Adaptive Quantum Computation, Constant Depth Quantum Circuits and   Arthur-Merlin Games
  We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then the complexity class BQP is contained in AM. 
Barbara M. Terhal and David P. DiVincenzo