Quantum dating was an extremely precise method of measuring a particle's date of origin. Unlike carbon dating, which measures a substance's subjective age, quantum dating was able to identify an accurate date of origin even if the substance had traveled through time.
In 2153, Jonathan Archer, acting on a tip from the Suliban Cabal's mysterious benefactor, quantum dated a component from the Xindi probe that attacked Earth. Archer showed the results, which read -420, to Admiral Forrest and Ambassador Soval, both of whom expressed surprise at the results, as quantum dating usually only registered in positive numbers. Using these results, Archer was able to prove that the component was from 420 years in the future. (ENT: "The Expanse")
In 2154, Degra quantum dated a Xindi initiation medal supplied to him by Captain Archer, who himself had received it from temporal agent Daniels, and determined that the medal itself was also from the future. (ENT: "Azati Prime")
In the Mirror universe in 2155, the Tholians quantum dated a piece of the USS Defiant's hull, and determined it was from about a hundred years in the future. That quantum dating evidence found it's way into the hands of Commander Jonathan Archer. (ENT: "In a Mirror, Darkly")