You have an unusual sense of history. Qanats are up to 3 millennia old.

The article notes that karez were constructed during the Ming dynasty, in the 1300s to 1600s, 2000 years after the earliest qanats in the middle east. Unless the karez builders were also time travellers they were long after the qanats.

The qanats lasted so long that the irrigated land salted up, forcing them to construct new qanats in areas which had not salted up yet. California has the same age old salts build up problem with irrigated land in arid regions.