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Make detector XOR graphic red

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Andreas Tsouchlos
2026-02-04 18:20:14 +01:00
parent f3ee9a32df
commit ed3a1f50fd
1 changed files with 137 additions and 134 deletions
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src/midterm_presentation/main.tex
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@@ -49,10 +49,11 @@
\usepackage{braket}
\usepackage{quantikz}
\usepackage{nicematrix}
\usepackage{xpatch}
\title{Fault Tolerant Quantum Error Correction}
\subtitle{Master's Thesis Midterm Presentation}
\author[Tsouchlos]{Andreas Tsouchlos}
\author[Andreas]{Andreas Tsouchlos}
\date[]{}
\DeclareFieldFormat{note}{}
@@ -77,6 +78,14 @@
\newcommand{\Y}{\textcolor{kit-red}{\bm{Y}}}
\newcommand{\I}{\bm{I}}
\xpatchcmd{\fullwire}
{\arrow[arrows,start anchor=#2startone,end anchor=#2endone]
{#1}\arrow[arrows,start anchor=#2starttwo,end anchor=#2endtwo,#4] {#1}}
{\arrow[arrows,start anchor=#2startone,end anchor=#2endone,#4]
{#1}\arrow[arrows,start anchor=#2starttwo,end anchor=#2endtwo,#4] {#1}}
{\typeout{Successfully patched fullwire for classical wires}}
{\typeout{Failed to patch fullwire for classical wires}}
%
%
% Acronyms
@@ -120,7 +129,7 @@
\DeclareAcronym{scldpc}{
short=SC-LDPC,
long=spatially - coupled low - density parity - check
long=spatially-coupled low-density parity-check
}
%
@@ -819,7 +828,7 @@
\hspace*{-75mm}
\scalebox{0.85}{
\parbox{.5\linewidth}{%
\vspace*{22.5mm}
\vspace*{22.6mm}
\begin{gather*}
\bm{\Omega} =
\left(
@@ -1100,34 +1109,46 @@
\end{frame}
% TODO: Journal not showing for derks_designing_2025
\begin{frame}
\begin{frame}[fragile]
\frametitle{The Detector Error Matrix I}
\vspace*{-17mm}
\begin{itemize}
\item A detector is a parity constraint on a set of
measurement outcomes \citereference{derks_designing_2025}
\item Each column of the \schlagwort{detector error matrix} $\bm{H}$
corresponds to a detector pattern an error produces
\item We can mitigate the propagation of errors into
subsequent rounds by XORing the measurements, i.e.,
defining detectors appropriately; this is equivalent to
row additions
\item \schlagwort{Detector error matrix} $\bm{H}$ contains
modified error patterns
\item Repetition of errors mitigated by XORing measurements
\end{itemize}
\begin{minipage}{0.5\textwidth}
\begin{figure}[H]
\newcommand{\redwire}[1]{
\wire[r][#1][style={draw=red, line width=2pt, double}]{q}
}
\newcommand{\inwire}{
\wire[l][1][style={draw=red, line width=2pt}]{q}
}
\newcommand{\redtarg}{
\targ[style={draw=red,line width=2pt}]{}%
\setwiretype{n}%
}
\newcommand{\redctrl}[1]{
\ctrl[style={draw=red,fill=red, line width=2pt}]{0}%
\wire[d][#1][style={draw=red, line width=2pt, double}]{q}
}
\newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}}
\newcommand{\redgate}[1]{\gate[style={draw=red,fill=red!20}]{\textcolor{red}{#1}}}
\centering
% tex-fmt: off
\begin{quantikz}[row sep=4mm, column sep=4mm, wire types={n,n,n,n,n,n}]
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & \ctrl[vertical wire=c]{2} & & \gate{D_1} \\
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & & \ctrl[vertical wire=c]{2} & \gate{D_2} \\
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & \ctrl[vertical wire=c]{2} & & \targ{} & & \gate{D_3} \\
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & \ctrl[vertical wire=c]{2} & & \targ{} & \gate{D_4} \\
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & \targ{} & & & & \gate{D_5} \\
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & \targ{} & & & \gate{D_6}
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & \ctrl[vertical wire=c]{2} & & \gate{D_1} \\
& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & & \ctrl[vertical wire=c]{2} & \gate{D_2} \\
& \redmeter{}\inwire\redwire{6} & & \redctrl{2} & & \targ{} & & \redgate{D_3} \\
& \redmeter{}\inwire\redwire{6} & & & \redctrl{2} & & \targ{} & \redgate{D_4} \\
& \redmeter{}\inwire\redwire{2} & & \redtarg\wire[r][4]{c} & & & & \gate{D_5} \\
& \redmeter{}\inwire\redwire{3} & & & \redtarg\wire[r][3]{c} & & & \gate{D_6}
\end{quantikz}
% tex-fmt: on
\end{figure}
@@ -1150,6 +1171,11 @@
\end{align*}
\end{minipage}
\begin{itemize}
\item A detector is a parity constraint on a set of
measurement outcomes \citereference{derks_designing_2025}
\end{itemize}
\vspace*{5mm}
\addreferences
@@ -1168,7 +1194,7 @@
% qubit state)}
\end{itemize}
\vspace*{5mm}
\vspace*{2mm}
\begin{figure}[H]
\centering
@@ -1182,7 +1208,7 @@
% tex-fmt: off
\begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}]
& \gate[3]{SE_1} & & \gate[3]{SE_2} & & \gate[3]{SE_3} & & \gate[3]{SE_4} & \\
& \gate[3]{\text{SE}_1} & & \gate[3]{\text{SE}_2} & & \gate[3]{\text{SE}_3} & & \gate[3]{\text{SE}_4} & \\
\lstick{$\ket{\psi}$} & & & & & & & & & \setwiretype{n} & \ldots \\
& \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\
& \ctrl[wire=c]{0}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \\
@@ -1193,30 +1219,24 @@
\end{figure}
\begin{itemize}
\item E.g., for \ac{bb} codes, the resulting detector
error matrix under circuit-level noise has the form
\item E.g., for \ac{bb} codes under circuit-level noise
\citereference{gong_toward_2024}
\end{itemize}
\vspace*{-15mm}
\vspace*{-4mm}
\begin{align*}
\bm{H} =
\begin{pmatrix}
\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 & \\
\bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0}
& \bm{H}_2 & \\
\vdots & & & &
& & \ddots
\bm{H}_0 & \bm{H}_1 & & & & & \\
& \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & & & \\
& & & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & \\
& & & & & \bm{H}_2 & \\
& & & & & & & \ddots
\end{pmatrix}
\end{align*}
\vspace*{3mm}
\vspace*{5mm}
\addreferences
{gong_toward_2024}
@@ -1348,17 +1368,15 @@
\vspace*{-18mm}
\begin{itemize}
\item Many window-based approaches exist to combat the
decoding complexity
\item Decoding complexity addressed with window-based approaches
\begin{itemize}
\item Parallel decoding of syndromes
\citereference{skoric_parallel_2023}
\item Using sliding windows
\item Parallel decoding \citereference{skoric_parallel_2023}
\item Sliding windows
\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
\item Degraded \ac{bp} performance addressed with
modification or extension
\begin{itemize}
\item \Ac{osd} post-processing
\citereference{roffe_decoding_2020}
@@ -1388,48 +1406,16 @@
\begin{frame}[fragile]
\frametitle{Sliding-Window Decoding}
\vspace*{-18mm}
\vspace*{-15mm}
\begin{itemize}
\item The sliding window approach taken in
\citereference{gong_toward_2024} resembles a \ac{scldpc}
code decoder
\item However, they don't pass soft information between
windows (only update of syndrome based on hard decision
in previous window)
\item Approach taken in \citereference{gong_toward_2024}
resembles \acf{scldpc} code
\item They try \ac{bp} + \ac{osd} and a modification of
\ac{bp} with guided decimation
\end{itemize}
\vspace*{-8mm}
\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{0} \\
\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
\end{pmatrix}
\begin{pmatrix}
\hat{\bm{e}}_0 \\
\vdots \\
\hat{\bm{e}}_5
\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*{2mm}
\caption{Equations for the decoding of the first window}
\end{subfigure}%
\begin{subfigure}[b]{0.5\textwidth}
\newcommand{\pz}{\phantom{\bm{0}}}
\[
@@ -1477,14 +1463,45 @@
\caption{Visualization of sliding window procedure}
\end{subfigure}%
\begin{subfigure}[b]{0.5\textwidth}
\begin{gather*}
\begin{pmatrix}
\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 &
\bm{0} & \bm{0} \\
\bm{0} & \bm{0} & \bm{0} & \bm{H}_2 &
\bm{H}_0 & \bm{H}_1
\end{pmatrix}
\begin{pmatrix}
\hat{\bm{e}}_0 \\
\vdots \\
\hat{\bm{e}}_5
\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*{2mm}
\caption{Equations for the decoding of the first window}
\end{subfigure}%
\end{figure}
\begin{itemize}
\item They try \ac{bp} + \ac{osd} and a modification of
\ac{bp} with guided decimation
\end{itemize}
\vspace*{3mm}
\vspace*{5mm}
\visible<2->{
\begin{itemize}
\item However, no passing of soft information between windows
\end{itemize}
}
\vspace*{8mm}
\addreferences
{gong_toward_2024}
@@ -1492,34 +1509,44 @@
\end{frame}
%%%%%%%%%%%%%%%%
\subsection{Proposed Research}
\label{subsec:Proposed Research}
\subsection{Future Work}
\label{subsec:Future Work}
\begin{frame}
\frametitle{Proposed Research}
\frametitle{Future Work}
\vspace*{-5mm}
\vspace*{-15mm}
\begin{itemize}
\item Completed work
\begin{itemize}
\item Review of literature on fault-tolerant \ac{qec}
\item Identification of research gap
\end{itemize}
\vspace*{7mm}
\item Research gap
\begin{itemize}
\item Existing literature into circuit-level noise
fails to properly consider the \ac{scldpc} like
structure of the detector error matrix
fails to properly consider \ac{scldpc}-like
structure
\end{itemize}
\vspace*{7mm}
\item Proposed Methodology
\begin{itemize}
\item Adapt modified guided decimation decoder from
\citereference{gong_toward_2024} to pass soft information
\item Investigate performance of different
modifications of \ac{bp} for "inner decoder"
(e.g., quaternary neural \ac{bp}
\citereference{miao_quaternary_2025})
\end{itemize}
\visible<2->{
\item Future directions
\begin{itemize}
\item Adapt modified guided decimation decoder from
\citereference{gong_toward_2024} to pass soft
information
\item Investigate performance of different
modifications of \ac{bp} for "inner decoder"
(e.g., quaternary neural \ac{bp}
\citereference{miao_quaternary_2025})
\item \ldots
\end{itemize}
}
\end{itemize}
\vspace*{15mm}
\vspace*{10mm}
\addreferences
{gong_toward_2024}
@@ -1536,18 +1563,6 @@
\subsection{The Code and Other Parameters}
\label{subsec:The Code and Other Parameters}
% TODO: I have to mention somewhere that I am interested in decoder
% design specifically
\begin{frame}
\frametitle{Memory and Stability experiments}
\begin{itemize}
\item \red{What is a memory experiment? Communications Engineering
view (what are my inputs and outpus? What do I expect?)}
\item \red{What is a stability experiment?}
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Noise Models and Figures of Merit}
@@ -1579,34 +1594,23 @@
\label{subsec:Proposed Methodology}
\begin{frame}
\frametitle{Proposed Simulation Methodology}
\frametitle{Conclusion}
\begin{itemize}
\item \red{Noise model}
\item \red{Memory or stability experiment}
\item \red{Figure of merit: Footprint plot}
\item \red{Comparison with BB code also simulated by
\citereference{gong_toward_2024}}
\item \red{Comparison with surface code}
\end{itemize}
\vspace*{15mm}
\addreferences
{gong_toward_2024}
\stopreferences
\end{frame}
\begin{frame}[t]
\frametitle{Questions}
\vspace*{-15mm}
\begin{minipage}[c]{0.65\textwidth}
\centering
\LARGE Thank you for your attention!\\ Any questions?
\begin{itemize}
\item \red{Noise model}
\item \red{Memory or stability experiment}
\item \red{Figure of merit: Footprint plot}
\item \red{Comparison with BB code also simulated by
\citereference{gong_toward_2024}}
\item \red{Comparison with surface code}
\end{itemize}
\end{minipage}%
\begin{minipage}[c]{0.35\textwidth}
\centering
\pause
\begin{figure}[H]
\centering
@@ -1616,7 +1620,6 @@
\end{tikzpicture}
\end{figure}
\end{minipage}
\end{frame}
\appendix