diff --git a/src/qec-meeting-presentation/main.tex b/src/qec-meeting-presentation/main.tex index f5acdca..1fa3ceb 100644 --- a/src/qec-meeting-presentation/main.tex +++ b/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}