Recently, Watrous et al proved that QIP(3) = PSPACE a remarkable result. This was a surprising result to myself to say the least and it set me off thinking...

I wondered what if Quantum Computers could be efficiently simulated by Classical Computers. Could this be SIMPLY related to the Divide between IP and AM? What I mean is that IP is characterized by Polynomial number of rounds of classical interaction, while AM has 2 rounds of classical interaction. Could simulating a Quantum Computing reduced the amount of interaction for IP from polynomial to a constant value?