Efficiently contractable quantum circuits cannot produce much   entanglement
  We show a similarity between two different classical simulation methods for measurement based quantum computation -- one relying on a low entanglement (tree tensor network) representation of the computer's state, and the other a tensor contraction method based on the topology of the graph state. We use this similarity to show that any quantum circuit that can be efficiently simulated via tensor contraction cannot produce much entanglement. 
Nadav Yoran