From 1fbcf0d2e6e8b845fb7fd30c751b771bab15a8e7 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Fri, 17 Apr 2026 23:36:06 +0200 Subject: [PATCH] Fix DEM explanation E_X offset --- src/final_presentation/main.tex | 552 ++++++++++++++++---------------- 1 file changed, 276 insertions(+), 276 deletions(-) diff --git a/src/final_presentation/main.tex b/src/final_presentation/main.tex index 1f31021..ad79544 100644 --- a/src/final_presentation/main.tex +++ b/src/final_presentation/main.tex @@ -687,273 +687,273 @@ \subsection{Detector Error Models} \label{subsec:Detector Error Models} -% \begin{frame}[fragile] -% \frametitle{The Measurement Syndrome Matrix I} -% -% \vspace*{-18mm} -% -% \begin{itemize} -% \item \schlagwort{Measurement syndrome matrix} $\bm{\Omega}$ \\ -% contains error patterns \citereferencemanual{DTB$^+$25} -% \item Example: 3-qubit repetition code -% \end{itemize} -% -% \vspace*{-25mm} -% -% \centering -% \only<1>{ -% \begin{minipage}{0.4\textwidth} -% \centering -% -% \vspace*{40mm} -% \begin{tikzpicture} -% \node{$% -% \bm{\Omega} = -% \left( -% \begin{array}{ccc} -% 1 & 1 & 0 \\ -% 0 & 1 & 1 \\ -% 1 & 1 & 0 \\ -% 0 & 1 & 1 \\ -% 1 & 1 & 0 \\ -% 0 & 1 & 1 -% \end{array} -% \right)$ -% }; -% -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,mirror,amplitude=3mm,raise=5mm} -% ] -% (2.5,1.2) -- (2.5,2.85) -% node[midway,right,xshift=10mm]{$\text{SE}_1$}; -% -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,mirror,amplitude=3mm,raise=5mm} -% ] -% (2.5,-0.75) -- (2.5,0.9) -% node[midway,right,xshift=10mm]{$\text{SE}_2$}; -% -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,mirror,amplitude=3mm,raise=5mm} -% ] -% (2.5,-2.7) -- (2.5,-1.1) -% node[midway,right,xshift=10mm]{$\text{SE}_3$}; -% \end{tikzpicture} -% -% \vspace*{-10mm} -% -% \begin{gather*} -% \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} -% \end{gather*} -% \end{minipage}% -% \begin{minipage}{0.6\textwidth} -% \begin{figure}[H] -% \newcommand{\preperr}[1]{ -% \gate[style={fill=orange!20}]{\scriptstyle ##1} -% } -% -% \centering -% -% \begin{quantikz}[ -% row sep=4mm, column sep=4mm, -% wire types={q,q,q,q,q,n,n,n,n}, -% execute at end picture={ -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,amplitude=3mm,raise=9mm} -% ] -% (\tikzcdmatrixname-4-19.north east) -% -- -% (\tikzcdmatrixname-5-19.south east) -% node[midway,right,xshift=14mm]{$\text{SE}_1$}; -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,amplitude=3mm,raise=9mm} -% ] -% (\tikzcdmatrixname-6-19.north east) -% -- -% (\tikzcdmatrixname-7-19.south east) -% node[midway,right,xshift=14mm]{$\text{SE}_2$}; -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,amplitude=3mm,raise=9mm} -% ] -% (\tikzcdmatrixname-8-19.north east) -% -- -% (\tikzcdmatrixname-9-19.south east) -% node[midway,right,xshift=14mm]{$\text{SE}_3$}; -% } -% ] -% % tex-fmt: off -% & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ -% \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} & & \\ -% \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ -% \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} \\ -% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ -% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} -% % tex-fmt: on -% \end{quantikz} -% \end{figure} -% \end{minipage} -% } -% \only<2>{ -% \begin{minipage}{0.4\textwidth} -% \centering -% -% \vspace*{40mm} -% \begin{tikzpicture} -% \node{$% -% \bm{\Omega} = -% \left( -% \begin{array}{>{\columncolor{red!20}}ccc} -% 1 & 1 & 0 \\ -% 0 & 1 & 1 \\ -% 1 & 1 & 0 \\ -% 0 & 1 & 1 \\ -% 1 & 1 & 0 \\ -% 0 & 1 & 1 -% \end{array} -% \right)$ -% }; -% -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,mirror,amplitude=3mm,raise=5mm} -% ] -% (2.5,1.2) -- (2.5,2.85) -% node[midway,right,xshift=10mm]{$\text{SE}_1$}; -% -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,mirror,amplitude=3mm,raise=5mm} -% ] -% (2.5,-0.75) -- (2.5,0.9) -% node[midway,right,xshift=10mm]{$\text{SE}_2$}; -% -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,mirror,amplitude=3mm,raise=5mm} -% ] -% (2.5,-2.7) -- (2.5,-1.1) -% node[midway,right,xshift=10mm]{$\text{SE}_3$}; -% \end{tikzpicture} -% -% \vspace*{-10mm} -% -% \begin{gather*} -% \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} -% \end{gather*} -% \end{minipage}% -% \begin{minipage}{0.6\textwidth} -% \begin{figure}[H] -% \newcommand{\preperr}[1]{ -% \gate[style={fill=orange!20}]{\scriptstyle ##1} -% } -% \newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}} -% -% \newcommand{\noise}{ -% \gate[style={noisy}]{\text{\small X}}% -% \setwiretype{n}% -% \wire[l][1]{q} -% } -% \newcommand{\redwire}[1]{ -% \wire[r][##1][style={draw=red, line width=2pt}]{q} -% } -% \newcommand{\redtarg}{ -% \targ[style={draw=red}]{}% -% \setwiretype{n}% -% \wire[l][1]{q} -% } -% \newcommand{\redctrl}[1]{ -% \ctrl[style={draw=red,fill=red,line width=2pt}]{##1} -% } -% \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}} -% -% \tikzset{ -% noisy/.style={ -% starburst, -% starburst point height=2mm, -% fill=red!25, draw=red!85!black, -% line width=2pt, -% inner xsep=-2pt, inner ysep=-2pt -% }, -% } -% -% \centering -% -% \begin{quantikz}[ -% row sep=4mm, column sep=4mm, -% wire types={q,q,q,q,q,n,n,n,n}, -% execute at end picture={ -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,amplitude=3mm,raise=9mm} -% ] -% (\tikzcdmatrixname-4-19.north east) -% -- -% (\tikzcdmatrixname-5-19.south east) -% node[midway,right,xshift=14mm]{$\text{SE}_1$}; -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,amplitude=3mm,raise=9mm} -% ] -% (\tikzcdmatrixname-6-19.north east) -% -- -% (\tikzcdmatrixname-7-19.south east) -% node[midway,right,xshift=14mm]{$\text{SE}_2$}; -% \draw [ -% line width=1pt, -% decorate, -% decoration={brace,amplitude=3mm,raise=9mm} -% ] -% (\tikzcdmatrixname-8-19.north east) -% -- -% (\tikzcdmatrixname-9-19.south east) -% node[midway,right,xshift=14mm]{$\text{SE}_3$}; -% } -% ] -% % tex-fmt: off -% & \noise\redwire{18} & \redctrl{3} & & & & & & \redctrl{5} & & & & & & \redctrl{7} & & & & & \\ -% \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} & & \\ -% \lstick{$\ket{0}_{\text{A}_1}$} & & \redtarg{}\redwire{16} & \targ{} & & & & & & & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ -% \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} \\ -% & & & & & & & & & & & & \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} \\ -% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} -% % tex-fmt: on -% \end{quantikz} -% \end{figure} -% \end{minipage} -% } -% -% \vspace*{8mm} -% -% \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] + \frametitle{The Measurement Syndrome Matrix I} + + \vspace*{-18mm} + + \begin{itemize} + \item \schlagwort{Measurement syndrome matrix} $\bm{\Omega}$ \\ + contains error patterns \citereferencemanual{DTB$^+$25} + \item Example: 3-qubit repetition code + \end{itemize} + % + \vspace*{-25mm} + + \centering + \only<1>{ + \begin{minipage}{0.4\textwidth} + \centering + + \vspace*{40mm} + \begin{tikzpicture} + \node{$% + \bm{\Omega} = + \left( + \begin{array}{ccc} + 1 & 1 & 0 \\ + 0 & 1 & 1 \\ + 1 & 1 & 0 \\ + 0 & 1 & 1 \\ + 1 & 1 & 0 \\ + 0 & 1 & 1 + \end{array} + \right)$ + }; + + \draw [ + line width=1pt, + decorate, + decoration={brace,mirror,amplitude=3mm,raise=5mm} + ] + (2.5,1.2) -- (2.5,2.85) + node[midway,right,xshift=10mm]{$\text{SE}_1$}; + + \draw [ + line width=1pt, + decorate, + decoration={brace,mirror,amplitude=3mm,raise=5mm} + ] + (2.5,-0.75) -- (2.5,0.9) + node[midway,right,xshift=10mm]{$\text{SE}_2$}; + + \draw [ + line width=1pt, + decorate, + decoration={brace,mirror,amplitude=3mm,raise=5mm} + ] + (2.5,-2.7) -- (2.5,-1.1) + node[midway,right,xshift=10mm]{$\text{SE}_3$}; + \end{tikzpicture} + + \vspace*{-10mm} + + \begin{gather*} + \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} + \end{gather*} + \end{minipage}% + \begin{minipage}{0.6\textwidth} + \begin{figure}[H] + \newcommand{\preperr}[1]{ + \gate[style={fill=orange!20}]{\scriptstyle ##1} + } + + \centering + + \begin{quantikz}[ + row sep=4mm, column sep=4mm, + wire types={q,q,q,q,q,n,n,n,n}, + execute at end picture={ + \draw [ + line width=1pt, + decorate, + decoration={brace,amplitude=3mm,raise=9mm} + ] + (\tikzcdmatrixname-4-19.north east) + -- + (\tikzcdmatrixname-5-19.south east) + node[midway,right,xshift=14mm]{$\text{SE}_1$}; + \draw [ + line width=1pt, + decorate, + decoration={brace,amplitude=3mm,raise=9mm} + ] + (\tikzcdmatrixname-6-19.north east) + -- + (\tikzcdmatrixname-7-19.south east) + node[midway,right,xshift=14mm]{$\text{SE}_2$}; + \draw [ + line width=1pt, + decorate, + decoration={brace,amplitude=3mm,raise=9mm} + ] + (\tikzcdmatrixname-8-19.north east) + -- + (\tikzcdmatrixname-9-19.south east) + node[midway,right,xshift=14mm]{$\text{SE}_3$}; + } + ] + % tex-fmt: off + & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ + \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} & & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ + \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} \\ + & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ + & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} + % tex-fmt: on + \end{quantikz} + \end{figure} + \end{minipage} + } + \only<2>{ + \begin{minipage}{0.4\textwidth} + \centering + + \vspace*{40mm} + \begin{tikzpicture} + \node{$% + \bm{\Omega} = + \left( + \begin{array}{>{\columncolor{red!20}}ccc} + 1 & 1 & 0 \\ + 0 & 1 & 1 \\ + 1 & 1 & 0 \\ + 0 & 1 & 1 \\ + 1 & 1 & 0 \\ + 0 & 1 & 1 + \end{array} + \right)$ + }; + + \draw [ + line width=1pt, + decorate, + decoration={brace,mirror,amplitude=3mm,raise=5mm} + ] + (2.5,1.2) -- (2.5,2.85) + node[midway,right,xshift=10mm]{$\text{SE}_1$}; + + \draw [ + line width=1pt, + decorate, + decoration={brace,mirror,amplitude=3mm,raise=5mm} + ] + (2.5,-0.75) -- (2.5,0.9) + node[midway,right,xshift=10mm]{$\text{SE}_2$}; + + \draw [ + line width=1pt, + decorate, + decoration={brace,mirror,amplitude=3mm,raise=5mm} + ] + (2.5,-2.7) -- (2.5,-1.1) + node[midway,right,xshift=10mm]{$\text{SE}_3$}; + \end{tikzpicture} + + \vspace*{-10mm} + + \begin{gather*} + \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} + \end{gather*} + \end{minipage}% + \begin{minipage}{0.6\textwidth} + \begin{figure}[H] + \newcommand{\preperr}[1]{ + \gate[style={fill=orange!20}]{\scriptstyle ##1} + } + \newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}} + + \newcommand{\noise}{ + \gate[style={noisy}]{\text{\small X}}% + \setwiretype{n}% + \wire[l][1]{q} + } + \newcommand{\redwire}[1]{ + \wire[r][##1][style={draw=red, line width=2pt}]{q} + } + \newcommand{\redtarg}{ + \targ[style={draw=red}]{}% + \setwiretype{n}% + \wire[l][1]{q} + } + \newcommand{\redctrl}[1]{ + \ctrl[style={draw=red,fill=red,line width=2pt}]{##1} + } + \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}} + + \tikzset{ + noisy/.style={ + starburst, + starburst point height=2mm, + fill=red!25, draw=red!85!black, + line width=2pt, + inner xsep=-2pt, inner ysep=-2pt + }, + } + + \centering + + \begin{quantikz}[ + row sep=4mm, column sep=4mm, + wire types={q,q,q,q,q,n,n,n,n}, + execute at end picture={ + \draw [ + line width=1pt, + decorate, + decoration={brace,amplitude=3mm,raise=9mm} + ] + (\tikzcdmatrixname-4-19.north east) + -- + (\tikzcdmatrixname-5-19.south east) + node[midway,right,xshift=14mm]{$\text{SE}_1$}; + \draw [ + line width=1pt, + decorate, + decoration={brace,amplitude=3mm,raise=9mm} + ] + (\tikzcdmatrixname-6-19.north east) + -- + (\tikzcdmatrixname-7-19.south east) + node[midway,right,xshift=14mm]{$\text{SE}_2$}; + \draw [ + line width=1pt, + decorate, + decoration={brace,amplitude=3mm,raise=9mm} + ] + (\tikzcdmatrixname-8-19.north east) + -- + (\tikzcdmatrixname-9-19.south east) + node[midway,right,xshift=14mm]{$\text{SE}_3$}; + } + ] + % tex-fmt: off + & \noise\redwire{18} & \redctrl{3} & & & & & & \redctrl{5} & & & & & & \redctrl{7} & & & & & \\ + \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} & & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & & \redtarg{}\redwire{16} & \targ{} & & & & & & & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ + \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} \\ + & & & & & & & & & & & & \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} \\ + & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} + % tex-fmt: on + \end{quantikz} + \end{figure} + \end{minipage} + } + + \vspace*{8mm} + + \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] \frametitle{The Measurement Syndrome Matrix} @@ -1065,7 +1065,7 @@ \scalebox{0.85}{ \parbox{.5\linewidth}{% \begin{gather*} - \hspace*{58.25mm}% + \hspace*{54.25mm}% \begin{array}{c} E_5 \\ \downarrow @@ -1163,7 +1163,7 @@ \scalebox{0.85}{ \parbox{.5\linewidth}{% \begin{gather*} - \hspace*{65.5mm}% + \hspace*{61.5mm}% \begin{array}{c} E_6 \\ \downarrow @@ -1987,13 +1987,13 @@ \temp } - \addplot+[mark=x, line width=2pt, - densely dashed, black] - table[ - col sep=comma, x=physical_p, - y=LER_per_round, - ] - {res/sim/one-shot/SyndromeMinSumDecoder/max_iter_32/LERs.csv}; + % \addplot+[mark=x, line width=2pt, + % densely dashed, black] + % table[ + % col sep=comma, x=physical_p, + % y=LER_per_round, + % ] + % {res/sim/one-shot/SyndromeMinSumDecoder/max_iter_32/LERs.csv}; \end{axis} \end{tikzpicture} \end{figure}