slidesC.tex

\documentclass{beamer}
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\usepackage{adjustbox}
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%\usepackage[section]{placeins}
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\usepackage{pdfcomment}

\newcommand{\rrangle}{\rangle\!\rangle} \newcommand{\llangle}{\langle\!\langle}
\newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
\newcommand{\bra}[1]{\ensuremath{\left\langle#1\right|}}
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%Command used for python automatic substitution
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\newtoggle{confidences}
\newtoggle{LsAndGermsSet}
\newtoggle{debuggingaidsappendix}
\newtoggle{pixelplotsappendix}
\newtoggle{whackamoleappendix}
\togglefalse{confidences}
\toggletrue{LsAndGermsSet}
\togglefalse{debuggingaidsappendix}
\togglefalse{pixelplotsappendix}
\togglefalse{whackamoleappendix}


\hypersetup{
  pdfinfo={ Author={pyGSTi},
Title={GST on $\mathcal{D}$},
Keywords={GST},
pyGSTi_Version={0.9.1-beta},
opt_long_tables={False},
opt_table_class={pygstiTbl},
opt_template_path={None},
opt_latex_cmd={pdflatex},
L_germ_tuple_base_string_dict={Dict[[0, Gx]: {}, [0, Gy]: {}, [0, Gi]: {}, [0, GxGy]: {}, [0, GxGyGi]: {}, [0, GxGiGy]: {}, [0, GxGiGi]: {}, [0, GyGiGi]: {}, [0, GxGxGiGy]: {}, [0, GxGyGyGi]: {}, [0, GxGxGyGxGyGy]: {}, [1, Gx]: [Gx], [1, Gy]: [Gy], [1, Gi]: [Gi], [1, GxGy]: {}, [1, GxGyGi]: {}, [1, GxGiGy]: {}, [1, GxGiGi]: {}, [1, GyGiGi]: {}, [1, GxGxGiGy]: {}, [1, GxGyGyGi]: {}, [1, GxGxGyGxGyGy]: {}, [2, Gx]: [Gx]2, [2, Gy]: [Gy]2, [2, Gi]: [Gi]2, [2, GxGy]: [GxGy], [2, GxGyGi]: {}, [2, GxGiGy]: {}, [2, GxGiGi]: {}, [2, GyGiGi]: {}, [2, GxGxGiGy]: {}, [2, GxGyGyGi]: {}, [2, GxGxGyGxGyGy]: {}, [4, Gx]: [Gx]4, [4, Gy]: [Gy]4, [4, Gi]: [Gi]4, [4, GxGy]: [GxGy]2, [4, GxGyGi]: [GxGyGi], [4, GxGiGy]: [GxGiGy], [4, GxGiGi]: [GxGiGi], [4, GyGiGi]: [GyGiGi], [4, GxGxGiGy]: [GxGxGiGy], [4, GxGyGyGi]: [GxGyGyGi], [4, GxGxGyGxGyGy]: {}, [8, Gx]: [Gx]8, [8, Gy]: [Gy]8, [8, Gi]: [Gi]8, [8, GxGy]: [GxGy]4, [8, GxGyGi]: [GxGyGi]2, [8, GxGiGy]: [GxGiGy]2, [8, GxGiGi]: [GxGiGi]2, [8, GyGiGi]: [GyGiGi]2, [8, GxGxGiGy]: [GxGxGiGy]2, [8, GxGyGyGi]: [GxGyGyGi]2, [8, GxGxGyGxGyGy]: [GxGxGyGxGyGy]]},
constrainToTP={True},
defaultBasename={None},
defaultDirectory={None},
fiducial_pairs={None},
gaugeOptParams={Dict[]},
hessianProjection={optimal gate CIs},
linlogPercentile={5},
max_length_list={[0, 1, 2, 4, 8]},
memLimit={None},
minProbClip={1e-06},
minProbClipForWeighting={0.0001},
objective={logl},
probClipInterval={[-1000000.0, 1000000.0]},
radius={0.0001},
weights={None}  }
}


\title{GST on $\mathcal{D}$}
\subtitle{A projector-friendly look at your GST results}
\author{PyGSTi}
\institute{Sandia National Labs}
\date{\today}

\begin{document}

\section{Title}
\begin{frame}
\titlepage
\end{frame}

\section{Contents}
\begin{frame}
\frametitle{Outline}
\tableofcontents
\end{frame}


\iftoggle{LsAndGermsSet}{
\section{Goodness-of-model}

\subsection{$\log{\mathcal{L}}$ progress}
\begin{frame}
\frametitle{$\log{\mathcal{L}}$ vs.~GST iteration}

\begin{itemize}
\item $N_S$ is the number of gate strings
\item $N_p$ is the number of parameters
\end{itemize}

\begin{table}[h]
\begin{center}
\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}[l]{|c|c|c|c|c|c|c|c|c|}
\hline
L & $2\Delta\log(\mathcal{L})$ & $k$ & $2\Delta\log(\mathcal{L})-k$ & $\sqrt{2k}$ & $p$ & $N_s$ & $N_p$ & Rating \\ \hline
0 & 53.746 & 61 & -7.2535 & 11.045 & 0.73 & 92 & 31 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
1 & 53.747 & 61 & -7.2535 & 11.045 & 0.73 & 92 & 31 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
2 & 106.74 & 137 & -30.255 & 16.553 & 0.97 & 168 & 31 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
4 & 354.36 & 410 & -55.645 & 28.636 & 0.98 & 441 & 31 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
8 & 691.08 & 786 & -94.916 & 39.648 & 0.99 & 817 & 31 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
\end{tabular}
}
\caption{Comparison between the computed and expected $2\Delta\log{\mathcal{L}}$ for different values of $L$}
\end{center}
\end{table}
\end{frame}


\subsection{Color box plot}
\begin{frame}
\frametitle{Detailed $\log{\mathcal{L}}$ analysis}

\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesC_files/bestLogLBoxes.pdf}
\end{center}
\end{figure}
\end{frame}

}{}

\section{Best gate set estimate}

\subsection{Estimate vs.~target}
\begin{frame}
\frametitle{GST Estimate vs.~target}

%\begin{itemize}
%\item Error generator is defined by the equation $\hat{G} = G_{\mathrm{target}}e^{\mathbb{L}}$.
%\end{itemize} 

\begin{table}[h]
\begin{center}

\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}{c}
\begin{tabular}[l]{|c|c|c|c|}
\hline
Gate & \begin{tabular}{c}Process\\Infidelity\end{tabular} & \begin{tabular}{c}$\nicefrac{1}{2}$ Trace\\Distance\end{tabular} & $\nicefrac{1}{2}$ $\Diamond$-Norm \\ \hline
Gi & 0.0399 & 0.0401 & 0.0401 \\ \hline
Gx & 0.0378 & 0.0379 & 0.0379 \\ \hline
Gy & 0.0377 & 0.0378 & 0.0378 \\ \hline
\end{tabular}

\\
\vspace{2em}
\\
\begin{tabular}[l]{|c|c|}
\hline
Gate & Error Generator \\ \hline
Gi & $ \left(\!\!\begin{array}{cccc}
0 & 0 & 0 & 0 \\ 
-0.001 & -0.0569 & -0.0066 & -0.0093 \\ 
0.0004 & 0.0011 & -0.0543 & 0.0041 \\ 
0.0011 & 3\e{-5} & 0.0008 & -0.0529
 \end{array}\!\!\right) $
 \\ \hline
Gx & $ \left(\!\!\begin{array}{cccc}
0 & 0 & 0 & 0 \\ 
0.0003 & -0.0508 & -0.0051 & -0.0057 \\ 
0.0002 & 0.0003 & -0.0523 & -0.0023 \\ 
-0.0002 & -0.0003 & -0.0001 & -0.0522
 \end{array}\!\!\right) $
 \\ \hline
Gy & $ \left(\!\!\begin{array}{cccc}
0 & 0 & 0 & 0 \\ 
0.0002 & -0.0523 & 0.0065 & 0.0005 \\ 
0.0003 & 0.0011 & -0.05 & 0.0012 \\ 
0.0002 & 0.0001 & -0.0042 & -0.0525
 \end{array}\!\!\right) $
 \\ \hline
\end{tabular}

\end{tabular}
}
\end{center}
\end{table}

\end{frame}


\subsection{Gate decomposition}
\begin{frame}
\frametitle{GST Estimate decomposition}

\begin{table}[h]
\begin{center}

\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}{c}
\begin{tabular}[l]{|c|c|c|c|c|c|}
\hline
Gate & Eigenvalues & Fixed pt & Rotn. axis & Diag. decay & Off-diag. decay \\ \hline
Gi & $ \begin{array}{c}
0.9487 \\ 
0.9458e^{i0.002} \\ 
0.9458e^{-i0.002} \\ 
1
 \end{array} $
 & $ \begin{array}{c}
0.999 \\ 
-0.0222 \\ 
0.0093 \\ 
0.0204
 \end{array} $
 & $ \begin{array}{c}
0 \\ 
0.9348 \\ 
-0.1473 \\ 
-0.3233
 \end{array} $
 & 0.0513 & 0.0542 \\ \hline
Gx & $ \begin{array}{c}
0.9491e^{i1.572} \\ 
0.9491e^{-i1.572} \\ 
0.9505 \\ 
1
 \end{array} $
 & $ \begin{array}{c}
1 \\ 
0.0064 \\ 
-9\e{-6} \\ 
0.0002
 \end{array} $
 & $ \begin{array}{c}
0 \\ 
-1 \\ 
1\e{-5} \\ 
-0.0003
 \end{array} $
 & 0.0495 & 0.0509 \\ \hline
Gy & $ \begin{array}{c}
0.9489e^{i1.571} \\ 
0.9489e^{-i1.571} \\ 
0.9512 \\ 
1
 \end{array} $
 & $ \begin{array}{c}
1 \\ 
-4\e{-6} \\ 
0.0067 \\ 
-0.0002
 \end{array} $
 & $ \begin{array}{c}
0 \\ 
-0.0054 \\ 
1 \\ 
-0.0012
 \end{array} $
 & 0.0488 & 0.0511 \\ \hline
\end{tabular}

\\
\vspace{2em}
\\
\begin{tabular}[l]{|c|c|c|c|c|}
\hline
\multirow{2}{*}{Gate} & \multirow{2}{*}{Angle} & \multicolumn{3}{c|}{Angle between Rotation Axes} \\ \cline{3-5}
 & & Gi & Gx & Gy \\ \hline
Gi & 0.0006$\pi$ &  & 0.8843$\pi$ & 0.5485$\pi$ \\ \hline
Gx & 0.5004$\pi$ & 0.8843$\pi$ &  & 0.4983$\pi$ \\ \hline
Gy & 0.5001$\pi$ & 0.5485$\pi$ & 0.4983$\pi$ &  \\ \hline
\end{tabular}

\end{tabular}
}
\caption{Eigen-decomposition of estimated gates}
\end{center}
\end{table}

\end{frame}


\subsection{Raw Gates}
\begin{frame}
\frametitle{Raw GST Estimate: Gates}

\begin{table}[h]
\begin{center}
\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}[l]{|c|c|}
\hline
Gate & Superoperator (Pauli basis) \\ \hline
Gi & $ \left(\!\!\begin{array}{cccc}
1 & 0 & 0 & 0 \\ 
-0.001 & 0.9447 & -0.0063 & -0.0088 \\ 
0.0004 & 0.0011 & 0.9471 & 0.0038 \\ 
0.001 & 3\e{-5} & 0.0007 & 0.9485
 \end{array}\!\!\right) $
 \\ \hline
Gx & $ \left(\!\!\begin{array}{cccc}
1 & 0 & 0 & 0 \\ 
0.0003 & 0.9505 & -0.0049 & -0.0054 \\ 
0.0002 & 0.0003 & 0.0001 & -0.9491 \\ 
0.0002 & 0.0003 & 0.949 & -0.0022
 \end{array}\!\!\right) $
 \\ \hline
Gy & $ \left(\!\!\begin{array}{cccc}
1 & 0 & 0 & 0 \\ 
0.0002 & 0.0001 & -0.004 & 0.9488 \\ 
0.0003 & 0.0011 & 0.9512 & 0.0011 \\ 
-0.0002 & -0.949 & -0.0062 & -0.0005
 \end{array}\!\!\right) $
 \\ \hline
\end{tabular}
}
\caption{GST estimate of the logic gate operations}
\end{center}
\end{table}

\end{frame}


\subsection{Raw SPAM}
\begin{frame}
\frametitle{Raw GST Estimate: SPAM}

\begin{table}[h]
\begin{center}
\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}{c}
\begin{tabular}[l]{|c|c|c|}
\hline
Operator & Hilbert-Schmidt vector (Pauli basis) & Matrix \\ \hline
$\rho_{0}$ & $ \begin{array}{c}
0.7071 \\ 
0.0016 \\ 
0.0003 \\ 
0.6373
 \end{array} $
 & $ \left(\!\!\begin{array}{cc}
0.9506 & 0.0012e^{-i0.159} \\ 
0.0012e^{i0.159} & 0.0494
 \end{array}\!\!\right) $
 \\ \hline
$E_{0}$ & $ \begin{array}{c}
0.7077 \\ 
-0.0002 \\ 
-0.0031 \\ 
-0.6429
 \end{array} $
 & $ \left(\!\!\begin{array}{cc}
0.0458 & 0.0022e^{i1.648} \\ 
0.0022e^{-i1.648} & 0.9551
 \end{array}\!\!\right) $
 \\ \hline
\end{tabular}

\\
\vspace{2em}
\\
\begin{tabular}[l]{|c|c|c|}
\hline
 & $E_{0}$ & $E_C$ \\ \hline
$\rho_{0}$ & 0.0907 & 0.9092 \\ \hline
\end{tabular}

\end{tabular}
}
\caption{The GST estimate of the SPAM operations and dot-product probabilities}
\end{center}
\end{table}

\end{frame}


\subsection{Choi Matrices}
\begin{frame}
\frametitle{Raw GST Choi Matrices}
\begin{table}[h]
\begin{center}
\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}[l]{|c|c|c|}
\hline
Gate & Choi matrix (Pauli basis) & Eigenvalues \\ \hline
Gi & $ \left(\!\!\begin{array}{cccc}
0.9601 & 0.0008e^{i1.878} & 0.0022e^{-i1.620} & 0.0019e^{-i1.429} \\ 
0.0008e^{-i1.878} & 0.0123 & 0.0013e^{-i0.199} & 0.0022e^{-i3.092} \\ 
0.0022e^{i1.620} & 0.0013e^{i0.199} & 0.0135 & 0.0012e^{i2.928} \\ 
0.0019e^{i1.429} & 0.0022e^{i3.092} & 0.0012e^{-i2.928} & 0.0142
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.0107 \\ 
0.0127 \\ 
0.0165 \\ 
0.9601
 \end{array} $
 \\ \hline
Gx & $ \left(\!\!\begin{array}{cccc}
0.4871 & 0.4745e^{-i1.571} & 0.0014e^{-i1.601} & 0.0013e^{-i1.532} \\ 
0.4745e^{i1.571} & 0.4882 & 0.0012e^{-i0.043} & 0.0013e^{-i3.108} \\ 
0.0014e^{i1.601} & 0.0012e^{i0.043} & 0.013 & 0.0001e^{-i1.247} \\ 
0.0013e^{i1.532} & 0.0013e^{i3.108} & 0.0001e^{i1.247} & 0.0118
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.0105 \\ 
0.0129 \\ 
0.0144 \\ 
0.9622
 \end{array} $
 \\ \hline
Gy & $ \left(\!\!\begin{array}{cccc}
0.4877 & 0.0018e^{i1.539} & 0.4745e^{i1.571} & 0.0013e^{-i1.607} \\ 
0.0018e^{-i1.539} & 0.0123 & 0.0007e^{i0.063} & 0.0001e^{-i2.116} \\ 
0.4745e^{-i1.571} & 0.0007e^{-i0.063} & 0.4879 & 0.0013e^{-i0.046} \\ 
0.0013e^{i1.607} & 0.0001e^{i2.116} & 0.0013e^{i0.046} & 0.0121
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.0107 \\ 
0.0123 \\ 
0.0148 \\ 
0.9623
 \end{array} $
 \\ \hline
\end{tabular}
}
\caption{Choi matrix representation of the GST estimated gateset.}
\end{center}
\end{table}
\end{frame}



\section{Inputs to GST}

\subsection{Target gate set}
\begin{frame}
\frametitle{Target SPAM}

\begin{table}[h]
\begin{center}
\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}[l]{|c|c|c|}
\hline
Operator & Hilbert-Schmidt vector (Pauli basis) & Matrix \\ \hline
$\rho_{0}$ & $ \begin{array}{c}
0.7071 \\ 
0 \\ 
0 \\ 
0.7071
 \end{array} $
 & $ \left(\!\!\begin{array}{cc}
1 & 0 \\ 
0 & 0
 \end{array}\!\!\right) $
 \\ \hline
$E_{0}$ & $ \begin{array}{c}
0.7071 \\ 
0 \\ 
0 \\ 
-0.7071
 \end{array} $
 & $ \left(\!\!\begin{array}{cc}
0 & 0 \\ 
0 & 1
 \end{array}\!\!\right) $
 \\ \hline
\end{tabular}
}
\caption{State preparation and measurement targets}
\end{center}
\end{table}

\end{frame}


\begin{frame}
\frametitle{Target Gates}

\begin{table}[h]
\begin{center}
\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}[l]{|c|c|c|c|}
\hline
Gate & Superoperator (Pauli basis) & Rotation axis & Angle \\ \hline
Gi & $ \left(\!\!\begin{array}{cccc}
1 & 0 & 0 & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0 \\ 
1 \\ 
0 \\ 
0
 \end{array} $
 & 0$\pi$ \\ \hline
Gx & $ \left(\!\!\begin{array}{cccc}
1 & 0 & 0 & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 0 & -1 \\ 
0 & 0 & 1 & 0
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0 \\ 
1 \\ 
0 \\ 
0
 \end{array} $
 & 0.5$\pi$ \\ \hline
Gy & $ \left(\!\!\begin{array}{cccc}
1 & 0 & 0 & 0 \\ 
0 & 0 & 0 & 1 \\ 
0 & 0 & 1 & 0 \\ 
0 & -1 & 0 & 0
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0 \\ 
0 \\ 
1 \\ 
0
 \end{array} $
 & 0.5$\pi$ \\ \hline
\end{tabular}
}
\caption{Summary of target gates}
\end{center}
\end{table}

\end{frame}


\iftoggle{LsAndGermsSet}{
\subsection{Fiducials and Germs}
\begin{frame}
\frametitle{Fiducial and Germ Gate Strings}

\begin{table}[h]
\footnotesize
\begin{center}
\begin{minipage}[b]{0.40\linewidth}
\centering
\adjustbox{max width=\linewidth}{
\begin{tabular}[l]{|c|c|c|}
\hline
 & \multicolumn{2}{c|}{Fiducials} \\ \hline
\# & Prep. & Measure \\ \hline
1 & $$ & $$ \\ \hline
2 & $\mbox{Gx}$ & $\mbox{Gx}$ \\ \hline
3 & $\mbox{Gy}$ & $\mbox{Gy}$ \\ \hline
4 & $\mbox{Gx}\cdot\mbox{Gx}$ & $\mbox{Gx}\cdot\mbox{Gx}$ \\ \hline
5 & $\mbox{Gx}\cdot\mbox{Gx}\cdot\mbox{Gx}$ & $\mbox{Gx}\cdot\mbox{Gx}\cdot\mbox{Gx}$ \\ \hline
6 & $\mbox{Gy}\cdot\mbox{Gy}\cdot\mbox{Gy}$ & $\mbox{Gy}\cdot\mbox{Gy}\cdot\mbox{Gy}$ \\ \hline
\end{tabular}

}
\end{minipage}
\begin{minipage}[b]{0.40\linewidth}
\adjustbox{max width=\linewidth}{
\begin{tabular}[l]{|c|c|}
\hline
\# & Germ \\ \hline
1 & $\mbox{Gx}$ \\ \hline
2 & $\mbox{Gy}$ \\ \hline
3 & $\mbox{Gi}$ \\ \hline
4 & $\mbox{Gx}\cdot\mbox{Gy}$ \\ \hline
5 & $\mbox{Gx}\cdot\mbox{Gy}\cdot\mbox{Gi}$ \\ \hline
6 & $\mbox{Gx}\cdot\mbox{Gi}\cdot\mbox{Gy}$ \\ \hline
7 & $\mbox{Gx}\cdot\mbox{Gi}\cdot\mbox{Gi}$ \\ \hline
8 & $\mbox{Gy}\cdot\mbox{Gi}\cdot\mbox{Gi}$ \\ \hline
9 & $\mbox{Gx}\cdot\mbox{Gx}\cdot\mbox{Gi}\cdot\mbox{Gy}$ \\ \hline
10 & $\mbox{Gx}\cdot\mbox{Gy}\cdot\mbox{Gy}\cdot\mbox{Gi}$ \\ \hline
11 & $\mbox{Gx}\cdot\mbox{Gx}\cdot\mbox{Gy}\cdot\mbox{Gx}\cdot\mbox{Gy}\cdot\mbox{Gy}$ \\ \hline
\end{tabular}

}
\end{minipage}
\end{center}
\end{table}

\end{frame}

}{}


\subsection{Dataset}
\begin{frame}
\frametitle{Dataset Overview}

\begin{table}[h]
\begin{center}
\adjustbox{max height=\dimexpr\textheight-5.5cm\relax, max width=\textwidth}{
\begin{tabular}[l]{|c|c|}
\hline
Quantity & Value \\ \hline
Number of strings & 817 \\ \hline
Gate labels & Gx, Gy, Gi \\ \hline
SPAM labels & plus, minus \\ \hline
Counts per string & 1000 \\ \hline
\begin{tabular}{c}Gram singular values\\ (right column gives the values\\when using the target gate set)\end{tabular} & \small$ \begin{array}{cc}
0.0029 & 0 \\ 
0.0205 & 0 \\ 
0.6626 & 1 \\ 
0.6789 & 1 \\ 
0.7472 & 1 \\ 
3.0074 & 3
 \end{array} $
 \\ \hline
\end{tabular}
}
\caption{General dataset properties}
\end{center}
\end{table}

\end{frame}



\iftoggle{debuggingaidsappendix}{
\section{Debugging Aids}

\begin{frame}
\frametitle{Direct-GST}

\begin{figure}
\begin{center}

\caption{How well direct GST analysis of each base sequence fits the observed data.}
\end{center}
\end{figure}

\end{frame}


\begin{frame}
\frametitle{Direct-GST Deviation}

\begin{figure}
\begin{center}

\caption{For each base sequence, the increase in ``upper bound of fidelity with unitary'' when using the direct-GST result for a gate sequence instead of the process given by the best gateset.}
\end{center}
\end{figure}

\end{frame}


\begin{frame}
\frametitle{Per-gate error rates}

\begin{figure}
\begin{center}

\caption{Extrapolated from the smallest magnitude eigenvalue of the direct GST gate matrix.}
\end{center}
\end{figure}

\end{frame}
}{}

\iftoggle{pixelplotsappendix}{
\section{Pixel Plots}

}{}


\iftoggle{whackamoleappendix}{
\section{Whack-a-mole}

}{}

\end{document}