Fast simulation of stabilizer circuits using a graph state   representation
  According to the Gottesman-Knill theorem, a class of quantum circuits, namely the so-called stabilizer circuits, can be simulated efficiently on a classical computer. We introduce a new algorithm for this task, which is based on the graph-state formalism. It shows significant improvement in comparison to an existing algorithm, given by Gottesman and Aaronson, in terms of speed and of the number of qubits the simulator can handle. We also present an implementation. 
Simon Anders and Hans J. Briegel