From c9cc7b914cf342f576e073add484208897c2fba3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= <daniel.knuettel@daknuett.eu>
Date: Mon, 9 Mar 2020 14:40:49 +0100
Subject: [PATCH] removed the pauses for now

---
 presentation/main.tex | 42 +++++++++++++++++++++---------------------
 1 file changed, 21 insertions(+), 21 deletions(-)

diff --git a/presentation/main.tex b/presentation/main.tex
index 0e41ccb..7a437e4 100644
--- a/presentation/main.tex
+++ b/presentation/main.tex
@@ -63,9 +63,9 @@
 
     \begin{itemize}
         \item Some (physical) problems are classically hard to solve.
-        \pause
+        %\pause
         \item The quantum simulator: Mapping a hard problem to quantum hardware that can simulate this specific problem.
-        \pause
+        %\pause
         \item The (universal) quantum computer: able to simulate any unitary transformation on the system.
     \end{itemize}
 
@@ -76,9 +76,9 @@
 \begin{frame}{Quantum Errors and Quantum Error Correction}
     \begin{itemize}
         \item Quantum systems at non-zero temperature often have dephasing effects and a finite population lifetime (relaxation).
-        \pause
+        %\pause
         \item Fault tolerant QC needs a way to correct for those errors.
-        \pause
+        %\pause
         \item Several strategies exist; one important class of quantum error correction codes are \textbf{stabilizer codes}.
     \end{itemize}
 
@@ -111,7 +111,7 @@
                 A $n$-qbit system is the tensor product of the single-qbit systems.
             }
         }
-    \pause
+    %\pause
         %\item{
         %        For $n$ qbits define the integer state $\ket{j}$ as
 
@@ -126,7 +126,7 @@
                 U_i := \left(\bigotimes\limits_{k < i} I\right) \otimes \bar{U} \otimes \left(\bigotimes\limits_{k > i} I\right)
             \end{equation}
         }
-    \pause
+    %\pause
         \item{
             For $\bar{U} \in SU(2)$ and qbits $i \neq j$ 
             \begin{equation}
@@ -134,7 +134,7 @@
             \end{equation}
             is the controlled $\ket{U}$ gate acting on $i$ with control-qbit $j$.
         }
-    \pause
+    %\pause
     \end{itemize}
 \end{frame}
 }
@@ -150,13 +150,13 @@
                 H := \frac{1}{\sqrt{2}}\left(\begin{array}{cc} 1 & 1 \\ 1 & -1\end{array}\right)
             \end{equation}
              which transforms from the $Z$ to the $X$ basis}
-        \pause
+        %\pause
         \item{the rotation gate
              \begin{equation}
                 R_{\phi} := \left(\begin{array}{cc} 1 & 0 \\ 0 & \exp(i\phi)\end{array}\right)
              \end{equation}
              that performs a rotation around the $Z$ axis.}
-            \pause
+            %\pause
 
     \end{itemize}
 \end{frame}
@@ -175,7 +175,7 @@
              The $S$ gate transforms from $X$ to $Y$ basis.
 
             }
-        \pause
+        %\pause
         \item{
             \textbf{Theorem}
             {\itshape
@@ -196,7 +196,7 @@
                 \ket{j} = \ket{\mbox{0b}l_1...l_n} = \ket{l_1}_s \otimes ... \otimes \ket{l_n}s
             \end{equation}
             }
-        \pause
+        %\pause
         \item{
             For $n$ qbits there exist $2^n$ such states and they form a basis
 
@@ -235,23 +235,23 @@
             Writing a unitary transformation as a product of the generator gates is unreadable.
             To fix this problem quantum circuits have been introduced.
             }
-        \pause
+        %\pause
         \item{
             Qbits are represented by horizontal lines.
         }
-    \pause
+    %\pause
         \item{
             Gates acting on a qbit are boxes on the lines.
         }
-    \pause
+    %\pause
     \item{
             Control-qbits are connected to the gate via a vertical line.
         }
-    \pause
+    %\pause
     \item{
             Circuits are read left to right.
         }
-    \pause
+    %\pause
     \item{
             Example:
             \Qcircuit @C=1em @R=.7em {
@@ -273,14 +273,14 @@
                 H = -\sum\limits_{i=1}^{n-1} Z_i Z_{i-1} + g\sum\limits_{i=0}^{n-1} X_i
             \end{equation}
             }
-        \pause
+        %\pause
         \item{
             The time evolution of such a system is given by the transfer matrix
             \begin{equation}
                 T := \exp(-itH) \in SU(2^n)
             \end{equation}
         }
-    \pause
+    %\pause
     \item{
             By associating every qbit with one spin (both are two-level systems)
             one should be able to simulate the behaviour of the spin chain using 
@@ -334,7 +334,7 @@
                 is called the Pauli group.\\
             $P_n := \left\{p_1 \otimes ... \otimes p_n \middle| p_i \in P \right\}$ is called the multilocal Pauli group.
             }}
-            \pause
+            %\pause
         \item{
             \textbf{Definition}
             {\itshape
@@ -342,7 +342,7 @@
             is called the Clifford group
             }
             }
-            \pause
+            %\pause
         \item{
                 One can show that $C_n$ is generated by $H, S, CZ_{i,j}$.
             }
@@ -370,7 +370,7 @@
         \item{
             The generators are not unique. For instance $C_1$ can be generated using $H, S$ or $\sqrt{-iX}, \sqrt{iZ}$.
             }
-        \pause
+        %\pause
         \item{
             The generators of a group have some kind of independence property.
             }