Add previous work slide; Add sliding window decoding slide

src/midterm_presentation/main.tex

@@ -24,7 +24,7 @@
 
 \usepackage{tikz}
 \usepackage{tikz-3dplot}
-\usetikzlibrary{spy, external, intersections, positioning}
+\usetikzlibrary{spy, external, intersections, positioning, tikzmark}
 
 % \ifdefined\ishandout\else
 \tikzexternalize
@@ -47,8 +47,8 @@
 \usepackage{amssymb}
 \usepackage{acro}
 \usepackage{braket}
-% \usepackage{qcircuit}
 \usepackage{quantikz}
+\usepackage{nicematrix}
 
 \title{Fault Tolerant Quantum Error Correction}
 \subtitle{Master's Thesis Midterm Presentation}
@@ -103,6 +103,21 @@
     long=belief propagation
 }
 
+\DeclareAcronym{osd}{
+    short=OSD,
+    long=ordered statistics decoding,
+}
+
+\DeclareAcronym{qldpc}{
+    short=QLDPC,
+    long=quantum low density parity check,
+}
+
+\DeclareAcronym{scldpc}{
+    short=SC-LDPC,
+    long=spatially coupled low density parity check
+}
+
 %
 %
 % Document body
@@ -376,8 +391,8 @@
     \begin{itemize}
         \item We entangle the state with \emph{ancilla qubits} to
             perform syndrome measurements \citereference{nielsen_quantum_2010}
-        \item \red{Do I need to show what the syndrome extraction
+            % \item \red{Do I need to show what the syndrome extraction
-            circuitry for Z errors looks like?}
+            %     circuitry for Z errors looks like?}
         \item Example: The 3-qubit repetition code%
             \footnote {
                 Note that, for simplicity, this chosen example is a
@@ -436,7 +451,7 @@
 \begin{frame}
     \frametitle{Fault Tolerance}
 
-    \vspace*{-15mm}
+    \vspace*{-18mm}
 
     \begin{itemize}
         \item The quantum gates we use for syndrome extraction are
@@ -448,7 +463,7 @@
             \citereference{derks_designing_2025}
     \end{itemize}
 
-    \vspace*{3mm}
+    % \vspace*{3mm}
 
     \begin{figure}[H]
         \centering
@@ -472,9 +487,12 @@
             \node[above] at (internal.north) {\small QEC};
             \node[above] at (output.north) {\small Output State};
         \end{tikzpicture}
+
+        \caption{Overview of the flow of errors in a \ac{qec} system.
+        Adapted from \citereference{derks_designing_2025}.}
     \end{figure}
 
-    \vspace*{3mm}
+    % \vspace*{3mm}
 
     \begin{itemize}
         \item We have to modify the syndrome extraction circuitry to
@@ -484,7 +502,7 @@
         \item We generally perform multiple rounds of syndrome extraction
     \end{itemize}
 
-    \vspace*{10mm}
+    \vspace*{8mm}
 
     \addreferences
     {shor_fault-tolerant_1997}
@@ -971,8 +989,9 @@
     \vspace*{-17mm}
 
     \begin{itemize}
-        \item Visualization of general process \red{Deal with 3-qubit
+        \item Visualization of general process
-            state (somehow represent arbitrary qubit state)}
+            % \red{Deal with 3-qubit state (somehow represent arbitrary
+            % qubit state)}
     \end{itemize}
 
     \vspace*{5mm}
@@ -1092,7 +1111,7 @@
             % tex-fmt: on
 
             \caption{Circuit-level noise model for the 3-qubit
-            repetition code (for X errors)}
+            repetition code (for X errors).}
         \end{figure}
     \end{minipage}
 
@@ -1107,8 +1126,15 @@
 \begin{frame}
     \frametitle{Decoding using Detector Error Models}
 
+    % Related interesting stuff
+    % - Roffe et al. use the min-sum variant of BP.
+    % - Babar et al. use the SPA
+    % - A lot of publications use Roffe's ldpc package -> min-sum
+
     \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}
@@ -1138,28 +1164,150 @@
 \subsection{State of the Art}
 \label{subsec:State of the Art}
 
+% TODO: Mention somewhere that we are particularly interested in QLDPC codes
 \begin{frame}
-    \frametitle{Sliding Window Decoding}
+    \frametitle{Addressing the Challenges}
+
+    \vspace*{-18mm}
 
     \begin{itemize}
-            % TODO: Do I have to explain BP?
+        \item Many window-based approaches exist to combat the
-        \item \red{Do I have to explain BP}
+            decoding complexity
-        \item Give overview of existing research
+            \begin{itemize}
-        \item Explain exactly what they do in the main paper I am
+                \item Parallel decoding of syndromes
-            basing my work on
+                    \citereference{skoric_parallel_2023}
-        \item \red{$\rightarrow$ We generally don't use "normal BP"
+                \item Using sliding windows
-            (BP + OSD, BPGD, etc.)}
+                    \citereference{huang_improved_2023}
+                    \citereference{gong_toward_2024}
             \end{itemize}
+        \item To deal with the degraded \ac{bp} performance, it is
+            usually modified or extended
+            \begin{itemize}
+                \item \Ac{osd} post-processing
+                    \citereference{roffe_decoding_2020}
+                \item Guided decimation \citereference{gong_toward_2024}
+                \item Neural approaches
+                    \citereference{kuo_exploiting_2022}
+                    \citereference{miao_quaternary_2025}
+                \item Ensemble decoding
+                    \citereference{koutsioumpas_automorphism_2025}
+            \end{itemize}
+    \end{itemize}
+
+    \vspace*{5mm}
+
+    \addreferences
+    {roffe_decoding_2020}
+    {kuo_exploiting_2022}
+    {huang_improved_2023}
+    {skoric_parallel_2023}
+    {gong_toward_2024}
+    {miao_quaternary_2025}
+    {koutsioumpas_automorphism_2025}
+    \stopreferences
 \end{frame}
 
-\begin{frame}
+\begin{frame}[fragile]
-    \frametitle{Guided Decimation Guessing Decoding}
+    \frametitle{Sliding-Window Decoding}
+
+    \vspace*{-18mm}
 
     \begin{itemize}
-        \item Update equations
+        \item The sliding window approach taken in
-        \item Key ideas
+            \citereference{gong_toward_2024} resembles a \ac{scldpc}
-        \item Syndrome Based BP
+            code decoder
+        \item However, they don't pass soft information between
+            windows (only update of syndrome based on hard decision
+            in previous window)
     \end{itemize}
+
+    \vspace*{-10mm}
+
+    \begin{figure}
+        \begin{subfigure}[b]{0.5\textwidth}
+            \begin{gather*}
+                \begin{pmatrix}
+                    \bm{H}_0 & \bm{H}_1 & \bm{0}   & \bm{0}   \\
+                    \bm{0}   & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 \\
+                    \bm{0}   & \bm{0}   & \bm{0}   & \bm{H}_2
+                \end{pmatrix}
+                \begin{pmatrix}
+                    \hat{\bm{e}}_0 \\
+                    \hat{\bm{e}}_1 \\
+                    \vdots
+                \end{pmatrix}
+                =
+                \begin{pmatrix}
+                    \bm{s}_1 \\
+                    \bm{s}_2 \\
+                    \bm{s}_3
+                \end{pmatrix} \\[5mm]
+                \bm{s}_2' = \bm{s}_2 + \bm{H}_2 \hat{\bm{e}}_1
+            \end{gather*}
+
+            \vspace*{5mm}
+
+            \caption{Equations for the decoding of the first window}
+        \end{subfigure}%
+        \begin{subfigure}[b]{0.5\textwidth}
+            \[
+                \left(
+                    \begin{tikzpicture}[baseline=(m.center)]
+                        \matrix (m)[
+                            matrix of math nodes,
+                            nodes in empty cells,
+                            column sep={14mm,between origins},
+                            row sep={10mm,between origins},
+                        ] {
+                            % tex-fmt: off
+                            \bm{H}_0 & \bm{H}_1         & \bm{0}   & \bm{0}    & \bm{0}   & \bm{0}   & \cdots   &                  &        \\
+                            \bm{0}   & \bm{H}_2         & \bm{H}_0 & \bm{H}_1  & \bm{0}   & \bm{0}   &          &                  &        \\
+                            \bm{0}   & \bm{0}           & \bm{0}   & \bm{H}_2  & \bm{H}_0 & \bm{H}_1 &          & \phantom{\bm{0}} &        \\
+                            \bm{0}   & \bm{0}           & \bm{0}   & \bm{0}    & \bm{0}   & \bm{H}_2 & \bm{H}_0 & \bm{H}_1         &        \\
+                            \bm{0}   & \bm{0}           & \bm{0}   & \bm{0}    & \bm{0}   & \bm{0}   & \bm{0}   & \bm{H}_2         &        \\
+                            \vdots   & \phantom{\bm{0}} &          &           &          &          &          &                  & \ddots \\
+                            % tex-fmt: on
+                        } ;
+
+                        \draw[kit-red, line width=2pt]
+                        ($(m-3-1.south west) + (-0.1,-0.1)$)
+                        rectangle
+                        ($(m-1-4.north east) + (0.1,0.1)$);
+
+                        \draw[kit-orange, line width=2pt]
+                        ($(m-4-3.south west) + (-0.1,-0.1)$)
+                        rectangle
+                        ($(m-2-6.north east) + (0.1,0.1)$);
+
+                        \draw[kit-blue, line width=2pt]
+                        ($(m-5-5.south west) + (-0.1,-0.1)$)
+                        rectangle
+                        ($(m-3-8.north east) + (0.1,0.1)$);
+
+                        \draw[-{Latex},line width=2pt]
+                        ($(m-1-5.north) + (0,0.8)$)
+                        --
+                        ($(m-2-8.north) + (0,0.8)$);
+                    \end{tikzpicture}
+                \right)
+            \]
+
+            \caption{Visualization of sliding window procedure}
+        \end{subfigure}%
+    \end{figure}
+
+    \vspace*{-5mm}
+
+    \begin{itemize}
+        \item They try \ac{bp} + \ac{osd} and a modification of
+            \ac{bp} with guided decimation
+    \end{itemize}
+
+    \vspace*{4mm}
+
+    \addreferences
+    {gong_toward_2024}
+    \stopreferences
 \end{frame}
 
 \begin{frame}