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Daniel Knüttel 2020-04-14 11:50:09 +02:00
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\begin{frame}{Stabilizers and Stabilizer Spaces} \begin{frame}{Stabilizers and Stabilizer Spaces}
\begin{itemize} \begin{itemize}
\item{ \item{
Choose a finite Abelian subgroup $S$ of $P_n$ with $-I \notin S$. Choose a finite commuting Abelian subgroup $S$ of $P_n$ with $-I \notin S$.
One can show that all elements of $S$ are hermitian. One can show that all elements of $S$ are hermitian.
} }
\item{ \item{
@ -423,9 +423,17 @@
} }
\item{If the vertices $a, b$ are isolated the resulting state after \item{If the vertices $a, b$ are isolated the resulting state after
applying $CZ_{a,b}$ can be precomputed. } applying $CZ_{a,b}$ can be precomputed. }
\item{When none of the above is possible one can clear at least one \end{itemize}
\end{frame}
}
{
\begin{frame}{Dynamics of Graphical States}
\begin{itemize}
\item{When the VOPs do not commute with $CZ$ and the vertices are not isolated one can clear at least one
vertex operator (i.e. transforming it to $I$).} vertex operator (i.e. transforming it to $I$).}
\item{If both vertex operators can be cleared $\{a,b\}$ is toggled in $E$. \item{If both vertex operators can be cleared $\{a,b\}$ is toggled in $E$.
}
\item{
If just one vertex operator has been cleared the other vertex is isolated If just one vertex operator has been cleared the other vertex is isolated
and one can precompute all resulting states.} and one can precompute all resulting states.}
\end{itemize} \end{itemize}