an.tsouchlos/ma-thesis
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases 12 Wiki Activity

Add three-qubit rep. code syndrome extraction circuit under bit-flip noise

Browse Source
This commit is contained in:
Andreas Tsouchlos
2026-04-25 17:28:17 +02:00
parent 6de9cec27e
commit 4da37dbddc
1 changed files with 86 additions and 34 deletions
Download Patch File Download Diff File Expand all files Collapse all files

120
src/thesis/chapters/3_fault_tolerant_qec.tex
View File

@@ -129,6 +129,37 @@
\caption{Sources of error in a fault-tolerant \ac{qec} system.} \caption{Sources of error in a fault-tolerant \ac{qec} system.}
\end{figure} \end{figure}
\begin{figure}[t]
\centering
\begin{minipage}{0.5\textwidth}
\begin{align*}
\bm{H} =
\begin{pmatrix}
1 & 1 & 0 \\
0 & 1 & 1
\end{pmatrix}
\end{align*}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
% tex-fmt: off
\begin{quantikz}%[row sep=4mm, column sep=4mm]
\lstick[3]{$\ket{\psi}$} & \ctrl{3} & & & & & \\
& & \ctrl{2} & \ctrl{3} & & & \\
& & & & \ctrl{2} & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
\end{quantikz}
% tex-fmt: on
\end{minipage}%
\caption{
Syndrome extraction circuit for the three-qubit repetition
code under bit-flip noise.
}
\label{fig:}
\end{figure}
\begin{figure}[t] \begin{figure}[t]
\centering \centering
@@ -182,10 +213,10 @@
\end{minipage} \end{minipage}
\newcommand{\preperr}[1]{ \newcommand{\preperr}[1]{
\gate[style={fill=orange!20}]{\scriptstyle #1} \gate[style={fill=blue!20}]{\scriptstyle #1}
} }
\vspace*{10mm} \vspace*{5mm}
\begin{quantikz}[ \begin{quantikz}[
row sep=4mm, column sep=4mm, row sep=4mm, column sep=4mm,
@@ -234,7 +265,7 @@
\end{quantikz} \end{quantikz}
\caption{ \caption{
Repeated syndrome extraction circuit for the two-qubit Repeated syndrome extraction circuit for the three-qubit
repetition code under bit flip noise. repetition code under bit flip noise.
} }
\end{figure} \end{figure}
@@ -275,10 +306,10 @@
\bm{\Omega} \mright\} \bm{\Omega} \mright\}
\end{gather*} \end{gather*}
\vspace*{10mm} \vspace*{5mm}
\newcommand{\preperr}[1]{ \newcommand{\preperr}[1]{
\gate[style={fill=orange!20}]{\scriptstyle #1} \gate[style={fill=blue!20}]{\scriptstyle #1}
} }
\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}} \newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
@@ -312,21 +343,19 @@
\centering \centering
\scalebox{0.9}{ % tex-fmt: off
% tex-fmt: off \begin{quantikz}[row sep=4mm, column sep=3mm, wire types={q,q,q,q,q,n,n,n,n}]
\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} & & & & & & \\
\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_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} & & & \\
& \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{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \preperr{E_3} & \meter{} & \setwiretype{c} \\ \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \preperr{E_4} & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \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{$\ket{0}_{\text{A}_3}$} & \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{$\ket{0}_{\text{A}_4}$} & \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{$\ket{0}_{\text{A}_5}$} & \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}
& & & & & & & & & & & & \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}
\end{quantikz} % tex-fmt: on
% tex-fmt: on
}
\caption{ \caption{
Repeated syndrome extraction circuit for the two-qubit Repeated syndrome extraction circuit for the two-qubit
@@ -356,21 +385,19 @@
\newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}} \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}}
\newcommand{\redgate}[1]{\gate[style={draw=red,fill=red!20}]{\textcolor{red}{#1}}} \newcommand{\redgate}[1]{\gate[style={draw=red,fill=red!20}]{\textcolor{red}{#1}}}
\scalebox{0.9}{ % tex-fmt: off
% tex-fmt: off \begin{quantikz}[row sep=4mm, column sep=3mm, wire types={n,n,n,n,n,n}]
\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_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} & \gate{D_2} \\ & \redmeter{}\inwire\redwire{6} & & \redctrl{2} & & \targ{} & & \redgate{D_3} \\
& \redmeter{}\inwire\redwire{6} & & \redctrl{2} & & \targ{} & & \redgate{D_3} \\ & \redmeter{}\inwire\redwire{6} & & & \redctrl{2} & & \targ{} & \redgate{D_4} \\
& \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{2} & & \redtarg\wire[r][4]{c} & & & & \gate{D_5} \\ & \redmeter{}\inwire\redwire{3} & & & \redtarg\wire[r][3]{c} & & & \gate{D_6}
& \redmeter{}\inwire\redwire{3} & & & \redtarg\wire[r][3]{c} & & & \gate{D_6} \end{quantikz}
\end{quantikz} % tex-fmt: on
% tex-fmt: on
}
\end{minipage}% \end{minipage}%
\begin{minipage}{0.56\textwidth} \begin{minipage}{0.56\textwidth}
\newcommand\cc{\cellcolor{blue!20}} \newcommand\cc{\cellcolor{orange!20}}
\begin{align*} \begin{align*}
\bm{H} = \bm{H} =
@@ -387,10 +414,35 @@
\end{align*} \end{align*}
\end{minipage} \end{minipage}
\caption{Construction of the detectors from the measurements.} \caption{Construction of detectors from the measurements of a
three-qubit repetition code.}
\label{fig:Construction of the detectors from the measurements} \label{fig:Construction of the detectors from the measurements}
\end{figure} \end{figure}
\begin{figure}[t]
\centering
\tikzset{
gate/.style={
draw, %line width=1pt,
minimum height=2cm,
}
}
% tex-fmt: off
\begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}]
& \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} & \\
& & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \\
& \gate[1]{\bm{D}_1} & & \gate[1]{\bm{D}_2} & & \gate[1]{\bm{D}_3} & & \gate[1]{\bm{D}_4} & \\
\end{quantikz}
% tex-fmt: on
\caption{Construction of detectors from measurements in the general case.}
\end{figure}
\begin{figure}[t] \begin{figure}[t]
\centering \centering