added example on clearing VOPs

presentation/graphs/clear_vop_01.dot

@@ -1,7 +1,8 @@
 graph start
 {
     labelloc="t";
-    label="Initial Graph";
+    label="#0: Initial Graph";
+
 
     0 [label="0, VOP = 7"]
     1 [label="1, VOP = 19"]
@@ -9,6 +10,9 @@ graph start
     3 [label="3, VOP = 7"]
     4 [label="4, VOP = 3"]
 
+    {rank=same; 0; 1}
+    {rank=same; 2; 3}
+
     0 -- 1 -- 2 -- 3 -- 4 -- 1
     2 -- 4
 }

presentation/graphs/clear_vop_02.dot

@@ -1,11 +1,18 @@
 graph intermediate
 {
+    labelloc="t";
+    label="#1: La(1)";
+
     0 [label="0, VOP = 10"]
     1 [label="1, VOP = 21"]
     2 [label="2, VOP = 5"]
     3 [label="3, VOP = 7"]
     4 [label="4, VOP = 6"]
 
+    {rank=same; 0; 1}
+    {rank=same; 2; 3}
+
+
     0 -- 1
     0 -- 2
     0 -- 4

presentation/graphs/clear_vop_03.dot

@@ -1,11 +1,18 @@
 graph intermediate
 {
+    labelloc="t";
+    label="#2: La(1)";
+
     0 [label="0, VOP = 0"]
     1 [label="1, VOP = 11"]
     2 [label="2, VOP = 8"]
     3 [label="3, VOP = 7"]
     4 [label="4, VOP = 9"]
 
+    {rank=same; 0; 1}
+    {rank=same; 2; 3}
+
+
     0 -- 1 -- 2 -- 3 -- 4 -- 1
     2 -- 4
 }

presentation/graphs/clear_vop_04.dot

@@ -1,11 +1,18 @@
 graph intermediate
 {
+    labelloc="t";
+    label="#3: La(1)";
+
     0 [label="0, VOP = 4"]
     1 [label="1, VOP = 5"]
     2 [label="2, VOP = 2"]
     3 [label="3, VOP = 7"]
     4 [label="4, VOP = 11"]
 
+    {rank=same; 0; 1}
+    {rank=same; 2; 3}
+
+
     0 -- 1
     0 -- 2
     0 -- 4

presentation/graphs/clear_vop_05.dot

@@ -1,11 +1,18 @@
 graph intermediate
 {
+    labelloc="t";
+    label="#4: La(2)";
+
     0 [label="0, VOP = 7"]
     1 [label="1, VOP = 8"]
     2 [label="2, VOP = 6"]
     3 [label="3, VOP = 10"]
     4 [label="4, VOP = 11"]
 
+    {rank=same; 0; 1}
+    {rank=same; 2; 3}
+
+
     0 -- 2
     0 -- 4
     0 -- 3

presentation/graphs/clear_vop_06.dot

@@ -1,11 +1,18 @@
 graph intermediate
 {
+    labelloc="t";
+    label="#5: La(2)";
+
     0 [label="0, VOP = 10"]
     1 [label="1, VOP = 2"]
     2 [label="2, VOP = 14"]
     3 [label="3, VOP = 0"]
     4 [label="4, VOP = 11"]
 
+    {rank=same; 0; 1}
+    {rank=same; 2; 3}
+
+
     0 -- 1
     0 -- 2
     0 -- 4

presentation/main.tex

@@ -715,6 +715,56 @@
 \end{frame}
 }
 
+{
+\begin{frame}{Clearing VOPs: Example}
+    \begin{itemize}
+        \item{Vertex operators are represented by an integer; most of the VOPs are not important.}
+        \item{Some notable VOPs are $0 = H$, $1 = S$, $2 = I$, $19 = \sqrt{iZ}^2\sqrt{-iX}^3$.}
+        \item{
+            \includegraphics[width=0.5\textwidth]{graphs/clear_vop_01.png}
+            Clearing the VOP on vertex $1$ uses the transformation $La(1) La(1) La(1) La(2) La(2)$.
+        }
+    \end{itemize}
+\end{frame}
+}
+
+{
+\begin{frame}{Clearing VOPs: Example}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_01.png}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_02.png}
+\end{frame}
+}
+{
+\begin{frame}{Clearing VOPs: Example}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_02.png}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_03.png}
+\end{frame}
+}
+{
+\begin{frame}{Clearing VOPs: Example}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_03.png}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_04.png}
+\end{frame}
+}
+{
+\begin{frame}{Clearing VOPs: Example}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_04.png}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_05.png}
+\end{frame}
+}
+{
+\begin{frame}{Clearing VOPs: Example}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_05.png}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_06.png}
+\end{frame}
+}
+{
+\begin{frame}{Clearing VOPs: Example}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_01.png}
+    \includegraphics[width=0.5\textwidth]{graphs/clear_vop_06.png}
+\end{frame}
+}
+
 {
 \begin{frame}{Measurements on Graph States}
     \begin{itemize}