Add first version of DEM explanation slides
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@ -27,7 +27,7 @@
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\usetikzlibrary{spy, external, intersections, positioning}
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% \ifdefined\ishandout\else
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\tikzexternalize
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% \tikzexternalize
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% \fi
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\usepackage{pgfplots}
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@ -40,14 +40,15 @@
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\usepackage{subcaption}
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\usepackage{bbm}
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\usepackage{multirow}
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\usepackage{xcolor}
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\usepackage[table]{xcolor}
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\usepackage{amsmath}
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\usepackage{graphicx}
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\usepackage{calc}
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\usepackage{amssymb}
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\usepackage{acro}
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\usepackage{braket}
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\usepackage{qcircuit}
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% \usepackage{qcircuit}
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\usepackage{quantikz}
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\title{Fault Tolerant Quantum Error Correction}
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\subtitle{Master's Thesis Midterm Presentation}
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@ -271,6 +272,7 @@
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\caption{Phase flip (Z) error}
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\end{subfigure}
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\end{figure}
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\item \red{Introduce Y errors}
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\item Measuring the qubits directly destroys superpositions
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and entanglement \\
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$\rightarrow$ We generally only work with the syndrome,
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@ -321,14 +323,9 @@
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$\mathcal{C}_2 \left[ n, k_2 \right]$ with
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$\mathcal{C}_2 \subset \mathcal{C}_1$
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\end{itemize}
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\vspace*{10mm}
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\item \red{Do I need to go more in depth for either
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stabilizer codes or CSS codes?}
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\end{itemize}
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\vspace*{10mm}
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\vspace*{20mm}
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\addreferences
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{nielsen_quantum_2010}
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@ -371,22 +368,22 @@
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\vspace*{5mm}
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\begin{figure}[H]
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% \newcommand{\anyerrgate}{\gate[style={fill=red!20}]{\mathcal{E}_\text{XYZ}}}
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\newcommand{\preperr}{\gate[style={fill=orange!20}]{\phantom{1}}}
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\newcommand{\gateerr}{\gate[style={fill=red!20}]{\phantom{1}}}
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\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
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\centering
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\mbox{
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% tex-fmt: off
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\Qcircuit @C=1em @R=.7em {
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& & \ctrl{3} & \qw & \qw & \qw & \qw & \qw \\
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\ket{\psi} & & \qw & \ctrl{2} & \ctrl{3} & \qw & \qw & \qw \\
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& & \qw & \qw & \qw & \ctrl{2} & \qw & \qw \\
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\ket{0}_{\text{A}_1} & & \targ & \targ & \qw & \qw & \meter & \\
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\ket{0}_{\text{A}_2} & & \qw & \qw & \targ & \targ & \meter &
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}
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% tex-fmt: on
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}
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\vspace*{5mm}
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\caption{Syndrome extraction circuit for the 3-qubit repetition code}
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% tex-fmt: off
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\begin{quantikz}%[row sep=4mm, column sep=4mm]
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& \ctrl{3} & & & & & \\
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\lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & \\
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& & & & \ctrl{2} & & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & \meter{}
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\end{quantikz}
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% tex-fmt: on
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% \caption{Circuit-level noise model for the 3-qubit repetition code}
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\end{figure}
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% \vspace*{5mm}
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@ -405,18 +402,19 @@
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\subsection{Fault Tolerance}
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\label{subsec:Fault Tolerance}
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% TODO: Fix journal for {shor_fault-tolerant_1997} not showing
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\begin{frame}
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\frametitle{Fault Tolerance}
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\vspace*{-18mm}
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\vspace*{-20mm}
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\begin{itemize}
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\item The quantum gates we use for syndrome extraction are
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faulty themselves \\
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$\rightarrow$ We need \emph{fault-tolerant} \ac{qec}
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\citereference{roffe_quantum_2019}
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\item A \ac{qec} procedure is said to be fault tolerant if it
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can account for errors that occur at any location in the circuit
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can account for errors that occur at any location in the
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circuit \citereference{roffe_quantum_2019}
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\item We have to modify the syndrome extraction circuitry to
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be fault tolerant (e.g., by using specially prepared
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multi-qubit states for each ancilla
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@ -424,31 +422,24 @@
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\item We generally perform multiple rounds of syndrome extraction
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\end{itemize}
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\vspace*{-3mm}
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\vspace*{1mm}
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\begin{figure}[H]
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\centering
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\scalebox{0.6}{
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\mbox{
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% tex-fmt: off
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\Qcircuit @C=1em @R=.7em {
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& & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \qw & \qw & \qw & \qw & \qw \\
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\ket{\psi} & & \qw & \ctrl{2} & \ctrl{3} & \qw & \qw & \qw & \qw & \ctrl{4} & \ctrl{5} & \qw & \qw & \qw \\
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& & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \qw & \qw \\
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\ket{0}_{\text{A}_1} & & \targ & \targ & \qw & \qw & \meter & & & & & & & \\
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\ket{0}_{\text{A}_2} & & \qw & \qw & \targ & \targ & \meter & & & & & & & \\
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& & & & & & \ket{0}_{\text{A}_3} & & \targ & \targ & \qw & \qw & \meter & \\
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& & & & & & \ket{0}_{\text{A}_4} & & \qw & \qw & \targ & \targ & \meter & & \cdots
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}
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% tex-fmt: on
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}
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}
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\caption{Multiple rounds of syndrome measurements for the
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3-qubit repetition code}
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% tex-fmt: off
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\begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,q,q,n,n}]
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& \ctrl{3} & & & & & & \ctrl{5} & & & & \\
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\lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & \setwiretype{n}\ldots \\
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& & & & \ctrl{2} & & & & & & \ctrl{4} & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & & & & & & & \meter{} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & & & & & & & \meter{} \\
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& & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} \\
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& & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{}
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\end{quantikz}
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% tex-fmt: on
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\end{figure}
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% \vspace*{-2mm}
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\vspace*{1mm}
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\addreferences
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{roffe_quantum_2019}
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@ -456,35 +447,411 @@
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\stopreferences
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\end{frame}
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\begin{frame}
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\frametitle{Noise models}
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\begin{itemize}
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\item The depolarizing channel
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\item Phenomenological noise
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\item Circuit-level noise (we generally have all error
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probabilities equal the same value \\
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for simulations \citereference{fowler_high-threshold_2009})
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\end{itemize}
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\vspace*{15mm}
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\addreferences
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{fowler_high-threshold_2009}
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\stopreferences
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\end{frame}
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%%%%%%%%%%%%%%%%
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\subsection{Detector Error Models}
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\label{subsec:Detector Error Models}
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\begin{frame}
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\frametitle{Detector Error Models}
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\begin{frame}[fragile]
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\frametitle{The Detector Error Model}
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\vspace*{-10mm}
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\begin{itemize}
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\item Idea: Go "one layer of abstraction higher" \\
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$\rightarrow$ Redefine syndrome and create new PC matrix from that
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\item \red{Introduce the concept of a detector (it may be
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better to do this on the next slide, and in doing so
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explain that the syndrome results are XORed together)}
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\item Example: 3-qubit repetition code for X errors,
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phenomenological noise model, two rounds of syndrome extraction
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\end{itemize}
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\centering
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\only<1>{
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\begin{minipage}{0.3\textwidth}
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\centering
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\begin{align*}
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\bm{H} =
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\left(
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\begin{array}{ccc}
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1 & 1 & 0 \\
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0 & 1 & 1 \\
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1 & 1 & 0 \\
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0 & 1 & 1
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\end{array}\right)
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\end{align*}
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\end{minipage}%
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\begin{minipage}{0.7\textwidth}
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\begin{figure}[H]
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\newcommand{\preperr}{\gate[style={fill=orange!20}]{\phantom{1}}}
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\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
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\centering
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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}]
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& \preperr & \ctrl{3} & & & & & & \ctrl{5} & & & & \\
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\lstick{$\ket{\psi}$} & \preperr & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & \\
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& \preperr & & & & \ctrl{2} & & & & & & \ctrl{4} & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & \meter{} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & \meter{} \\
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& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} \\
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& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{}
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\end{quantikz}
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% tex-fmt: on
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\end{figure}
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\end{minipage}
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}
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\only<2>{
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\begin{minipage}{0.3\textwidth}
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\centering
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\begin{align*}
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\bm{H} =
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\left(
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\begin{array}{>{\columncolor{red!20}}ccc}
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1 & 1 & 0 \\
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0 & 1 & 1 \\
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1 & 1 & 0 \\
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0 & 1 & 1
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\end{array}\right)
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\end{align*}
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\end{minipage}%
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\begin{minipage}{0.7\textwidth}
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\begin{figure}[H]
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\newcommand{\preperr}[1]{\gate[style={fill=orange!20}]{##1}}
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\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
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\newcommand{\noise}{
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\gate[style={noisy}]{\text{\small X}}\setwiretype{n}
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}
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\newcommand{\redwire}[1]{
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\wire[r][##1][style={draw=red, line width=2pt}]{q}
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}
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\newcommand{\redtarg}{\targ[style={draw=red}]{}\setwiretype{n}}
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\newcommand{\redctrl}[1]{
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\ctrl[style={draw=red,fill=red,line width=2pt}]{##1}
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}
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\tikzset{
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noisy/.style={
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starburst,
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starburst point height=2.5mm,
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fill=red!25, draw=red!85!black,
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line width=2pt,
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inner xsep=-2pt, inner ysep=-2pt
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},
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}
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\centering
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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}]
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& \noise\redwire{11}\wire[l][1]{q} & \redctrl{3} & & & & & & \redctrl{5} & & & & \\
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\lstick{$\ket{\psi}$} & \preperr{\phantom{1}} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & \\
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& \preperr{\phantom{1}} & & & & \ctrl{2} & & & & & & \ctrl{4} & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & & \redtarg\redwire{10}\wire[l][1]{q} & \targ{} & & & & & & & & & \meter[style={draw=red,fill=red!20}]{} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & \meter{} \\
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& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \redtarg{}\redwire{4}\wire[l][1]{q} & \targ{} & & & \meter[style={draw=red,fill=red!20}]{} \\
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& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{}
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\end{quantikz}
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% tex-fmt: on
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\end{figure}
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\end{minipage}
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}
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\only<3>{
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\begin{minipage}{0.3\textwidth}
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\centering
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\begin{align*}
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\bm{H} =
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\left(
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\begin{array}{ccc>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c}
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1 & 1 & 0 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0} \\
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0 & 1 & 1 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0} \\
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1 & 1 & 0 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0} \\
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0 & 1 & 1 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}
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\end{array}\right)
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\end{align*}
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\end{minipage}%
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\begin{minipage}{0.7\textwidth}
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\begin{figure}[H]
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\newcommand{\preperr}[1]{\gate[style={fill=orange!20}]{##1}}
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\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
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\newcommand{\noise}{
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\gate[style={noisy}]{\text{\small X}}\setwiretype{n}
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}
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\newcommand{\redwire}[1]{
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\wire[r][##1][style={draw=red, line width=2pt}]{q}
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}
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\newcommand{\redtarg}{\targ[style={draw=red}]{}\setwiretype{n}}
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\newcommand{\redctrl}[1]{
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\ctrl[style={draw=red,fill=red,line width=2pt}]{##1}
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}
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\tikzset{
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noisy/.style={
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starburst,
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starburst point height=2.5mm,
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fill=red!25, draw=red!85!black,
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line width=2pt,
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inner xsep=-2pt, inner ysep=-2pt
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},
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}
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\centering
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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}]
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& \preperr{\phantom{1}} & \ctrl{3} & & & & \preperr{\phantom{1}} & & \ctrl{5} & & & & & \\
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\lstick{$\ket{\psi}$} & \preperr{\phantom{1}} & & \ctrl{2} & \ctrl{3} & & \preperr{\phantom{1}} & & & \ctrl{4} & \ctrl{5} & & & \\
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& \preperr{\phantom{1}} & & & & \ctrl{2} & \preperr{\phantom{1}} & & & & & \ctrl{4} & & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & \preperr{\phantom{1}} & \meter{} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & \preperr{\phantom{1}} & \meter{} \\
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& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & \preperr{\phantom{1}} & \meter{} \\
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& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \preperr{\phantom{1}} & \meter{}
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\end{quantikz}
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% tex-fmt: on
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\end{figure}
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\end{minipage}
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}
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\only<4>{
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\begin{minipage}{0.3\textwidth}
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\centering
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\begin{align*}
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\bm{H} =
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\left(
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\begin{array}{ccc>{\columncolor{red!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c}
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1 & 1 & 0 & 0 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}& \phantom{0} \\
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0 & 1 & 1 & 0 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}& \phantom{0} \\
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1 & 1 & 0 & 1 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}& \phantom{0} \\
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0 & 1 & 1 & 0 & \phantom{0}& \phantom{0}&
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\phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}
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\end{array}\right)
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\end{align*}
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\end{minipage}%
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\begin{minipage}{0.7\textwidth}
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\begin{figure}[H]
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\newcommand{\preperr}[1]{\gate[style={fill=orange!20}]{##1}}
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\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
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\newcommand{\noise}{
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\gate[style={noisy}]{\text{\small X}}\setwiretype{n}
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}
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\newcommand{\redwire}[1]{
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\wire[r][##1][style={draw=red, line width=2pt}]{q}
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}
|
||||
\newcommand{\redtarg}{\targ[style={draw=red}]{}\setwiretype{n}}
|
||||
\newcommand{\redctrl}[1]{
|
||||
\ctrl[style={draw=red,fill=red,line width=2pt}]{##1}
|
||||
}
|
||||
|
||||
\tikzset{
|
||||
noisy/.style={
|
||||
starburst,
|
||||
starburst point height=2.5mm,
|
||||
fill=red!25, draw=red!85!black,
|
||||
line width=2pt,
|
||||
inner xsep=-2pt, inner ysep=-2pt
|
||||
},
|
||||
}
|
||||
|
||||
\centering
|
||||
|
||||
% tex-fmt: off
|
||||
\begin{quantikz}[row sep=4mm, column sep=4mm, wire types={q,q,q,q,q,n,n}]
|
||||
& \preperr{\phantom{1}} & \ctrl{3} & & & & \noise\wire[l][1]{q}\redwire{7} & & \redctrl{5} & & & & & \\
|
||||
\lstick{$\ket{\psi}$} & \preperr{\phantom{1}} & & \ctrl{2} & \ctrl{3} & & \preperr{\phantom{1}} & & & \ctrl{4} & \ctrl{5} & & & \\
|
||||
& \preperr{\phantom{1}} & & & & \ctrl{2} & \preperr{\phantom{1}} & & & & & \ctrl{4} & & \\
|
||||
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & \preperr{\phantom{1}} & \meter{} \\
|
||||
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & \preperr{\phantom{1}} & \meter{} \\
|
||||
& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \redtarg\wire[l][1]{q}\redwire{5} & \targ{} & & & \preperr{\phantom{1}} & \meter[style={draw=red,fill=red!20}]{} \\
|
||||
& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \preperr{\phantom{1}} & \meter{}
|
||||
\end{quantikz}
|
||||
% tex-fmt: on
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
}
|
||||
\only<5>{
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
\begin{align*}
|
||||
\bm{H} =
|
||||
\left(
|
||||
\begin{array}{cccc>{\columncolor{red!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c>{\columncolor{gray!20}}c}
|
||||
1 & 1 & 0 & 0 & 0 & \phantom{0}& \phantom{0}&
|
||||
\phantom{0}& \phantom{0}& \phantom{0} \\
|
||||
0 & 1 & 1 & 0 & 0 & \phantom{0}& \phantom{0}&
|
||||
\phantom{0}& \phantom{0}& \phantom{0} \\
|
||||
1 & 1 & 0 & 1 & 1 & \phantom{0}& \phantom{0}&
|
||||
\phantom{0}& \phantom{0}& \phantom{0} \\
|
||||
0 & 1 & 1 & 0 & 1 & \phantom{0}& \phantom{0}&
|
||||
\phantom{0}& \phantom{0}& \phantom{0}
|
||||
\end{array}\right)
|
||||
\end{align*}
|
||||
\end{minipage}%
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
\begin{figure}[H]
|
||||
\newcommand{\preperr}[1]{\gate[style={fill=orange!20}]{##1}}
|
||||
\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
|
||||
\newcommand{\noise}{
|
||||
\gate[style={noisy}]{\text{\small X}}\setwiretype{n}
|
||||
}
|
||||
\newcommand{\redwire}[1]{
|
||||
\wire[r][##1][style={draw=red, line width=2pt}]{q}
|
||||
}
|
||||
\newcommand{\redtarg}{\targ[style={draw=red}]{}\setwiretype{n}}
|
||||
\newcommand{\redctrl}[1]{
|
||||
\ctrl[style={draw=red,fill=red,line width=2pt}]{##1}
|
||||
}
|
||||
|
||||
\tikzset{
|
||||
noisy/.style={
|
||||
starburst,
|
||||
starburst point height=2.5mm,
|
||||
fill=red!25, draw=red!85!black,
|
||||
line width=2pt,
|
||||
inner xsep=-2pt, inner ysep=-2pt
|
||||
},
|
||||
}
|
||||
|
||||
\centering
|
||||
|
||||
% tex-fmt: off
|
||||
\begin{quantikz}[row sep=4mm, column sep=4mm, wire types={q,q,q,q,q,n,n}]
|
||||
& \preperr{\phantom{1}} & \ctrl{3} & & & & \preperr{\phantom{1}} & & \ctrl{5} & & & & & \\
|
||||
\lstick{$\ket{\psi}$} & \preperr{\phantom{1}} & & \ctrl{2} & \ctrl{3} & & \noise\wire[l][1]{q}\redwire{7} & & & \redctrl{4} & \redctrl{5} & & & \\
|
||||
& \preperr{\phantom{1}} & & & & \ctrl{2} & \preperr{\phantom{1}} & & & & & \ctrl{4} & & \\
|
||||
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & \preperr{\phantom{1}} & \meter{} \\
|
||||
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & \preperr{\phantom{1}} & \meter{} \\
|
||||
& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \redtarg\wire[l][1]{q}\redwire{4} & & & \preperr{\phantom{1}} & \meter[style={draw=red,fill=red!20}]{} \\
|
||||
& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \redtarg\wire[l][1]{q}\redwire{3} & \targ{} & \preperr{\phantom{1}} & \meter[style={draw=red,fill=red!20}]{}
|
||||
\end{quantikz}
|
||||
% tex-fmt: on
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
}
|
||||
\only<6>{
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\centering
|
||||
\begin{align*}
|
||||
\bm{H} =
|
||||
\left(
|
||||
\begin{array}{cccccccccc}
|
||||
1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
|
||||
0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
|
||||
1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\
|
||||
0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1
|
||||
\end{array}\right)
|
||||
\end{align*}
|
||||
\end{minipage}%
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
\begin{figure}[H]
|
||||
\newcommand{\preperr}[1]{\gate[style={fill=orange!20}]{##1}}
|
||||
\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
|
||||
\newcommand{\noise}{
|
||||
\gate[style={noisy}]{\text{\small X}}\setwiretype{n}
|
||||
}
|
||||
\newcommand{\redwire}[1]{
|
||||
\wire[r][##1][style={draw=red, line width=2pt}]{q}
|
||||
}
|
||||
\newcommand{\redtarg}{\targ[style={draw=red}]{}\setwiretype{n}}
|
||||
\newcommand{\redctrl}[1]{
|
||||
\ctrl[style={draw=red,fill=red,line width=2pt}]{##1}
|
||||
}
|
||||
|
||||
\tikzset{
|
||||
noisy/.style={
|
||||
starburst,
|
||||
starburst point height=2.5mm,
|
||||
fill=red!25, draw=red!85!black,
|
||||
line width=2pt,
|
||||
inner xsep=-2pt, inner ysep=-2pt
|
||||
},
|
||||
}
|
||||
|
||||
\centering
|
||||
|
||||
% tex-fmt: off
|
||||
\begin{quantikz}[row sep=4mm, column sep=4mm, wire types={q,q,q,q,q,n,n}]
|
||||
& \preperr{\phantom{1}} & \ctrl{3} & & & & \preperr{\phantom{1}} & & \ctrl{5} & & & & & \\
|
||||
\lstick{$\ket{\psi}$} & \preperr{\phantom{1}} & & \ctrl{2} & \ctrl{3} & & \preperr{\phantom{1}} & & & \ctrl{4} & \ctrl{5} & & & \\
|
||||
& \preperr{\phantom{1}} & & & & \ctrl{2} & \preperr{\phantom{1}} & & & & & \ctrl{4} & & \\
|
||||
\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & \preperr{\phantom{1}} & \meter{} \\
|
||||
\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & \preperr{\phantom{1}} & \meter{} \\
|
||||
& & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & \preperr{\phantom{1}} & \meter{} \\
|
||||
& & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \preperr{\phantom{1}} & \meter{}
|
||||
\end{quantikz}
|
||||
% tex-fmt: on
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}[fragile]
|
||||
\frametitle{Noise models}
|
||||
|
||||
\vspace*{-7mm}
|
||||
|
||||
\begin{minipage}{0.60\textwidth}
|
||||
\begin{itemize}
|
||||
\item The \emph{depolarizing channel} considers
|
||||
\citereference{nielsen_quantum_2010}
|
||||
\begin{itemize}
|
||||
\item X, Y or Z errors on the data qubits
|
||||
\end{itemize}
|
||||
\item \emph{Phenomenological noise} considers
|
||||
\citereference{derks_designing_2025}
|
||||
\begin{itemize}
|
||||
\item X errors on data qubits before each \\
|
||||
measurement round
|
||||
\item X errors on measurement outcomes
|
||||
\end{itemize}
|
||||
\item \emph{Circuit-level noise} considers
|
||||
\citereference{derks_designing_2025}
|
||||
\begin{itemize}
|
||||
\item \colorbox{orange!20}{X, Y or Z errors after
|
||||
state preparation}
|
||||
\item \colorbox{red!20}{$n$-qubit X, Y or Z
|
||||
errors after any $n$-qubit gate}
|
||||
\item \colorbox{blue!20}{X errors on measurement outcomes}
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{minipage}%
|
||||
\hfill%
|
||||
\begin{minipage}{0.39\textwidth}
|
||||
\begin{figure}[H]
|
||||
\newcommand{\preperr}{\gate[style={fill=orange!20}]{\phantom{1}}}
|
||||
\newcommand{\gateerr}{\gate[style={fill=red!20}]{\phantom{1}}}
|
||||
\newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}}
|
||||
|
||||
\hspace*{-18mm}
|
||||
% tex-fmt: off
|
||||
\begin{quantikz}[row sep=2mm, column sep=2mm]
|
||||
& \preperr & \ctrl{3} & \gateerr \wire[d][3]{q} & & & & & & & & & \\
|
||||
\lstick{$\ket{\psi}$} & \preperr & & & \ctrl{2} & \gateerr \wire[d][2]{q} & \ctrl{3} & \gateerr \wire[d][3]{q} & & & & & \\
|
||||
& \preperr & & & & & & & \ctrl{2} & \gateerr \wire[d][2]{q} & & & \\
|
||||
\lstick{$\ket{0}_{\text{A}_1}$} & \preperr & \targ{} & \gateerr & \targ{} & \gateerr & & & & & \measerr & \meter{} \\
|
||||
\lstick{$\ket{0}_{\text{A}_2}$} & \preperr & & & & & \targ{} & \gateerr & \targ{} & \gateerr & \measerr & \meter{}
|
||||
\end{quantikz}
|
||||
% tex-fmt: on
|
||||
|
||||
\caption{Circuit-level noise model for the 3-qubit
|
||||
repetition code (for X errors)}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\vspace*{15mm}
|
||||
|
||||
\addreferences
|
||||
{derks_designing_2025}
|
||||
{nielsen_quantum_2010}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
@ -562,13 +929,20 @@
|
||||
\begin{itemize}
|
||||
\item Top level overview of entire system: X and Z syndrome
|
||||
extraction, logical operator measurement, where decoding
|
||||
takes place, etc. (fig. 3 of \citereference{derks_designing_2025})
|
||||
takes place, etc. (fig. 3 of
|
||||
\citereference{derks_designing_2025})
|
||||
\item For circuit-level noise, often, all error probabilities
|
||||
are set to the same value for simulations
|
||||
\citereference{fowler_high-threshold_2009}. There are
|
||||
other approaches (e.g., SDMB noise, SI noise)
|
||||
\citereference{derks_designing_2025}
|
||||
\end{itemize}
|
||||
|
||||
\vspace*{15mm}
|
||||
|
||||
\addreferences
|
||||
{derks_designing_2025}
|
||||
{fowler_high-threshold_2009}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
@ -667,7 +1041,8 @@
|
||||
\scalebox{0.7}{
|
||||
\begin{tikzpicture}[node distance=15mm and 20mm]
|
||||
\node[block] (encoding) {Encoding};
|
||||
\node[block, below=of encoding] (channel) {Quantum Channel};
|
||||
\node[block, below=of encoding] (channel)
|
||||
{Quantum Channel};
|
||||
\node[block, below=of channel] (reverse-op)
|
||||
{Reverse Operation};
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user