diff --git a/presentation/main.tex b/presentation/main.tex
index 7fba7b2..2f271df 100644
--- a/presentation/main.tex
+++ b/presentation/main.tex
@@ -97,6 +97,12 @@
 
 {
 \begin{frame}{The Universal Quantum Computer}
+    \begin{itemize}
+        \item{A quantum system to which any unitary transformation can be applied.}
+        \item{Any quantum system with sufficiently small hilbert space can be simulated.}
+        \item{Quantum algorithms such as the Phase Estimation Algorithm have physical applications.}
+        \item{Applications in other fields: Quantum AI, breaking encryption (via prime factorization), Quantum Search, ...}
+    \end{itemize}
 
 \end{frame}
 }
@@ -859,7 +865,7 @@
 
 {
 \begin{frame}{Performance: Circuit Length on Graphical Representation}
-    \includegraphics[width=\textwidth]{../performance/scaling_circuits_linear.png}
+    \includegraphics[width=\textwidth]{../performance/regimes/scaling_circuits_linear.png}
 \end{frame}
 }
 
@@ -948,7 +954,7 @@
         \item{It would probably be enough to search for matrices $g_1, g_2$
             for which
                 \begin{equation}
-                    CX_{1,2} (g_1 \otimes g_2) CX_{1,2} = g_1' \otimes g_2'
+                    \langle CX_{1,2} (g_1 \otimes g_2) CX_{1,2}\rangle = \langle g_1' \otimes g_2'\rangle
                 \end{equation}
             holds. The Pauli matrices are one group that fulfills this property.
             }