Quantum warp theory is a course taught at Starfleet Academy.
In 2372, Ensign Harry Kim, along with Lieutenants Tom Paris and B'Elanna Torres of the USS Voyager tried to break the transwarp threshold by running simulations in the ship's holodeck. However, the nacelles on the holographic shuttle were torn off due to the pressure of traveling to warp 10. After the failure of the test, Kim, Torres and Paris tried to solve the problem together in the mess hall. Neelix, the ship's morale officer, tried to help the group. Paris asked Neelix if he knew anything about quantum warp theory, which he did not. (VOY: "Threshold")