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\section{The Stabilizer Formalism}

The stabilizer formalism was originally introduced by Gottesman\cite{gottesman1997}
for quantum error correction and is a useful tool to encode quantum information
such that it is protected against noise. The prominent Shor code \cite{shor1995}
is an example of a stabilizer code (although it was discovered before the stabilizer 
formalism was discovered), as are the 3-qbit bit-flip and phase-flip codes.

It was only later that Gottesman and Knill discovered that stabilizer states can
be simulated in polynomial time on a classical machine \cite{gottesman2008}. This
performance has since been improved to $n\log(n)$ time on average \cite{andersbriegel2005}.

\subsection{Stabilizers and Stabilizer States}