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Add general syndrome extraction circuit

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Andreas Tsouchlos
2026-04-24 00:36:34 +02:00
parent e792141afd
commit 6e2cf5b8ba
1 changed files with 19 additions and 75 deletions
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94
src/thesis/chapters/2_fundamentals.tex
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@@ -1206,62 +1206,13 @@ the ancilla qubit. Similarly, if $E \ket{\psi}_\text{L} \in
\begin{figure}[t]
\centering
\tikzset{
meter/.append style={
draw, rectangle,
font=\vphantom{A}, minimum width=8mm, minimum height=8mm,
path picture={
\draw[black]
([shift={(.1,.3)}]path picture bounding box.south west)
to[bend left=50]
([shift={(-.1,.3)}]path picture bounding box.south east);
\draw[black,-latex]
([shift={(0,.1)}]path picture bounding box.south)
-- ([shift={(.3,-.1)}]path picture bounding box.north);
}
}
}
\begin{tikzpicture}
\node[rectangle, minimum width=2cm, minimum height=3cm, draw]
(ZZ) {$Z_1Z_2$};
\coordinate (qi1) at (-3, 1);
\coordinate (qi2) at (-3, -1);
\coordinate (qi3) at (-3, -3);
\coordinate (qo1) at (4, 1);
\coordinate (qo2) at (4, -1);
\coordinate (qo3) at (4, -3);
\node[rectangle, minimum width=8mm, minimum height=8mm, draw]
(H1) at ($(qo3 -| ZZ) + (-2, 0)$) {H};
\node[rectangle, minimum width=8mm, minimum height=8mm, draw]
(H2) at ($(qo3 -| ZZ) + (2, 0)$) {H};
\node[circle, fill] (not) at (H1 -| ZZ) {};
\node[meter, right=5mm of H2] (mes) {};
\draw (qi1) -- (ZZ.west |- qi1);
\draw (qi2) -- (ZZ.west |- qi2);
\draw (qo1) -- (ZZ.east |- qo1);
\draw (qo2) -- (ZZ.east |- qo2);
\draw (qi3) -- (H1) -- (not) -- (H2) -- (mes);
\draw (not) -- (ZZ);
\coordinate (qo3u) at ($(qo3) + (0, .5mm)$);
\coordinate (qo3d) at ($(qo3) + (0, -.5mm)$);
\draw (mes.east |- qo3u) -- (qo3u);
\draw (mes.east |- qo3d) -- (qo3d);
\node[left] at (qi3) {$\ket{0}_\text{A}$};
\node[left] at ($(qi1)!.5!(qi2)$) {$E\ket{\psi}_\text{L}$};
\node[right] at ($(qo1)!.5!(qo2)$) {$E\ket{\psi}_\text{L}$};
\end{tikzpicture}
% tex-fmt: off
\begin{quantikz}
\lstick[2]{$E\ket{\psi}_\text{L}$} & & \gate[2]{Z_1Z_2} & & & \\
& & & & & \\
\lstick{$\ket{0}_\text{A}$} & \gate{H} & \ctrl{-1} & \gate{H} & \meter{} & \setwiretype{c} \\
\end{quantikz}
% tex-fmt: on
\caption{Stabilizer measurement circuit for the two-qubit repetition code.}
\label{fig:stabilizer_measurement}
@@ -1373,27 +1324,20 @@ Hadamard gates \cite[Sec.~10.5.8]{nielsen_quantum_2010}]} \\
\begin{figure}[t]
\centering
\tikzset{
meter/.append style={
draw, rectangle,
font=\vphantom{A}, minimum width=8mm, minimum height=8mm,
path picture={
\draw[black]
([shift={(.1,.3)}]path picture bounding box.south west)
to[bend left=50]
([shift={(-.1,.3)}]path picture bounding box.south east);
\draw[black,-latex]
([shift={(0,.1)}]path picture bounding box.south)
-- ([shift={(.3,-.1)}]path picture bounding box.north);
}
}
}
\red{Hier könnte Ihre Werbung stehen.}
% tex-fmt: off
\begin{quantikz}
\lstick[2]{$E\ket{\psi}_\text{L}$} & & \gate[2]{P_1} & \gate[2]{P_2} & \gate[style={draw=none},2]{\ldots} & \gate[2]{P_{n-k}} & & & \\
& & & & & & & & \\
\lstick{$\ket{0}_{\text{A}_1}$} & \gate{H} & \ctrl{-1} & & & & \gate{H} & \meter{} & \setwiretype{c} \\
\lstick{$\ket{0}_{\text{A}_2}$} & \gate{H} & & \ctrl{-2} & & & \gate{H} & \meter{} & \setwiretype{c} \\
\vdots\setwiretype{n} & & & & & & & & \vdots \\
\lstick{$\ket{0}_{\text{A}_{n-k}}$} & \gate{H} & & & & \ctrl{-4} & \gate{H} & \meter{} & \setwiretype{c} \\
\end{quantikz}
% tex-fmt: on
\caption{
\red{Illustration of a general syndrome extraction circuit.
Adapted from \cite[Figure~4]{roffe_quantum_2019}.}
Illustration of a general syndrome extraction circuit.
Adapted from \cite[Figure~4]{roffe_quantum_2019}.
}
\label{fig:sec}
\end{figure}