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

Add bit-flip noise and modify phenomenological and circuit-level noise figures

Browse Source
This commit is contained in:
Andreas Tsouchlos
2026-04-25 18:49:03 +02:00
parent 163ef926e7
commit 93f310d843
1 changed files with 83 additions and 60 deletions
Download Patch File Download Diff File Expand all files Collapse all files

143
src/thesis/chapters/3_fault_tolerant_qec.tex
View File

@@ -41,53 +41,75 @@
} }
}]{\phantom{1}}} }]{\phantom{1}}}
\begin{subfigure}{0.48\textwidth} \begin{minipage}{0.7\textwidth}
\centering \begin{minipage}{\textwidth}
% tex-fmt: off \centering
\begin{quantikz}[row sep=4mm, column sep=4mm] % tex-fmt: off
\lstick[3]{$\ket{\psi}$} & \xyzerr & \ctrl{3} & & & & & \\ \begin{quantikz}[row sep=4mm, column sep=4mm]
& \xyzerr & & \ctrl{2} & \ctrl{3} & & & \\ \lstick[3]{$\ket{\psi}_\text{L}$} & \xerr & \ctrl{3} & & & & & \\
& \xyzerr & & & & \ctrl{2} & & \\ & \xerr & & \ctrl{2} & \ctrl{3} & & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ & \xerr & & & & \ctrl{2} & & \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
\end{quantikz} \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
% tex-fmt: on \end{quantikz}
% tex-fmt: on
\caption{Depolarizing channel.} \subcaption{Bit-flip noise.}
\end{subfigure}% \end{minipage}
\begin{subfigure}{0.48\textwidth}
\centering
% tex-fmt: off
\begin{quantikz}[row sep=4mm, column sep=4mm]
\lstick[3]{$\ket{\psi}$} & \xerr & \ctrl{3} & & & & & & \\
& \xerr & & \ctrl{2} & \ctrl{3} & & & & \\
& \xerr & & & & \ctrl{2} & & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \xerr & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \xerr & \meter{} & \setwiretype{c}
\end{quantikz}
% tex-fmt: on
\caption{Phenomenological noise.} \vspace*{5mm}
\end{subfigure}
\vspace*{3mm} \begin{minipage}{\textwidth}
\centering \centering
\begin{subfigure}[c]{0.75\textwidth} % tex-fmt: off
\centering \begin{quantikz}[row sep=4mm, column sep=4mm]
% tex-fmt: off \lstick[3]{$\ket{\psi}_\text{L}$} & \xyzerr & \ctrl{3} & & & & & \\
\begin{quantikz}[row sep=4mm, column sep=2mm] & \xyzerr & & \ctrl{2} & \ctrl{3} & & & \\
\lstick[3]{$\ket{\psi}$} & \xyzerr & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & & & & & \\ & \xyzerr & & & & \ctrl{2} & & \\
& \xyzerr & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & \\ \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
& \xyzerr & & & & & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & & & \\ \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
\lstick{$\ket{0}_{\text{A}_1}$} & \xyzerr & \targ{} & \xyzerr & \targ{} & \xyzerr & & & & & \xerr & \meter{} & \setwiretype{c} \\ \end{quantikz}
\lstick{$\ket{0}_{\text{A}_2}$} & \xyzerr & & & & & \targ{} & \xyzerr & \targ{} & \xyzerr & \xerr & \meter{} & \setwiretype{c} % tex-fmt: on
\end{quantikz}
% tex-fmt: on
\caption{Circuit-level noise.} \subcaption{Depolarizing channel.}
\end{subfigure}% \end{minipage}
\vspace*{5mm}
\begin{minipage}{\textwidth}
\centering
% tex-fmt: off
\begin{quantikz}[row sep=4mm, column sep=4mm]
\lstick[3]{$\ket{\psi}_\text{L}$} & \xerr & \ctrl{3} & & & & & & \xerr & & \setwiretype{n} & \\
& \xerr & & \ctrl{2} & \ctrl{3} & & & & \xerr & & \setwiretype{n} & \gate[style={left,draw=none}]{\cdots} \\
& \xerr & & & & \ctrl{2} & & & \xerr & & \setwiretype{n} & \\
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \xerr & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \xerr & \meter{} & \setwiretype{c}
\end{quantikz}
% tex-fmt: on
\subcaption{Phenomenological noise.}
\end{minipage}
\vspace*{5mm}
\begin{minipage}{\textwidth}
\centering
% tex-fmt: off
\begin{quantikz}[row sep=4mm, column sep=2mm]
\lstick[3]{$\ket{\psi}_\text{L}$} & \xyzerr & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & & & & & \xyzerr & & \setwiretype{n} & \\
& \xyzerr & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & \xyzerr & & \setwiretype{n} & \gate[style={left,draw=none,xshift=3.5mm}]{\cdots} \\
& \xyzerr & & & & & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & & & \xyzerr & & \setwiretype{n} & \\
\lstick{$\ket{0}_{\text{A}_1}$} & \xyzerr & \targ{} & \xyzerr & \targ{} & \xyzerr & & & & & \xerr & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & \xyzerr & & & & & \targ{} & \xyzerr & \targ{} & \xyzerr & \xerr & \meter{} & \setwiretype{c}
\end{quantikz}
% tex-fmt: on
\subcaption{Circuit-level noise.}
\end{minipage}
\end{minipage}%
\hfill% \hfill%
\begin{subfigure}[c]{0.25\textwidth} \begin{minipage}{0.23\textwidth}
\centering \centering
% tex-fmt: off % tex-fmt: off
\begin{quantikz}[row sep=4mm, column sep=2mm] \begin{quantikz}[row sep=4mm, column sep=2mm]
@@ -97,7 +119,7 @@
\setwiretype{n} & \gate{\phantom{1}} & \setwiretype{n} & \gate{\phantom{1}} &
\end{quantikz} \end{quantikz}
% tex-fmt: on % tex-fmt: on
\end{subfigure} \end{minipage}
\caption{Types of noise models.} \caption{Types of noise models.}
\label{fig:Types of noise models.} \label{fig:Types of noise models.}
@@ -144,7 +166,7 @@
\begin{minipage}{0.5\textwidth} \begin{minipage}{0.5\textwidth}
% tex-fmt: off % tex-fmt: off
\begin{quantikz}%[row sep=4mm, column sep=4mm] \begin{quantikz}%[row sep=4mm, column sep=4mm]
\lstick[3]{$\ket{\psi}$} & \ctrl{3} & & & & & \\ \lstick[3]{$\ket{\psi}_\text{L}$} & \ctrl{3} & & & & & \\
& & \ctrl{2} & \ctrl{3} & & & \\ & & \ctrl{2} & \ctrl{3} & & & \\
& & & & \ctrl{2} & & \\ & & & & \ctrl{2} & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ \lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
@@ -252,7 +274,7 @@
} }
] ]
% tex-fmt: off % tex-fmt: off
\lstick[3]{$\ket{\psi}$} & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ \lstick[3]{$\ket{\psi}_\text{L}$} & \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_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\
& \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\
@@ -345,15 +367,15 @@
% 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=3mm, 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]{$\ket{\psi}_\text{L}$} & \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
@@ -431,14 +453,15 @@
% tex-fmt: off % tex-fmt: off
\begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}] \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[3]{$\ket{\psi}_\text{L}$} & \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 \\ & & & & & & & & & \setwiretype{n} & \ldots \\
& \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\ & \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} & \\ & \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} & \\ & & \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} & \\ & \gate[1]{\bm{D}_1} & & \gate[1]{\bm{D}_2} & & \gate[1]{\bm{D}_3} & & \gate[1]{\bm{D}_4} & \\
\end{quantikz} \end{quantikz}
% tex-fmt: on % tex-fmt: on
\caption{Construction of detectors from measurements in the general case.} \caption{Construction of detectors from measurements in the general case.}
\end{figure} \end{figure}