Add outline and main content points for QEC Meeting presentation

src/qec-meeting-presentation/main.tex

@@ -6,9 +6,11 @@
 \usepackage[minted, most]{tcolorbox}
 \usepackage{amsmath}
 \usepackage{bm}
+\usepackage[dvipsnames]{xcolor}
 \usepackage{siunitx}
 \usepackage{graphics}
 \usepackage{xfp}
+\usepackage{quantikz}
 
 \usepackage[T1]{fontenc}
 \usepackage[scaled=.92]{helvet}
@@ -126,12 +128,107 @@ decorations.pathreplacing, calc}
 \section{Motivation and Core Idea}
 \label{sec:Motivation and Core Idea}
 
+\newsavebox{\innercircuit}
 \begin{frame}
-    \frametitle{Syndrome Extraction Circuits for Fault-Tolerant QEC}
+    \frametitle{Sliding-Window Decoding for Fault-Tolerant QEC}
+
+    % \vspace*{-5mm}
+
+    \begin{figure}
+        \scalebox{0.8}{
+            \savebox{\innercircuit}{
+                \begin{tikzpicture}[
+                        block/.style={draw, rectangle, minimum
+                            height=1cm, minimum width=1.2cm, align=center,
+                        fill=white, font=\small},
+                        container/.style={draw, thick, inner sep=0.6cm}
+                    ]
+                    % Internal blocks
+                    \node (se1) [block]
+                    {$\text{SE}_1$ \\ + noise};
+                    \node (se2) [block, right=0.5cm of se1]
+                    {$\text{SE}_2$ \\ + noise};
+                    \node (dots) [right=0.3cm of se2] {\dots};
+
+                    % Wires
+                    \draw (se1.west) -- ++(-0.4,0);
+                    \draw (se1.east) -- (se2.west);
+                    \draw (se2.east) -- (dots.west);
+                    \draw (dots.east) -- ++(0.4,0);
+
+                    % The "Circuit" container
+                    \node (box) [
+                        container, fit=(se1) (se2) (dots),
+                        label={[anchor=north west, xshift=2pt]
+                        north west:Complete circuit}
+                    ] {};
+                \end{tikzpicture}
+            }
+
+            \begin{tikzpicture}[
+                    every edge/.style = {draw, -{latex}}
+                ]
+                \node (pcm) {Code~/~$\bm{H}_\text{PCM}$};
+
+                \node[
+                    rectangle,
+                    draw=black,
+                    minimum width=2cm, minimum height=1cm,
+                    right=of pcm,
+                    align=center
+                ] (sec) {Single\\ SE Circ.};
+
+                \node[right=of sec] (qc) {\usebox{\innercircuit}};
+
+                \node[right=of qc] (dem) {$\bm{H}_\text{DEM}$};
+
+                \draw (pcm.east) edge[bend left] (sec.west);
+                \draw (sec.east) edge[bend left] ($(qc.west) + (0.22,0)$);
+                \draw ($(qc.east) + (-0.22,0)$) edge[bend left]
+                node[midway, above] {Stim} (dem.west);
+            \end{tikzpicture}
+        }
+    \end{figure}
+
+    \only<1>{
+        \begin{figure}[H]
+            \centering
+            \includegraphics[scale=0.55]{./res/pcm.png}
+        \end{figure}
+    }
+    \only<2->{
+        \begin{figure}[H]
+            \centering
+            \includegraphics[scale=0.55]{./res/windowing.png}
+        \end{figure}
+    }
+
+    \vspace*{-5mm}
+
+    \visible<2->{
+        \begin{align*}
+            \colorbox{red!20}{$\bm{H}_1 \bm{e}_1 = \bm{s}_1$}
+            \hspace{2mm}\rightarrow\hspace{2mm} \hat{\bm{e_1}} = \cdots
+            \hspace{2mm}\rightarrow\hspace{2mm} \bm{s}_2' = \cdots \\
+            \colorbox{ForestGreen!20}{$\bm{H}_2 \bm{e}_2 = \bm{s}_2'$}
+            \hspace{2mm}\rightarrow\hspace{2mm} \hat{\bm{e_2}} = \cdots
+            \hspace{2mm}\rightarrow\hspace{2mm} \bm{s}_3' = \cdots \\
+            \colorbox{blue!20}{$\bm{H}_3 \bm{e}_3 = \bm{s}_3'$}
+            \hspace{2mm}\rightarrow\hspace{2mm} \hat{\bm{e_3}} = \cdots
+            \hspace{2mm}\rightarrow\hspace{2mm} \bm{s}_4' = \cdots
+            % &\hspace{2.25mm}\vdots
+        \end{align*}
+    }
 \end{frame}
 
 \begin{frame}
-    \frametitle{Windowed Decoding}
+    \frametitle{Similarities to Spatially-Coupled LDPC Codes}
+
+    \begin{figure}[H]
+        \centering
+        \includegraphics[scale=0.1]{./res/sc-tanner-graph.png}
+        \includegraphics[scale=0.1]{./res/sc-pcm.png}
+    \end{figure}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -140,14 +237,29 @@ decorations.pathreplacing, calc}
 
 \begin{frame}
     \frametitle{An ``Upper Bound'' on the Performance}
+
+    \begin{itemize}
+        \item \red{Whole vs windowed for min sum and spa, different
+            window sizes }
+    \end{itemize}
 \end{frame}
 
 \begin{frame}
     \frametitle{Soft- vs. Hard-Information Decoding Behavior I}
+
+    \begin{itemize}
+        \item \red{Soft vs hard for min sum and spa (4 plots)}
+        \item \red{Different window sizes}
+    \end{itemize}
 \end{frame}
 
 \begin{frame}
     \frametitle{Soft- vs. Hard-Information Decoding Behavior II}
+
+    \begin{itemize}
+        \item \red{Comparison of numbers of iterations for soft vs hard}
+        \item \red{Convergence analysis}
+    \end{itemize}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -156,10 +268,23 @@ decorations.pathreplacing, calc}
 
 \begin{frame}
     \frametitle{Future Work}
-\end{frame}
 
-\begin{frame}
-    \frametitle{Questions}
+    \vspace*{15mm}
+
+    \begin{itemize}
+        \item Deeper investigation into difference between hard- and
+            soft-info decoding for BP
+        \item Move from BP to BPGD
+        \item Spend much more effort to decode first window (inspired
+            by rate-loss of SC-LDPC codes in first window)
+
+            \vspace{15mm}
+
+        \item Q: Theoretically rigorous proof for the
+            ``window-friendly'' structure of the detector error matrix?
+        \item Q: Min-sum seems to perform better than SPA? \red{Make
+            sure this question even makes sense}
+    \end{itemize}
 \end{frame}
 
 \end{document}