Add three-qubit rep. code syndrome extraction circuit under bit-flip noise
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@@ -129,6 +129,37 @@
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\caption{Sources of error in a fault-tolerant \ac{qec} system.}
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\end{figure}
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\begin{figure}[t]
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\centering
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\begin{minipage}{0.5\textwidth}
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\begin{align*}
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\bm{H} =
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\begin{pmatrix}
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1 & 1 & 0 \\
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0 & 1 & 1
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\end{pmatrix}
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\end{align*}
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\end{minipage}%
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\begin{minipage}{0.5\textwidth}
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% tex-fmt: off
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\begin{quantikz}%[row sep=4mm, column sep=4mm]
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\lstick[3]{$\ket{\psi}$} & \ctrl{3} & & & & & \\
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& & \ctrl{2} & \ctrl{3} & & & \\
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& & & & \ctrl{2} & & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
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\end{quantikz}
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% tex-fmt: on
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\end{minipage}%
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\caption{
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Syndrome extraction circuit for the three-qubit repetition
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code under bit-flip noise.
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}
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\label{fig:}
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\end{figure}
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\begin{figure}[t]
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\centering
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@@ -182,10 +213,10 @@
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\end{minipage}
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\newcommand{\preperr}[1]{
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\gate[style={fill=orange!20}]{\scriptstyle #1}
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\gate[style={fill=blue!20}]{\scriptstyle #1}
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}
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\vspace*{10mm}
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\vspace*{5mm}
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\begin{quantikz}[
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row sep=4mm, column sep=4mm,
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@@ -234,7 +265,7 @@
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\end{quantikz}
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\caption{
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Repeated syndrome extraction circuit for the two-qubit
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Repeated syndrome extraction circuit for the three-qubit
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repetition code under bit flip noise.
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}
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\end{figure}
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@@ -275,10 +306,10 @@
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\bm{\Omega} \mright\}
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\end{gather*}
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\vspace*{10mm}
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\vspace*{5mm}
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\newcommand{\preperr}[1]{
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\gate[style={fill=orange!20}]{\scriptstyle #1}
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\gate[style={fill=blue!20}]{\scriptstyle #1}
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}
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\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
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@@ -312,9 +343,8 @@
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\centering
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\scalebox{0.9}{
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% tex-fmt: off
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\begin{quantikz}[row sep=4mm, column sep=4mm, wire types={q,q,q,q,q,n,n,n,n}]
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\begin{quantikz}[row sep=4mm, column sep=3mm, wire types={q,q,q,q,q,n,n,n,n}]
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\lstick[3]{$\ket{\psi}$} & \preperr{E_0} & \ctrl{3} & & & & \preperr{E_5} & & \ctrl{5} & & & & \preperr{E_{10}} & & \ctrl{7} & & & & & & \\
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& \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & \noise\redwire{14} & & & \redctrl{4} & \redctrl{5} & & \preperr{E_{11}} & & & \redctrl{6} & \redctrl{7} & & & & \\
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& \preperr{E_2} & & & & \ctrl{2} & \preperr{E_7} & & & & & \ctrl{4} & \preperr{E_{12}} & & & & & \ctrl{6} & & & \\
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@@ -326,7 +356,6 @@
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& & & & & & & & & & & & \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}
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\end{quantikz}
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% tex-fmt: on
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}
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\caption{
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Repeated syndrome extraction circuit for the two-qubit
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@@ -356,9 +385,8 @@
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\newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}}
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\newcommand{\redgate}[1]{\gate[style={draw=red,fill=red!20}]{\textcolor{red}{#1}}}
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\scalebox{0.9}{
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% tex-fmt: off
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\begin{quantikz}[row sep=4mm, column sep=4mm, wire types={n,n,n,n,n,n}]
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\begin{quantikz}[row sep=4mm, column sep=3mm, wire types={n,n,n,n,n,n}]
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& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & \ctrl[vertical wire=c]{2} & & \gate{D_1} \\
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& \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & & \ctrl[vertical wire=c]{2} & \gate{D_2} \\
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& \redmeter{}\inwire\redwire{6} & & \redctrl{2} & & \targ{} & & \redgate{D_3} \\
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@@ -367,10 +395,9 @@
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& \redmeter{}\inwire\redwire{3} & & & \redtarg\wire[r][3]{c} & & & \gate{D_6}
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\end{quantikz}
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% tex-fmt: on
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}
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\end{minipage}%
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\begin{minipage}{0.56\textwidth}
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\newcommand\cc{\cellcolor{blue!20}}
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\newcommand\cc{\cellcolor{orange!20}}
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\begin{align*}
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\bm{H} =
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@@ -387,10 +414,35 @@
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\end{align*}
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\end{minipage}
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\caption{Construction of the detectors from the measurements.}
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\caption{Construction of detectors from the measurements of a
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three-qubit repetition code.}
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\label{fig:Construction of the detectors from the measurements}
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\end{figure}
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\begin{figure}[t]
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\centering
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\tikzset{
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gate/.style={
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draw, %line width=1pt,
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minimum height=2cm,
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}
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}
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% tex-fmt: off
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\begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}]
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& \gate[3]{\text{SE}_1} & & \gate[3]{\text{SE}_2} & & \gate[3]{\text{SE}_3} & & \gate[3]{\text{SE}_4} & \\
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\lstick{$\ket{\psi}$} & & & & & & & & & \setwiretype{n} & \ldots \\
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& \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\
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& \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} & \\
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& & \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} & \\
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& \gate[1]{\bm{D}_1} & & \gate[1]{\bm{D}_2} & & \gate[1]{\bm{D}_3} & & \gate[1]{\bm{D}_4} & \\
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\end{quantikz}
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% tex-fmt: on
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\caption{Construction of detectors from measurements in the general case.}
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\end{figure}
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\begin{figure}[t]
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\centering
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