All that non-physicists tend to remember about Erwin Schrödinger was his cat thought experiment. The one with the cat in the box with one atom of radioactive material and the diabolical setup that will kill the cat if the atom decays, and the nonsensical result of the cat being both alive and dead at the same time. And suddenly, my unsleeping mind goes to some very strange places.
I'm imagining a car that works by controlling, sort of, quantum teleportation. It restricts the teleports to one particular direction, so you move forward at a random, not readily predictable speed. Teleporting against that direction is prevented by a brownian-ratchet type of mechanism. Given this much, it wouldn't even really need fuel. You will get there, eventually.
It's probably not even technically possible, but it would be so much fun to try.