I'm not familiar with the syncro/quattro setup that VAG used on the Quantum and Audi 4000 (hint: anything between a Quantum and an Audi 4000 is interchangable. They're the same car.), and therefore, can't give any advice on hooking it up in such a swap.
However, everything else... the Quantum and Audi 4000 were both sold with factory diesels - both naturally aspirated and turbo.
Seeing as these vehicles are heavier than Golfs and Jettas, and have more drivetrain losses due to the longitudal transmission (and, if you hook it up, syncro), you'll want more power to push them around, and that calls for a turbodiesel.
You will need (to do this right) the engine, transmission, possibly driveshafts, instrument cluster, some wiring, and a diesel filler neck. A diesel fuel pickup may not be a bad idea either, but the gasser pickup may have a pre-pump, meaning it may actually work better than the diesel pickup.
Your best bet for a motor is likely a totalled vehicle, preferably one that has recieved a rear-end collision.
Another motor option that you might consider, although you'll want all of the rest of the drivetrain from the factory diesel, is a 1.9L turbodiesel out of a Candian-spec early Mk3 Golf or Jetta, or B3 or early B4 Passat, engine code AAZ.