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

src/thesis/chapters/3_fault_tolerant_qec.tex

@@ -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}
+

src/thesis/main.tex

@@ -25,6 +25,8 @@
 \usepackage{stmaryrd}
 \usepackage{algorithm}
 \usepackage[noEnd=false]{algpseudocodex}
+\usepackage{nicematrix}
+\usepackage{colortbl}
 
 \usetikzlibrary{calc, positioning, arrows, fit}
 \usetikzlibrary{external}