A simpler proof of zero-knowledge against quantum attacks using Grover's   amplitude amplification
  Watrous had presented the first proof of zero-knowledge property of a proof system against a quantum verifier. The key of the proof is the construction of a quantum simulator. In the construction, the 'failure state' is rotated to the 'success' state by a tricky operation which is initially developped for the amplification of QMA proof systems.   This manuscript presents a new and simpler construction of a simulator. In the construction, we simply amplify the success probability of a classical simulator using Grover's amplification. 
Keiji Matsumoto