Curious, seems to me that they all come from the same Akkadian (ancient Semitic language) root:
"From earlier form کاهریز (/ kāhrēz /) or کهریز (/ kahrēz /), from Middle Persian [Book Pahlavi needed] (ksryc / kahrēz /) (compare Manichaean Middle Persian 𐫞𐫍𐫡𐫏𐫉 (qhryz / kahrēz /, “qanat”), Parthian 𐫞𐫍𐫡𐫏𐫝 (qhryc / kahrēz /, “qanat”) and Khunsari کیریز (/ kēirīz) /), or compound of کاه (kâh, “straw”) + ریز (rêz, “to throw”). They used to throw straws in qanats' wells to see how rapid the movement of water is for repair purposes."
Vs Latin "canal":
"For cannālis, from canna (“reed, cane”), from Ancient Greek κάννα (kánna, “reed”).*
And the Greek in turn comes, apparently, from Akkadian (Semitic) "qanûm" "reed".
And so I'd guess the Arabic 'qanat' either from either Akkadian or from its own Semitic vocabulary or was borrowed back in from Greek.
