At one point during development Nuka-Cola Quantum was to appear in Fallout: New Vegas. The item was fully implemented and even adjusted to work correctly with Hardcore mode. In addition to its standard effect from Fallout 3, Quantum was to provide a Sleep restoration of 100 and an added Dehydration of 10. Presumably, the role of Quantum as an Action Point boosting beverage was passed on to Nuka-Cola Victory.
Nuka-Cola Quantum still exists inside the game's resources and can be obtained using console commands. Its BaseID remains unchanged from Fallout 3. Nonetheless, a banner promoting Quantum hangs on one wall of Goodsprings General Store. Nuka-Cola Quantum was taken out due to the fact that it wasn't around before the war long enough to be sold anywhere besides Washington DC, but was intended to be sold in mass production before the bombs fell. This suggests the reason why there is a Nuka-Cola Quantum banner in Goodsprings, but no Nuka-Cola Quantum.
The crate that can contain this item can be "re-rolled" by loading a save from before exiting the silo for the first time. You will have to do the talk with Ulysses (through ED-E) every time, but exiting Hopeville Missile Silo Bunker for the first time is when the crate contents are set.
Nuka-Cola Quantum's proposed slogan "Take the leap... enjoy a Quantum!" is a pun dealing with the scientific term "quantum leap", which refers to the phenomenon where an electron nearly instantaneously (within a few nanoseconds) leaps from one energy level (aka quantum state) to another.
Nuka-Cola Quantum may be a reference to the short lived Coca-Cola C2 which was advertised as having "half the carbohydrates, sugars and calories" of regular Coca-Cola, an almost opposite of Quantum's advertisement of "twice the calories, twice the carbohydrates, twice the caffeine and twice the taste" of regular Nuka-Cola.