.

§2381. Treason Whoever, owing allegiance to the United States, levies war against them or adheres to their enemies, giving them aid and comfort within the United States or elsewhere, is guilty of treason and shall suffer death, or shall be imprisoned not less than five years and fined under this title but not less than $10,000; and shall be incapable of holding any office under the United States.

The method of death depends on the state even if it is a federal conviction.

Hanging: New Hampshire and Washington.

firing squad: Mississippi, Oklahoma and Utah.

electric chair: Alabama, Arkansas, Florida, Kentucky, Mississippi, Oklahoma, South Carolina, Tennessee, and Virginia.

gas chamber: Alabama, Arizona, California, Mississippi, Missouri, Oklahoma, and Wyoming.

Lethal injection: Alabama, Arizona, Arkansas, California, Colorado, Florida, Georgia, Idaho, Indiana, Kansas, Kentucky, Louisiana, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, North Carolina, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, Washington, and Wyoming

However all bets are out the window if the military does it, in that even I assume the Law of War would have jurisdiction.