The idea here is to use so-called Quantum Key Distribution where photons are transmitted over a physical line and the laws of physics guarantee its security.
But there's a problem (ok, there are many problems): Quantum Key Distribution relies on an authenticated channel that is simply assumed to already exists. How do you get that authenticated channel? Nobody knows.
(Apart from that QKD would be hugely expensive, wouldn't work over wifi or mobile connections and would have pretty severe distance limits, which all make a "Quantum Internet" a ridiculous enterprise - but the authenticated channel really kills the whole thing as a solution for Quantum Computer attacks.)