From 851262e01229401398d3875fb4f02a6ba583a8a0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= Date: Mon, 9 Mar 2020 15:29:32 +0100 Subject: [PATCH] added example on clearing VOPs --- presentation/graphs/clear_vop_01.dot | 6 +++- presentation/graphs/clear_vop_02.dot | 7 ++++ presentation/graphs/clear_vop_03.dot | 7 ++++ presentation/graphs/clear_vop_04.dot | 7 ++++ presentation/graphs/clear_vop_05.dot | 7 ++++ presentation/graphs/clear_vop_06.dot | 7 ++++ presentation/main.tex | 50 ++++++++++++++++++++++++++++ 7 files changed, 90 insertions(+), 1 deletion(-) diff --git a/presentation/graphs/clear_vop_01.dot b/presentation/graphs/clear_vop_01.dot index 257267e..576fd34 100644 --- a/presentation/graphs/clear_vop_01.dot +++ b/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 } diff --git a/presentation/graphs/clear_vop_02.dot b/presentation/graphs/clear_vop_02.dot index 8d2a6cb..a6b89fe 100644 --- a/presentation/graphs/clear_vop_02.dot +++ b/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 diff --git a/presentation/graphs/clear_vop_03.dot b/presentation/graphs/clear_vop_03.dot index 9498e27..b7d8606 100644 --- a/presentation/graphs/clear_vop_03.dot +++ b/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 } diff --git a/presentation/graphs/clear_vop_04.dot b/presentation/graphs/clear_vop_04.dot index a5abbb6..ded2fd1 100644 --- a/presentation/graphs/clear_vop_04.dot +++ b/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 diff --git a/presentation/graphs/clear_vop_05.dot b/presentation/graphs/clear_vop_05.dot index 6d14e52..6572cc5 100644 --- a/presentation/graphs/clear_vop_05.dot +++ b/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 diff --git a/presentation/graphs/clear_vop_06.dot b/presentation/graphs/clear_vop_06.dot index dc6a2c4..fb18d99 100644 --- a/presentation/graphs/clear_vop_06.dot +++ b/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 diff --git a/presentation/main.tex b/presentation/main.tex index 7a437e4..b4be715 100644 --- a/presentation/main.tex +++ b/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}