Make current thesis text use CEL template
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@@ -51,7 +51,7 @@ $\bm{u} \in \mathbb{F}_2^k$ of length $k \in \mathbb{N}$ (called the
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A measure of the amount of introduced redundancy is the \textit{code
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rate} $R = k/n$.
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We call the set of all codewords $\mathcal{C}$ the \textit{code}
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\cite[Section 3.1]{ryan_channel_2009}.
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\cite[Sec. 3.1]{ryan_channel_2009}.
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%
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% d_min and the [] Notation
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@@ -73,7 +73,7 @@ We define the \textit{minimum distance} of a code $\mathcal{C}$ as
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\end{align*}
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We can signify that a binary linear block code has information length
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$k$, block length $n$ and minimum distance $d_\text{min}$ using the
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notation $[n,k,d_\text{dmin}]$ \cite[Section 1.3]{macwilliams_theory_1977}.
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notation $[n,k,d_\text{dmin}]$ \cite[Sec. 1.3]{macwilliams_theory_1977}.
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%
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% Parity checks, H, and the syndrome
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@@ -88,9 +88,9 @@ additional degrees of freedom.
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These conditions, called parity checks, take the form of equations
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over $\mathbb{F}_2^n$, linking the individual positions of each codeword.
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We can arrange the coefficients of these equations in the
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\textit{parity check matrix} (\acs{pcm}) $\bm{H} \in
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\textit{parity-check matrix} (\acs{pcm}) $\bm{H} \in
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\mathbb{F}_2^{(n-k) \times n}$ and equivalently define the code as
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\cite[Section 3.1]{ryan_channel_2009}
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\cite[Sec. 3.1]{ryan_channel_2009}
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\begin{align*}
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\mathcal{C} = \left\{ \bm{x} \in \mathbb{F}_2^n :
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\bm{H}\bm{x}^\text{T} = \bm{0} \right\}
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@@ -107,7 +107,7 @@ exponentially with $n$, in contrast to keeping track of all codewords directly.
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%
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Figure \ref{fig:Diagram of a transmission system} visualizes the
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entire communication process \cite[Section 1.1]{ryan_channel_2009}.
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entire communication process \cite[Sec. 1.1]{ryan_channel_2009}.
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An input message $\bm{u}\in \mathbb{F}_2^k$ is mapped onto a codeword $\bm{x}
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\in \mathbb{F}_2^n$. This is passed on to a modulator, which
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interacts with the physical channel.
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@@ -120,7 +120,7 @@ This is done by first finding an estimate $\hat{\bm{x}}$ of the sent
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codeword and undoing the encoding.
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The decoding problem that we generally attempt to solve thus consists
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in finding the best estimate $\hat{\bm{x}}$ given $\bm{y}$.
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One approach is to use the \ac{ml} criterion \cite[Section
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One approach is to use the \ac{ml} criterion \cite[Sec.
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1.4]{ryan_channel_2009}
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\begin{align*}
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\hat{\bm{u}}_\text{ML} = \arg\max_{\bm{x} \in \mathcal{C}}
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@@ -129,7 +129,7 @@ One approach is to use the \ac{ml} criterion \cite[Section
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\end{align*}
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Finally, we differentiate between \textit{soft decision} decoding, where
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$\bm{y} \in \mathbb{R}^n$ and \textit{hard decision} decoding, where
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$\bm{y} \in \mathbb{F}_2^n$ \cite[Section 1.5.1.3]{ryan_channel_2009}.
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$\bm{y} \in \mathbb{F}_2^n$ \cite[Sec. 1.5.1.3]{ryan_channel_2009}.
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%
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\begin{figure}[h]
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\centering
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@@ -1,4 +1,4 @@
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\documentclass[dvipsnames]{report}
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\documentclass{lib/cel-thesis/cel-thesis}
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\usepackage[a4paper,left=3cm,right=3cm,top=2.5cm,bottom=2.5cm]{geometry}
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\usepackage{float}
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@@ -12,11 +12,11 @@
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\pgfplotsset{compat=newest}
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\usepackage{acro}
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\usepackage{braket}
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\usepackage[
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backend=biber,
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style=ieee,
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sorting=nty,
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]{biblatex}
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% \usepackage[
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% backend=biber,
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% style=ieee,
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% sorting=nty,
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% ]{biblatex}
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\usepackage{todonotes}
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\usetikzlibrary{calc, positioning, arrows}
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@@ -36,7 +36,16 @@
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%
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\input{acronyms.tex}
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\addbibresource{src/thesis/MA.bib}
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\usepackage{babelbib}
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\setlanguage
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\usepackage{caption}
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\usepackage{bm}
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\usepackage{subcaption}
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\usepackage{todonotes} % great for draft annotations
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\DeclareCaptionLabelFormat{bf-nodot}{\textbf{#1}~\textbf{#2}}
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\captionsetup{labelformat=bf-nodot,labelsep=colon}
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%
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%
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@@ -44,23 +53,46 @@
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%
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%
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\title{Fault Tolerant Quantum Error Correction}
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% \subtitle{Master's Thesis}
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\author{Andreas Tsouchlos}
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\thesisTitle{Fault Tolerant Quantum Error Correction}
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\thesisType{Master's Thesis}
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\thesisAuthor{Andreas Tsouchlos}
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\thesisAdvisor{Prof. Dr.-Ing. Laurent Schmalen}
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\thesisHeadOfInstitute{Prof. Dr.-Ing. Laurent Schmalen}
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% \thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost}
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%\thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost\\Prof. Dr.-Ing.
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% Laurent Schmalen}
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\thesisSupervisor{Jonathan Mandelbaum}
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\thesisStartDate{01.11.2025}
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\thesisEndDate{04.05.2026}
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\thesisSignatureDate{Signature date}
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\thesisLanguage{english}
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\begin{document}
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\pagenumbering{roman} % all the preliminaries should be counted roman style
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\maketitle
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\tableofcontents
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\newpage
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% \include{chapters/abstract}
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\cleardoublepage
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\pagenumbering{arabic}
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\tableofcontents
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\cleardoublepage
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\input{chapters/1_introduction.tex}
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\input{chapters/2_fundamentals.tex}
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\input{chapters/3_fault_tolerant_qec.tex}
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\input{chapters/4_decoding_under_dems.tex}
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\input{chapters/5_conclusion_and_outlook.tex}
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\printbibliography
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% \appendix
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% \listoffigures
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% \listoftables
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% \include{abbreviations}
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\bibliography{lib/cel-thesis/IEEEabrv,bibliography}
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\end{document}
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