\section{The graph Simulator}

\subsection{Introduction to the Graph Formalism}

The first step towards the simulation in the graph formalism has been
the discovery of the stabilizer states and stabilizer circuits \cite{gottesman2009}\cite{gottesman1997}.
They led to the faster simulation using stabilizer tableaux\cite{gottesman_aaronson2008} and later
to the graph formalism .

\subsection{Graph Storage}

One of the gread advantages of simulating in the graph formalism is a great increase 
in simulation performance and a lower memory requirement. The simulation of
at least $10^6$ qbits on a common desktop computer should be possible\cite{andersbriegel2005}.
Therefore  one has to take care when choosing a representation of the graph state. 
The following