OK, to be fair. This device isn't really a carpet so much as it's a 10cm2 of plastic and it doesn't so much fly as just sorta hover a few centimetres off the ground, but it does have one advantage over Aladdin's flying carpet -- Princeton's sheet is real.
Devised and developed by Princeton graduate student Noah Jafferis, the sheet is "ripple-powered" -- wired to an array of sensors and electrically-conductive threads that generate waves of electrical current to drive pockets of air underneath it and stay aloft. Basically, it pushes very shallow pockets of air from the front of the sheet to the back to provide both lift and thrust.
The project required two years of development to reach this level. According to the BBC, controlling the sheet was nearly impossible due to high-frequency deformations. These spontaneous deformations prevented the sheet from effectively manipulating the air currents below it. Jafferis' research group eventually had to wire a complex set of sensors throughout the plastic to monitor and provide feedback to the controller mechanism, allowing it to better regulate the air pockets.
Though it can only move at a rate of just 1cm/s right now, further design refinements are expected to have it zipping around closer to a 1m/s. Hopefully these improvements will benefit the sheet's lifting abilities as well, seeing as how one would currently need a 50m-wide sheet to carry an adult passenger.