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Add repeated syndrome extraction circuit figures for bit-flip and phenomenological noise

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This commit is contained in:
Andreas Tsouchlos
2026-04-25 14:59:26 +02:00
parent 569df381ee
commit 50a10ccb4f
2 changed files with 208 additions and 2 deletions
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208
src/thesis/chapters/3_fault_tolerant_qec.tex
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@@ -12,7 +12,7 @@
\subsection{Practical Methodology}
\subsection{Stim}
\begin{figure}[H]
\begin{figure}[t]
\centering
\newcommand{\xerr}{\gate[style={fill=KITblue!50}]{\phantom{1}}}
@@ -103,7 +103,7 @@
\label{fig:Types of noise models.}
\end{figure}
\begin{figure}[H]
\begin{figure}[t]
\centering
\begin{tikzpicture}
@@ -129,3 +129,207 @@
\caption{Sources of error in a fault-tolerant \ac{qec} system.}
\end{figure}
\begin{figure}[t]
\centering
\begin{minipage}{0.3\textwidth}
\centering
\begin{tikzpicture}
\node{$%
\bm{\Omega} =
\begin{pmatrix}
1 & 1 & 0 \\
0 & 1 & 1 \\
1 & 1 & 0 \\
0 & 1 & 1 \\
1 & 1 & 0 \\
0 & 1 & 1
\end{pmatrix}%
$
};
\draw [
line width=1pt,
decorate,
decoration={brace,mirror,amplitude=3mm,raise=5mm}
]
(1,0.55) -- (1,1.4)
node[midway,right,xshift=10mm]{$\text{SE}_1$};
\draw [
line width=1pt,
decorate,
decoration={brace,mirror,amplitude=3mm,raise=5mm}
]
(1,-0.4) -- (1,0.45)
node[midway,right,xshift=10mm]{$\text{SE}_2\hspace{2mm},$};
\draw [
line width=1pt,
decorate,
decoration={brace,mirror,amplitude=3mm,raise=5mm}
]
(1,-1.38) -- (1,-0.5)
node[midway,right,xshift=10mm]{$\text{SE}_3$};
\end{tikzpicture}
\end{minipage}%
\begin{minipage}{0.3\textwidth}
\centering
\vspace*{-6mm}
\begin{gather*}
\bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\}
\end{gather*}
\end{minipage}
\newcommand{\preperr}[1]{
\gate[style={fill=orange!20}]{\scriptstyle #1}
}
\vspace*{10mm}
\begin{quantikz}[
row sep=4mm, column sep=4mm,
wire types={q,q,q,q,q,n,n,n,n},
execute at end picture={
\draw [
line width=1pt,
decorate,
decoration={brace,amplitude=3mm,raise=9mm}
]
(\tikzcdmatrixname-4-19.north east)
--
(\tikzcdmatrixname-5-19.south east)
node[midway,right,xshift=14mm]{$\text{SE}_1$};
\draw [
line width=1pt,
decorate,
decoration={brace,amplitude=3mm,raise=9mm}
]
(\tikzcdmatrixname-6-19.north east)
--
(\tikzcdmatrixname-7-19.south east)
node[midway,right,xshift=14mm]{$\text{SE}_2$};
\draw [
line width=1pt,
decorate,
decoration={brace,amplitude=3mm,raise=9mm}
]
(\tikzcdmatrixname-8-19.north east)
--
(\tikzcdmatrixname-9-19.south east)
node[midway,right,xshift=14mm]{$\text{SE}_3$};
}
]
% tex-fmt: off
\lstick[3]{$\ket{\psi}$} & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\
& \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\
& \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\
& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & & & & & & & \meter{} & \setwiretype{c} \\
& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\
& & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
& & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
% tex-fmt: on
\end{quantikz}
\caption{
Repeated syndrome extraction circuit for the two-qubit
repetition code under bit flip noise.
}
\end{figure}
\begin{figure}[t]
\begin{gather*}
\hspace*{-33.3mm}%
\begin{array}{c}
E_6 \\
\downarrow
\end{array}
\end{gather*}
\vspace*{-8mm}
\begin{gather*}
\bm{\Omega} =
\left(
\begin{array}{
cccccc%
>{\columncolor{red!20}}c%
cccccccc
}
1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0
& 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0
& 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0
& 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1
& 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0
& 1 & 1 & 0 & 1 & 0 \\
0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0
& 0 & 1 & 1 & 0 & 1
\end{array}
\right),
\hspace*{7mm}
\bm{s} \in \text{span} \mleft\{
\bm{\Omega} \mright\}
\end{gather*}
\vspace*{10mm}
\newcommand{\preperr}[1]{
\gate[style={fill=orange!20}]{\scriptstyle #1}
}
\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
\newcommand{\noise}{
\gate[style={noisy}]{\text{\small X}}%
\setwiretype{n}%
\wire[l][1]{q}
}
\newcommand{\redwire}[1]{
\wire[r][#1][style={draw=red, line width=1.5pt}]{q}
}
\newcommand{\redtarg}{
\targ[style={draw=red}]{}%
\setwiretype{n}%
\wire[l][1]{q}
}
\newcommand{\redctrl}[1]{
\ctrl[style={draw=red,fill=red,line width=1.5pt}]{#1}
}
\newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}}
\tikzset{
noisy/.style={
starburst,
starburst point height=2.5mm,
fill=red!25, draw=red!85!black,
line width=1.5pt,
inner xsep=-2pt, inner ysep=-2pt
},
}
\centering
\hspace*{-7mm}
% tex-fmt: off
\begin{quantikz}[row sep=4mm, column sep=4mm, wire types={q,q,q,q,q,n,n,n,n}]
\lstick[3]{$\ket{\psi}$} & \preperr{E_0} & \ctrl{3} & & & & \preperr{E_5} & & \ctrl{5} & & & & \preperr{E_{10}} & & \ctrl{7} & & & & & & \\
& \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & \noise\redwire{14} & & & \redctrl{4} & \redctrl{5} & & \preperr{E_{11}} & & & \redctrl{6} & \redctrl{7} & & & & \\
& \preperr{E_2} & & & & \ctrl{2} & \preperr{E_7} & & & & & \ctrl{4} & \preperr{E_{12}} & & & & & \ctrl{6} & & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \preperr{E_3} & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \preperr{E_4} & \meter{} & \setwiretype{c} \\
& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \redtarg\redwire{10} & & & & & & & & & \preperr{E_8} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\
& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \redtarg\redwire{9} & \targ{} & & & & & & & \preperr{E_9} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\
& & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \redtarg\redwire{4} & & & \preperr{E_{13}} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n} \\
& & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \redtarg\redwire{3} & \targ{} & \preperr{E_{14}} & \redmeter\wire[r][1][style={draw=red,double, line width=1.5pt}]{q} & \setwiretype{n}
\end{quantikz}
% tex-fmt: on
\caption{
Repeated syndrome extraction circuit for the two-qubit
repetition code under phenomenological noise.
}
\end{figure}

2
src/thesis/main.tex
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@@ -25,6 +25,8 @@
\usepackage{stmaryrd}
\usepackage{algorithm}
\usepackage[noEnd=false]{algpseudocodex}
\usepackage{nicematrix}
\usepackage{colortbl}
\usetikzlibrary{calc, positioning, arrows, fit}
\usetikzlibrary{external}