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Add Tanner graph from AutDec paper

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Andreas Tsouchlos
2026-02-04 20:59:47 +01:00
parent 67264e74c9
commit a624e49f23
2 changed files with 95 additions and 60 deletions
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155
src/midterm_presentation/main.tex
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@@ -431,36 +431,47 @@
\item Example: The 3-qubit repetition code for $\X$ errors
\end{itemize}
\vspace*{-5mm}
\begin{align*}
\bm{H} =
\begin{pmatrix}
1 & 1 & 0 \\
0 & 1 & 1
\end{pmatrix}
\end{align*}
\vspace*{5mm}
\begin{figure}[H]
% \newcommand{\anyerrgate}{\gate[style={fill=red!20}]{\mathcal{E}_\text{XYZ}}}
\newcommand{\preperr}{\gate[style={fill=orange!20}]{\phantom{1}}}
\newcommand{\gateerr}{\gate[style={fill=red!20}]{\phantom{1}}}
\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
\centering
% tex-fmt: off
\begin{quantikz}%[row sep=4mm, column sep=4mm]
& \ctrl{3} & & & & & \\
\lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & \\
& & & & \ctrl{2} & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
\end{quantikz}
% tex-fmt: on
% \caption{Circuit-level noise model for the 3-qubit repetition code}
\hspace*{-25mm}
\begin{subfigure}{0.4\textwidth}
\centering
\begin{align*}
\bm{H} =
\begin{pmatrix}
1 & 1 & 0 \\
0 & 1 & 1
\end{pmatrix}
\end{align*}
% \newcommand{\anyerrgate}{\gate[style={fill=red!20}]{\mathcal{E}_\text{XYZ}}}
\newcommand{\preperr}{\gate[style={fill=orange!20}]{\phantom{1}}}
\newcommand{\gateerr}{\gate[style={fill=red!20}]{\phantom{1}}}
\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
\centering
% tex-fmt: off
\begin{quantikz}%[row sep=4mm, column sep=4mm]
& \ctrl{3} & & & & & \\
\lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & \\
& & & & \ctrl{2} & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
\end{quantikz}
% tex-fmt: on
\end{subfigure}%
\begin{subfigure}{0.15\textwidth}
\centering
\begin{align*}
\bm{H} \bm{y}^\text{T} = \bm{s}
\end{align*}
\vspace*{-5mm}
\end{subfigure}
\end{figure}
\vspace*{5mm}
\vspace*{10mm}
\addreferences
{nielsen_quantum_2010}
@@ -1115,8 +1126,6 @@
\vspace*{-17mm}
\begin{itemize}
\item \schlagwort{Detector error matrix} $\bm{H}$ contains
modified error patterns \citereference{derks_designing_2025}
\item Repetition of errors mitigated by XORing measurements
\end{itemize}
@@ -1171,19 +1180,21 @@
\begin{minipage}{0.6\textwidth}
\newcommand\cc{\cellcolor{blue!20}}
\begin{align*}
\bm{H} =
% tex-fmt: off
\left(\begin{array}{ccccccccccccccc}
1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1
\end{array}\right)
% tex-fmt: on
\end{align*}
\visible<3->{
\begin{align*}
\bm{H} =
% tex-fmt: off
\left(\begin{array}{ccccccccccccccc}
1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 \\
\cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1
\end{array}\right)
% tex-fmt: on
\end{align*}
}
\end{minipage}
\vspace*{5mm}
@@ -1192,6 +1203,8 @@
\begin{itemize}
\item A detector is a parity constraint on a set of
measurement outcomes
\item The \schlagwort{detector error matrix} $\bm{H}$ contains
modified error patterns \citereference{derks_designing_2025}
\end{itemize}
}
@@ -1328,16 +1341,20 @@
\fill[kit-blue!60]
($(path picture bounding box.south west)+(0,0)$) --
($(path picture bounding box.north west)+(0,0)$) --
($(path picture bounding box.north west)+(0.34,0)$) -- cycle;
($(path picture bounding box.north
west)+(0.34,0)$) -- cycle;
\fill[kit-orange!60]
($(path picture bounding box.north east)+(0,0)$) --
($(path picture bounding box.south east)+(0,0)$) --
($(path picture bounding box.south east)+(-0.34,0)$) -- cycle;
($(path picture bounding box.south
east)+(-0.34,0)$) -- cycle;
\fill[kit-red!60]
($(path picture bounding box.north east)+(0,0)$) --
($(path picture bounding box.south east)+(-0.34,0)$) --
($(path picture bounding box.south
east)+(-0.34,0)$) --
($(path picture bounding box.south west)+(0,0)$) --
($(path picture bounding box.north west)+(0.34,0)$) -- cycle;
($(path picture bounding box.north
west)+(0.34,0)$) -- cycle;
}
}]{\phantom{1}}}
@@ -1394,23 +1411,41 @@
% - Babar et al. use the SPA
% - A lot of publications use Roffe's ldpc package -> min-sum
\vspace*{-10mm}
\begin{itemize}
\item A \ac{dem} combines a detector error matrix and a noise model
\item When employing \ac{bp}, the syndrome-based variant must
be used \citereference{babar_fifteen_2015}
\item The likelihoods of different error locations can be
used as priors for decoding
\vspace*{5mm}
\item Challenges
\begin{itemize}
\item Repeated syndrome measurements come with
increased decoding complexity
\citereference{gong_toward_2024}
\item Degeneracy and short cycles lead to degraded
performance of \ac{bp} \citereference{babar_fifteen_2015}
\end{itemize}
\item A \schlagwort{\acl{dem}} (DEM) combines a detector error
matrix and a noise model
\visible<2->{
\item Tanner graph of detector error matrix of \ac{bb} code
\citereference{koutsioumpas_automorphism_2025}
}
\end{itemize}
\vspace*{5mm}
\visible<2->{
\begin{figure}[H]
\centering
\includegraphics[scale=5,angle=90]{res/stergios_tanner_graph}
\end{figure}
}
\visible<3->{
\begin{itemize}
\item Challenges
\begin{itemize}
\item Repeated syndrome measurements lead to
increased decoding complexity
\citereference{gong_toward_2024}
\item Degeneracy and short cycles lead to degraded
performance of \ac{bp}
\citereference{babar_fifteen_2015}
\end{itemize}
\end{itemize}
}
\vspace*{20mm}
\addreferences
@@ -1481,6 +1516,8 @@
\ac{bp} with guided decimation
\end{itemize}
\vspace*{5mm}
\begin{figure}
\begin{subfigure}[b]{0.5\textwidth}
\newcommand{\pz}{\phantom{\bm{0}}}
@@ -1559,8 +1596,6 @@
\end{subfigure}%
\end{figure}
\vspace*{3mm}
\visible<2->{
\begin{itemize}
\item However, no passing of soft information between windows

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