Add midterm presentation motivation and backup slide

.gitmodules

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+[submodule "lib/cel-slides-template-2025"]
+	path = lib/cel-slides-template-2025
+	url = git@gitlab.kit.edu:kit/cel/misc/cel-slides-template-2025.git

lib/cel-slides-template-2025

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+Subproject commit 3e5094ffdc60e1a0550f7c42be8a720b5e9eb6c5

src/midterm_presentation/main.tex

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+\documentclass[overviewatsection, showsubsectionsatfirstoverview]{CELbeamer}
+
+%
+%
+% CEL Template
+%
+%
+
+\newcommand{\templates}{preambles}
+\input{\templates/packages.tex}
+\input{\templates/macros.tex}
+
+\grouplogo{CEL_logo.pdf}
+
+\groupname{Communications Engineering Lab (CEL)}
+
+\fundinglogos{}
+
+%
+%
+% Document setup
+%
+%
+
+\usepackage{tikz}
+\usepackage{tikz-3dplot}
+\usetikzlibrary{spy, external, intersections, positioning}
+
+% \ifdefined\ishandout\else
+% \tikzexternalize
+% \fi
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=newest}
+\usepgfplotslibrary{fillbetween}
+\usepgfplotslibrary{groupplots}
+
+\usepackage{enumerate}
+\usepackage{listings}
+\usepackage{subcaption}
+\usepackage{bbm}
+\usepackage{multirow}
+\usepackage{xcolor}
+\usepackage{amsmath}
+\usepackage{graphicx}
+\usepackage{calc}
+\usepackage{amssymb}
+\usepackage{acro}
+\usepackage{braket}
+
+\title{Fault Tolerant Quantum Error Correction}
+\subtitle{Master's Thesis Midterm Presentation}
+\author[Tsouchlos]{Andreas Tsouchlos}
+\date[]{February 5th, 2026}
+
+\DeclareFieldFormat{note}{}
+\DeclareFieldFormat{issn}{}
+\DeclareFieldFormat{url}{}
+\DeclareFieldFormat{doi}{}
+\DeclareFieldFormat[article,book,inproceedings]{urldate}{}
+
+\addbibresource{MA.bib}
+
+%
+%
+% Custom commands
+%
+%
+
+\newcommand{\res}{src/midterm_presentation/res}
+
+%
+%
+% Acronyms
+%
+%
+
+\DeclareAcronym{qec}{
+    short=QEC,
+    long=quantum error correction
+}
+
+%
+%
+% Document body
+%
+%
+
+\begin{document}
+
+\begin{frame}[title white vertical, picture=images/IMG_7801-cut]
+    \titlepage
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Introduction to Quantum Error Correction}
+\label{sec:Introduction to Quantum Error Correction}
+
+%%%%%%%%%%%%%%%%
+\subsection{Motivation}
+\label{subsec:Motivation}
+
+\begin{frame}
+    \frametitle{Quantum Computing}
+
+    % Related interesting stuff
+    % - Gidney estimates we need 1399 (?) logical qubits to factor a 2048
+    %   bit RSA integer
+    % - He goes on to estimate that to factor such an integer in less
+    %   than a week would require around a million physical qubits
+    %   [How to factor 2048 bit RSA integers with less than a million
+    %   noisy qubits]
+
+    \vspace*{-19mm}
+
+    \begin{itemize}
+        \item Simulating quantum systems on classical hardware
+            is exponentially complex \\
+            $\rightarrow$ Can't we use quantum hardware to simulate
+            quantum systems? \citereference{feynman_simulating_1982}
+        \item Some problems that are ``hard'' to solve on classical
+            computers we can ``easily'' solve on quantum computers
+            \citereference{preskill_quantum_2018}
+        \item We are still in the early days of quantum computing
+    \end{itemize}
+
+    \vspace*{-5mm}
+
+    \begin{figure}[H]
+        \centering
+
+        \includegraphics[scale=0.43]{res/google_roadmap.png}
+
+        \vspace*{-3mm}
+        \caption{
+            Google Quantum AI's quantum computing roadmap
+            \citereference{google_quantum_ai_quantum_nodate}.
+        }
+    \end{figure}
+
+    \addreferences
+    {feynman_simulating_1982}
+    {preskill_quantum_2018}
+    {google_quantum_ai_quantum_nodate}
+    \stopreferences
+\end{frame}
+
+% TODO: Where should I quote Preskill? There are multiple bullet
+% points with info taken from his work
+\begin{frame}
+    \frametitle{The Need for Quantum Error Correction}
+
+    \vspace*{-10mm}
+
+    % Related interesting stuff
+    % - Qubits differ from bits in that they can be in superpositions
+    %   and be entangled with one another
+    % - Quantum computers derive their strenght from the exponential
+    %   scaling of the state-space because of the way the information is
+    %   encoded
+    % - Note that while a physical error rate of 10^{-3} may seem ok,
+    %   we need a couple trillion operations (~ 10^{13}) to factor a
+    %   2048 bit RSA integer
+    %   [How to factor 2048 bit RSA integers with less than a million
+    %   noisy qubits]
+    % - The backlog problem is the fact that an increasing backlog of
+    %   syndrome data will lead to an exponential slowdown during the
+    %   computation
+
+    \begin{itemize}
+        \item Quantum computers represent information through
+            correlations of qubits, not their values \\
+            directly \citereference{preskill_quantum_2018}
+        \item We want to not disturb the quantum state but need to
+            interact with the system \\
+            $\rightarrow$ Protect the state with \ac{qec}
+        \item We employ more physical qubits to introduce
+            redundancy and use the resulting \emph{physical} state to
+            represent the \emph{logical} state
+            \citereference{roffe_quantum_2019}
+        \item IBM recently introduced a scheme encoding 12 logical
+            qubits in 288 physical ones
+            \citereference{bravyi_high-threshold_2024}
+        \item The physical error rate is typically assumed to be $10^{-3}$ for
+            simulations (e.g., \citereference{bravyi_high-threshold_2024})
+        \item Decoding has to happen with ultra-low latency to avoid
+            the backlog problem (about $\SI{1}{us}$ per data
+            extraction round) \citereference{caune_demonstrating_2024}
+            % \citereference{terhal_quantum_2015}
+    \end{itemize}
+
+    \vspace*{12mm}
+
+    \addreferences
+    % {terhal_quantum_2015}
+    {caune_demonstrating_2024}
+    {preskill_quantum_2018}
+    {roffe_quantum_2019}
+    {bravyi_high-threshold_2024}
+    \stopreferences
+\end{frame}
+
+%%%%%%%%%%%%%%%%
+\subsection{Fundamentals of Quantum Error Correction}
+\label{subsec:Fundamentals of Quantum Error Correction}
+
+% TODO: Is this all of this really necessary?
+\begin{frame}
+    \frametitle{Peculiarities of the Quantum Setting}
+
+    % Related interesting stuff
+    % - No cloning theorem -> Not replication of state, protection
+    %   through further entanglement
+    % - States are superpositions -> We theoretically need to be able
+    %   to correct infinitely many different types of errors. Luckily,
+    %   it turns out that in actual fact we only really need to correct
+    %   two [Gottesman's Thesis]
+
+    \begin{itemize}
+        \item Measuring the system collapses the quantum state
+            $\rightarrow$ Loss of benefit of quantum system \\
+            $\rightarrow$ For BP, we work with the syndrome and not
+            the variable nodes \textcolor{red}{This can't be here,
+            it's before introducing how QEC works}
+        \item X and Z errors
+        \item With QEC we are able to restore the quantum state, not
+            "just the bits"
+        \item We don't care about the specific error, only the coset
+            its in $\rightarrow$ We only really care about the syndrome
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Fundamentals of Quantum Error Correction}
+
+    \begin{itemize}
+        \item Stabilizer codes: the quantum equivalent of binary linear codes
+        \item CSS codes: separate corection of X and Z errors
+            $\rightarrow$ simpler circuitry
+        \item Construction of CSS codes from binary linear codes
+            \textcolor{red}{Is this really necessary?}
+    \end{itemize}
+\end{frame}
+
+% TODO: Is this really necessary?
+\begin{frame}
+    \frametitle{The Quantum Error Correction Landscape}
+
+    \begin{itemize}
+        \item Give basic overview of most promising avenues of
+            research (as in ECCentric paper)
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{An Example: The Steane Code}
+
+    \begin{itemize}
+        \item \textcolor{red}{Give example slides grey background or something?}
+        \item The Steane code is the quantum equivalent of the
+            [7,4]-Hamming code
+        \item Construction from Hamming code
+        \item Syndrome Extraction Circuitry
+    \end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Fault Tolerance and Detector Error Models}
+\label{sec:Fault Tolerance and Detector Error Models}
+
+%%%%%%%%%%%%%%%%
+\subsection{Fault Tolerance}
+\label{subsec:Fault Tolerance}
+
+\begin{frame}
+    \frametitle{Fault Tolerance}
+
+    \begin{itemize}
+        \item Quantum gates are faulty $\rightarrow$ we need QEC \\
+            But we do QEC with faulty gates $\rightarrow$ we need
+            fault tolerant QEC %
+            \footnote{
+                Designing fault-tolerant circuits using detector
+                error models - Gong et al, Section 4.1
+            }
+        \item We generally do multiple rounds of syndrome extraction
+        \item The Threshold theorem
+            \setcounter{footnote}{0}
+        \item Definition of fault tolerance \footnotemark
+        \item \textcolor{red}{Different approaches to fault tolerance?}
+    \end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%
+\subsection{Detector Error Models}
+\label{subsec:Detector Error Models}
+
+\begin{frame}
+    \frametitle{Detector Error Models}
+
+    \begin{itemize}
+        \item Idea: Go "one layer of abstraction higher" \\
+            $\rightarrow$ Redefine syndrome and create new PC matrix from that
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{An Example: Steane Code Detector Error Model}
+
+    \begin{itemize}
+        \item New Syndrome Extraction Circuitry \textcolor{red}{Is a
+            repetition of the old circuitry needed?}
+        \item New parity check matrix
+        \item Highlighting of the SC-LDPC-code-like structure
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Challenges}
+
+    \begin{itemize}
+        \item Multiple different errors are summarized $\rightarrow$
+            short cycles \& degeneracy
+            \footnote{
+                \texttt{
+                    https://www.math.cit.tum.de/fileadmin/w00ccg/math/\_my\_direct\_uploads/Dan\_Browne.pdf
+                }
+            }
+            \\
+            $\rightarrow$ We generally don't use "normal BP" (BP +
+            OSD, BPGD, etc.)
+    \end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{State of the Art and Research Gap}
+\label{sec:State of the Art and Research Gap}
+
+%%%%%%%%%%%%%%%%
+\subsection{State of the Art}
+\label{subsec:State of the Art}
+
+\begin{frame}
+    \frametitle{Sliding Window Decoding}
+
+    \begin{itemize}
+        \item Give overview of existing research
+        \item Explain exactly what they do in the main paper I am
+            basing my work on
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Guided Decimation Guessing Decoding}
+
+    \begin{itemize}
+        \item Update equations
+        \item Key ideas
+        \item Syndrome Based BP
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Memory experiments}
+
+    \begin{itemize}
+        \item What is a memory experiment?
+        \item Communications Engineering view (what are my inputs and
+            outpus? What do I expect?)
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Systemic overview}
+
+    \begin{itemize}
+        \item Top level overview of entire system: X and Z syndrome
+            extraction, logical operator measurement, where decoding
+            takes place, etc.
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Research Gap}
+
+    \begin{itemize}
+        \item Use soft information for sliding window decoding
+            $\rightarrow$ Treat as spacially coupled LDPC code
+        \item Current work considers X and Z errors separately
+            (probably for latency reasons) $\rightarrow$ See how
+            decoding the jointly works out
+    \end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%
+\subsection{What we simulate}
+\label{subsec:What we simulate}
+
+\begin{frame}
+    \frametitle{The lack of a Standard Evaluation System}
+
+    \begin{itemize}
+        \item \textcolor{red}{Look into ECCentric}
+        \item There is not even a standard figure of merit (e.g.,
+            FER/BER over SNR in classical case) $\rightarrow$
+            Multiple different kinds of plots (e.g., footprint)
+        \item Overview of variables
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Proposed Evaluation Pipeline}
+
+    \begin{itemize}
+        \item To what values I will fix the parameters and why
+        \item What figure of merit I will use and why
+    \end{itemize}
+\end{frame}
+
+\appendix
+\beginbackup
+
+\begin{frame}
+    \frametitle{System Level Overview}
+
+    \vspace*{-15mm}
+
+    \begin{figure}[H]
+        \centering
+        \begin{subfigure}[t]{0.5\textwidth}
+            \centering
+
+            \includegraphics[scale=1.1]{res/architecture}
+
+            \vspace*{5mm}
+
+            \caption{Schematic workflow of surface code quantum
+            computation \citereference{zhang_classical_2023}.}
+        \end{subfigure}%
+        \begin{subfigure}[t]{0.5\textwidth}
+            \centering
+
+            \tikzset{
+                block/.style={
+                    draw, rectangle,
+                    fill = kit-blue!25,
+                    minimum width=75mm, minimum height=15mm,
+                }
+            }
+
+            \scalebox{0.7}{
+                \begin{tikzpicture}[node distance=15mm and 20mm]
+                    \node[block] (encoding) {Encoding};
+                    \node[block, below=of encoding] (channel) {Quantum Channel};
+                    \node[block, below=of channel] (reverse-op)
+                    {Reverse Operation};
+
+                    \node[block, right=of channel] (syn-extr)
+                    {Syndrome Extraction};
+                    \node[block, below=of syn-extr] (syn-dec)
+                    {Syndrome Decoder};
+
+                    \node[above=of encoding] (input) {$\ket{\phi}$};
+                    \node[below=of reverse-op] (output)
+                    {$\hat{\mathcal{E}}\mathcal{E}\ket{\psi}$};
+
+                    \draw [-{Latex}] (encoding) -- (channel) node[midway,
+                    right] {$\ket{\psi}$};
+                    \draw [-{Latex}] (channel) -- (reverse-op)
+                    node[midway, right] {$\mathcal{E}\ket{\psi}$};
+                    \draw [-{Latex}] (channel) -- (syn-extr)
+                    node[midway, above] {$\mathcal{E}\ket{\psi}$};
+                    \draw [-{Latex}] (syn-extr) -- (syn-dec)
+                    node[midway, right] {$z$};
+                    \draw [-{Latex}] (syn-dec) -- (reverse-op)
+                    node[midway, above] {$\hat{\mathcal{E}}$};
+
+                    \draw [-{Latex}] (input) -- (encoding);
+                    \draw [-{Latex}] (reverse-op) -- (output);
+                \end{tikzpicture}
+            }
+
+            \vspace*{5mm}
+
+            \caption{Block diagram of QEC using stabilizer codes
+            \citereference{miao_quaternary_2025}.}
+        \end{subfigure}
+    \end{figure}
+
+    % \vspace*{-2mm}
+
+    \addreferences
+    {zhang_classical_2023}
+    {miao_quaternary_2025}
+    \stopreferences
+\end{frame}
+
+\backupend
+
+\end{document}
+