  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.
