In short, Quantum Insert, (rather QUANTUMINSERT), is essentially a Man in the Middle attack, where the NSA (or GHCQ in this case) injects code (potentially zero days) into the response to the http request. The network of servers that perform the injection and interception is apparently codenamed QUANTUM, and has nothing to do (to our knowledge) with Quantum Computing or Quantum Cryptography.
https://www.schneier.com/blog/archives/2013/10/how_the_nsa_a...
In short, Quantum Insert, (rather QUANTUMINSERT), is essentially a Man in the Middle attack, where the NSA (or GHCQ in this case) injects code (potentially zero days) into the response to the http request. The network of servers that perform the injection and interception is apparently codenamed QUANTUM, and has nothing to do (to our knowledge) with Quantum Computing or Quantum Cryptography.