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Fix DEM explanation E_X offset

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Andreas Tsouchlos
2026-04-17 23:36:06 +02:00
parent 4763f6189c
commit 1fbcf0d2e6
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src/final_presentation/main.tex
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@@ -687,273 +687,273 @@
\subsection{Detector Error Models} \subsection{Detector Error Models}
\label{subsec:Detector Error Models} \label{subsec:Detector Error Models}
% \begin{frame}[fragile] \begin{frame}[fragile]
% \frametitle{The Measurement Syndrome Matrix I} \frametitle{The Measurement Syndrome Matrix I}
\vspace*{-18mm}
\begin{itemize}
\item \schlagwort{Measurement syndrome matrix} $\bm{\Omega}$ \\
contains error patterns \citereferencemanual{DTB$^+$25}
\item Example: 3-qubit repetition code
\end{itemize}
% %
% \vspace*{-18mm} \vspace*{-25mm}
%
% \begin{itemize} \centering
% \item \schlagwort{Measurement syndrome matrix} $\bm{\Omega}$ \\ \only<1>{
% contains error patterns \citereferencemanual{DTB$^+$25} \begin{minipage}{0.4\textwidth}
% \item Example: 3-qubit repetition code \centering
% \end{itemize}
% \vspace*{40mm}
% \vspace*{-25mm} \begin{tikzpicture}
% \node{$%
% \centering \bm{\Omega} =
% \only<1>{ \left(
% \begin{minipage}{0.4\textwidth} \begin{array}{ccc}
% \centering 1 & 1 & 0 \\
% 0 & 1 & 1 \\
% \vspace*{40mm} 1 & 1 & 0 \\
% \begin{tikzpicture} 0 & 1 & 1 \\
% \node{$% 1 & 1 & 0 \\
% \bm{\Omega} = 0 & 1 & 1
% \left( \end{array}
% \begin{array}{ccc} \right)$
% 1 & 1 & 0 \\ };
% 0 & 1 & 1 \\
% 1 & 1 & 0 \\ \draw [
% 0 & 1 & 1 \\ line width=1pt,
% 1 & 1 & 0 \\ decorate,
% 0 & 1 & 1 decoration={brace,mirror,amplitude=3mm,raise=5mm}
% \end{array} ]
% \right)$ (2.5,1.2) -- (2.5,2.85)
% }; node[midway,right,xshift=10mm]{$\text{SE}_1$};
%
% \draw [ \draw [
% line width=1pt, line width=1pt,
% decorate, decorate,
% decoration={brace,mirror,amplitude=3mm,raise=5mm} decoration={brace,mirror,amplitude=3mm,raise=5mm}
% ] ]
% (2.5,1.2) -- (2.5,2.85) (2.5,-0.75) -- (2.5,0.9)
% node[midway,right,xshift=10mm]{$\text{SE}_1$}; node[midway,right,xshift=10mm]{$\text{SE}_2$};
%
% \draw [ \draw [
% line width=1pt, line width=1pt,
% decorate, decorate,
% decoration={brace,mirror,amplitude=3mm,raise=5mm} decoration={brace,mirror,amplitude=3mm,raise=5mm}
% ] ]
% (2.5,-0.75) -- (2.5,0.9) (2.5,-2.7) -- (2.5,-1.1)
% node[midway,right,xshift=10mm]{$\text{SE}_2$}; node[midway,right,xshift=10mm]{$\text{SE}_3$};
% \end{tikzpicture}
% \draw [
% line width=1pt, \vspace*{-10mm}
% decorate,
% decoration={brace,mirror,amplitude=3mm,raise=5mm} \begin{gather*}
% ] \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\}
% (2.5,-2.7) -- (2.5,-1.1) \end{gather*}
% node[midway,right,xshift=10mm]{$\text{SE}_3$}; \end{minipage}%
% \end{tikzpicture} \begin{minipage}{0.6\textwidth}
% \begin{figure}[H]
% \vspace*{-10mm} \newcommand{\preperr}[1]{
% \gate[style={fill=orange!20}]{\scriptstyle ##1}
% \begin{gather*} }
% \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\}
% \end{gather*} \centering
% \end{minipage}%
% \begin{minipage}{0.6\textwidth} \begin{quantikz}[
% \begin{figure}[H] row sep=4mm, column sep=4mm,
% \newcommand{\preperr}[1]{ wire types={q,q,q,q,q,n,n,n,n},
% \gate[style={fill=orange!20}]{\scriptstyle ##1} execute at end picture={
% } \draw [
% line width=1pt,
% \centering decorate,
% decoration={brace,amplitude=3mm,raise=9mm}
% \begin{quantikz}[ ]
% row sep=4mm, column sep=4mm, (\tikzcdmatrixname-4-19.north east)
% wire types={q,q,q,q,q,n,n,n,n}, --
% execute at end picture={ (\tikzcdmatrixname-5-19.south east)
% \draw [ node[midway,right,xshift=14mm]{$\text{SE}_1$};
% line width=1pt, \draw [
% decorate, line width=1pt,
% decoration={brace,amplitude=3mm,raise=9mm} decorate,
% ] decoration={brace,amplitude=3mm,raise=9mm}
% (\tikzcdmatrixname-4-19.north east) ]
% -- (\tikzcdmatrixname-6-19.north east)
% (\tikzcdmatrixname-5-19.south east) --
% node[midway,right,xshift=14mm]{$\text{SE}_1$}; (\tikzcdmatrixname-7-19.south east)
% \draw [ node[midway,right,xshift=14mm]{$\text{SE}_2$};
% line width=1pt, \draw [
% decorate, line width=1pt,
% decoration={brace,amplitude=3mm,raise=9mm} decorate,
% ] decoration={brace,amplitude=3mm,raise=9mm}
% (\tikzcdmatrixname-6-19.north east) ]
% -- (\tikzcdmatrixname-8-19.north east)
% (\tikzcdmatrixname-7-19.south east) --
% node[midway,right,xshift=14mm]{$\text{SE}_2$}; (\tikzcdmatrixname-9-19.south east)
% \draw [ node[midway,right,xshift=14mm]{$\text{SE}_3$};
% line width=1pt, }
% decorate, ]
% decoration={brace,amplitude=3mm,raise=9mm} % tex-fmt: off
% ] & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\
% (\tikzcdmatrixname-8-19.north east) \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\
% -- & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\
% (\tikzcdmatrixname-9-19.south east) \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\
% node[midway,right,xshift=14mm]{$\text{SE}_3$}; \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\
% } & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & & & & & & & \meter{} & \setwiretype{c} \\
% ] & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\
% % tex-fmt: off & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
% & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
% \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\ % tex-fmt: on
% & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ \end{quantikz}
% \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ \end{figure}
% \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ \end{minipage}
% & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & & & & & & & \meter{} & \setwiretype{c} \\ }
% & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\ \only<2>{
% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ \begin{minipage}{0.4\textwidth}
% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} \centering
% % tex-fmt: on
% \end{quantikz} \vspace*{40mm}
% \end{figure} \begin{tikzpicture}
% \end{minipage} \node{$%
% } \bm{\Omega} =
% \only<2>{ \left(
% \begin{minipage}{0.4\textwidth} \begin{array}{>{\columncolor{red!20}}ccc}
% \centering 1 & 1 & 0 \\
% 0 & 1 & 1 \\
% \vspace*{40mm} 1 & 1 & 0 \\
% \begin{tikzpicture} 0 & 1 & 1 \\
% \node{$% 1 & 1 & 0 \\
% \bm{\Omega} = 0 & 1 & 1
% \left( \end{array}
% \begin{array}{>{\columncolor{red!20}}ccc} \right)$
% 1 & 1 & 0 \\ };
% 0 & 1 & 1 \\
% 1 & 1 & 0 \\ \draw [
% 0 & 1 & 1 \\ line width=1pt,
% 1 & 1 & 0 \\ decorate,
% 0 & 1 & 1 decoration={brace,mirror,amplitude=3mm,raise=5mm}
% \end{array} ]
% \right)$ (2.5,1.2) -- (2.5,2.85)
% }; node[midway,right,xshift=10mm]{$\text{SE}_1$};
%
% \draw [ \draw [
% line width=1pt, line width=1pt,
% decorate, decorate,
% decoration={brace,mirror,amplitude=3mm,raise=5mm} decoration={brace,mirror,amplitude=3mm,raise=5mm}
% ] ]
% (2.5,1.2) -- (2.5,2.85) (2.5,-0.75) -- (2.5,0.9)
% node[midway,right,xshift=10mm]{$\text{SE}_1$}; node[midway,right,xshift=10mm]{$\text{SE}_2$};
%
% \draw [ \draw [
% line width=1pt, line width=1pt,
% decorate, decorate,
% decoration={brace,mirror,amplitude=3mm,raise=5mm} decoration={brace,mirror,amplitude=3mm,raise=5mm}
% ] ]
% (2.5,-0.75) -- (2.5,0.9) (2.5,-2.7) -- (2.5,-1.1)
% node[midway,right,xshift=10mm]{$\text{SE}_2$}; node[midway,right,xshift=10mm]{$\text{SE}_3$};
% \end{tikzpicture}
% \draw [
% line width=1pt, \vspace*{-10mm}
% decorate,
% decoration={brace,mirror,amplitude=3mm,raise=5mm} \begin{gather*}
% ] \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\}
% (2.5,-2.7) -- (2.5,-1.1) \end{gather*}
% node[midway,right,xshift=10mm]{$\text{SE}_3$}; \end{minipage}%
% \end{tikzpicture} \begin{minipage}{0.6\textwidth}
% \begin{figure}[H]
% \vspace*{-10mm} \newcommand{\preperr}[1]{
% \gate[style={fill=orange!20}]{\scriptstyle ##1}
% \begin{gather*} }
% \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} \newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
% \end{gather*}
% \end{minipage}% \newcommand{\noise}{
% \begin{minipage}{0.6\textwidth} \gate[style={noisy}]{\text{\small X}}%
% \begin{figure}[H] \setwiretype{n}%
% \newcommand{\preperr}[1]{ \wire[l][1]{q}
% \gate[style={fill=orange!20}]{\scriptstyle ##1} }
% } \newcommand{\redwire}[1]{
% \newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}} \wire[r][##1][style={draw=red, line width=2pt}]{q}
% }
% \newcommand{\noise}{ \newcommand{\redtarg}{
% \gate[style={noisy}]{\text{\small X}}% \targ[style={draw=red}]{}%
% \setwiretype{n}% \setwiretype{n}%
% \wire[l][1]{q} \wire[l][1]{q}
% } }
% \newcommand{\redwire}[1]{ \newcommand{\redctrl}[1]{
% \wire[r][##1][style={draw=red, line width=2pt}]{q} \ctrl[style={draw=red,fill=red,line width=2pt}]{##1}
% } }
% \newcommand{\redtarg}{ \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}}
% \targ[style={draw=red}]{}%
% \setwiretype{n}% \tikzset{
% \wire[l][1]{q} noisy/.style={
% } starburst,
% \newcommand{\redctrl}[1]{ starburst point height=2mm,
% \ctrl[style={draw=red,fill=red,line width=2pt}]{##1} fill=red!25, draw=red!85!black,
% } line width=2pt,
% \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}} inner xsep=-2pt, inner ysep=-2pt
% },
% \tikzset{ }
% noisy/.style={
% starburst, \centering
% starburst point height=2mm,
% fill=red!25, draw=red!85!black, \begin{quantikz}[
% line width=2pt, row sep=4mm, column sep=4mm,
% inner xsep=-2pt, inner ysep=-2pt wire types={q,q,q,q,q,n,n,n,n},
% }, execute at end picture={
% } \draw [
% line width=1pt,
% \centering decorate,
% decoration={brace,amplitude=3mm,raise=9mm}
% \begin{quantikz}[ ]
% row sep=4mm, column sep=4mm, (\tikzcdmatrixname-4-19.north east)
% wire types={q,q,q,q,q,n,n,n,n}, --
% execute at end picture={ (\tikzcdmatrixname-5-19.south east)
% \draw [ node[midway,right,xshift=14mm]{$\text{SE}_1$};
% line width=1pt, \draw [
% decorate, line width=1pt,
% decoration={brace,amplitude=3mm,raise=9mm} decorate,
% ] decoration={brace,amplitude=3mm,raise=9mm}
% (\tikzcdmatrixname-4-19.north east) ]
% -- (\tikzcdmatrixname-6-19.north east)
% (\tikzcdmatrixname-5-19.south east) --
% node[midway,right,xshift=14mm]{$\text{SE}_1$}; (\tikzcdmatrixname-7-19.south east)
% \draw [ node[midway,right,xshift=14mm]{$\text{SE}_2$};
% line width=1pt, \draw [
% decorate, line width=1pt,
% decoration={brace,amplitude=3mm,raise=9mm} decorate,
% ] decoration={brace,amplitude=3mm,raise=9mm}
% (\tikzcdmatrixname-6-19.north east) ]
% -- (\tikzcdmatrixname-8-19.north east)
% (\tikzcdmatrixname-7-19.south east) --
% node[midway,right,xshift=14mm]{$\text{SE}_2$}; (\tikzcdmatrixname-9-19.south east)
% \draw [ node[midway,right,xshift=14mm]{$\text{SE}_3$};
% line width=1pt, }
% decorate, ]
% decoration={brace,amplitude=3mm,raise=9mm} % tex-fmt: off
% ] & \noise\redwire{18} & \redctrl{3} & & & & & & \redctrl{5} & & & & & & \redctrl{7} & & & & & \\
% (\tikzcdmatrixname-8-19.north east) \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\
% -- & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\
% (\tikzcdmatrixname-9-19.south east) \lstick{$\ket{0}_{\text{A}_1}$} & & \redtarg{}\redwire{16} & \targ{} & & & & & & & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\
% node[midway,right,xshift=14mm]{$\text{SE}_3$}; \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\
% } & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \redtarg\redwire{10} & \targ{} & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\
% ] & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\
% % tex-fmt: off & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \redtarg\redwire{4} & \targ{} & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\
% & \noise\redwire{18} & \redctrl{3} & & & & & & \redctrl{5} & & & & & & \redctrl{7} & & & & & \\ & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
% \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\ % tex-fmt: on
% & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ \end{quantikz}
% \lstick{$\ket{0}_{\text{A}_1}$} & & \redtarg{}\redwire{16} & \targ{} & & & & & & & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ \end{figure}
% \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ \end{minipage}
% & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \redtarg\redwire{10} & \targ{} & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ }
% & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\
% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \redtarg\redwire{4} & \targ{} & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ \vspace*{8mm}
% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
% % tex-fmt: on \addreferencesmanual
% \end{quantikz} {DTB$^+$25}{
% \end{figure} P.- J. H. S. Derks et al., ``Designing fault-tolerant
% \end{minipage} circuits using detector error models,'' \emph{Quantum}, 2025.
% } }
% \stopreferencesmanual
% \vspace*{8mm} \end{frame}
%
% \addreferencesmanual
% {DTB$^+$25}{
% P.- J. H. S. Derks et al., ``Designing fault-tolerant
% circuits using detector error models,'' \emph{Quantum}, 2025.
% }
% \stopreferencesmanual
% \end{frame}
\begin{frame}[fragile] \begin{frame}[fragile]
\frametitle{The Measurement Syndrome Matrix} \frametitle{The Measurement Syndrome Matrix}
@@ -1065,7 +1065,7 @@
\scalebox{0.85}{ \scalebox{0.85}{
\parbox{.5\linewidth}{% \parbox{.5\linewidth}{%
\begin{gather*} \begin{gather*}
\hspace*{58.25mm}% \hspace*{54.25mm}%
\begin{array}{c} \begin{array}{c}
E_5 \\ E_5 \\
\downarrow \downarrow
@@ -1163,7 +1163,7 @@
\scalebox{0.85}{ \scalebox{0.85}{
\parbox{.5\linewidth}{% \parbox{.5\linewidth}{%
\begin{gather*} \begin{gather*}
\hspace*{65.5mm}% \hspace*{61.5mm}%
\begin{array}{c} \begin{array}{c}
E_6 \\ E_6 \\
\downarrow \downarrow
@@ -1987,13 +1987,13 @@
\temp \temp
} }
\addplot+[mark=x, line width=2pt, % \addplot+[mark=x, line width=2pt,
densely dashed, black] % densely dashed, black]
table[ % table[
col sep=comma, x=physical_p, % col sep=comma, x=physical_p,
y=LER_per_round, % y=LER_per_round,
] % ]
{res/sim/one-shot/SyndromeMinSumDecoder/max_iter_32/LERs.csv}; % {res/sim/one-shot/SyndromeMinSumDecoder/max_iter_32/LERs.csv};
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\end{figure} \end{figure}