slidesB.tex

\documentclass{beamer}
\usetheme{Boadilla}

\usepackage{adjustbox}
\usepackage{longtable}
\usepackage{fix-cm}
%\usepackage[section]{placeins}
%\usepackage{flafter}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage{units}
\usepackage{multirow}
\usepackage{hyperref}
\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|}}
\newcommand{\braket}[2]{\ensuremath{\left\langle#1|#2\right\rangle}}
\newcommand{\expec}[1]{\ensuremath{\left\langle#1\right\rangle}}
\newcommand{\ketbra}[2]{\ket{#1}\!\!\bra{#2}}
\newcommand{\braopket}[3]{\ensuremath{\bra{#1}#2\ket{#3}}}
\newcommand{\proj}[1]{\ketbra{#1}{#1}}
\newcommand{\sket}[1]{\ensuremath{\left|#1\right\rrangle}}
\newcommand{\sbra}[1]{\ensuremath{\left\llangle#1\right|}}
\newcommand{\sbraket}[2]{\ensuremath{\left\llangle#1|#2\right\rrangle}}
\newcommand{\sketbra}[2]{\sket{#1}\!\!\sbra{#2}}
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\newcommand{\sproj}[1]{\sketbra{#1}{#1}}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\def\Id{1\!\mathrm{l}}
\newcommand{\Tr}[0]{\mathrm{Tr}}
\providecommand{\e}[1]{\ensuremath{\times 10^{#1}}}

%Command used for python automatic substitution
\newcommand{\putfield}[2]{#2}

\newtoggle{confidences}
\newtoggle{LsAndGermsSet}
\newtoggle{debuggingaidsappendix}
\newtoggle{pixelplotsappendix}
\newtoggle{whackamoleappendix}
\toggletrue{confidences}
\toggletrue{LsAndGermsSet}
\toggletrue{debuggingaidsappendix}
\toggletrue{pixelplotsappendix}
\toggletrue{whackamoleappendix}


\hypersetup{
  pdfinfo={ Author={pyGSTi},
Title={GST on MyDefaultReportName},
Keywords={GST},
pyGSTi_Version={0.9.3},
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]]},
cptpPenaltyFactor={0},
defaultBasename={MyDefaultReportName},
defaultDirectory={temp_test_files},
distributeMethod={deriv},
fiducial_pairs={None},
gaugeOptParams={Dict[TPpenalty: 0, CPpenalty: 0, gatesMetric: frobenius, spamMetric: frobenius, itemWeights: Dict[gates: 1.0, spam: 0.001]]},
hessianProjection={optimal gate CIs},
linlogPercentile={5},
max_length_list={[0, 1, 2, 4, 8]},
memLimit={None},
minProbClip={1e-06},
minProbClipForWeighting={0.0001},
objective={chi2},
probClipInterval={[-1000000.0, 1000000.0]},
radius={0.0001},
weights={None}  }
}


\title{GST on MyDefaultReportName}
\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{$\chi^2$ progress}
\begin{frame}
\frametitle{$\chi^2$ 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 & $\chi^2$ & $k$ & $\chi^2-k$ & $\sqrt{2k}$ & $N_\sigma$ & $N_s$ & $N_p$ & Rating \\ \hline
0 & 53.25 & 52 & 1.245 & 10.2 & 0.12 & 92 & 40 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
1 & 53.25 & 52 & 1.245 & 10.2 & 0.12 & 92 & 40 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
2 & 106.4 & 128 & -21.64 & 16 & -1.35 & 168 & 40 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
4 & 353.9 & 401 & -47.15 & 28.32 & -1.66 & 441 & 40 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
8 & 690.8 & 777 & -86.18 & 39.42 & -2.19 & 817 & 40 & $\bigstar\bigstar\bigstar\bigstar\bigstar$ \\ \hline
\end{tabular}
}
\caption{Comparison between the computed and expected $\chi^2$ for different values of $L$}
\end{center}
\end{table}
\end{frame}


\subsection{Color box plot}
\begin{frame}
\frametitle{Detailed $\chi^2$ analysis}

\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesB_files/bestChi2Boxes.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 & $ \begin{array}{c} 0.04 \\ \pm 0.002 \end{array} $ & $ \begin{array}{c} 0.04 \\ \pm 0.002 \end{array} $ & $ \begin{array}{c} 0.04 \\ \pm 0.002 \end{array} $ \\ \hline
Gx & $ \begin{array}{c} 0.038 \\ \pm 0.002 \end{array} $ & $ \begin{array}{c} 0.038 \\ \pm 0.002 \end{array} $ & $ \begin{array}{c} 0.038 \\ \pm 0.002 \end{array} $ \\ \hline
Gy & $ \begin{array}{c} 0.038 \\ \pm 0.002 \end{array} $ & $ \begin{array}{c} 0.038 \\ \pm 0.002 \end{array} $ & $ \begin{array}{c} 0.038 \\ \pm 0.002 \end{array} $ \\ \hline
\end{tabular}

\\
\vspace{2em}
\\
\begin{tabular}[l]{|c|c|}
\hline
Gate & Error Generator \\ \hline
Gi & $ \left(\!\!\begin{array}{cccc}
5\e{-7} & 3\e{-4} & 3\e{-4} & 8\e{-5} \\ 
-0.001 & -0.057 & -0.007 & -0.009 \\ 
0.001 & 0.001 & -0.054 & 0.004 \\ 
0.001 & 2\e{-5} & 0.001 & -0.053
 \end{array}\!\!\right) $
 \\ \hline
Gx & $ \left(\!\!\begin{array}{cccc}
-8\e{-6} & 7\e{-5} & 4\e{-5} & 5\e{-5} \\ 
4\e{-4} & -0.051 & -0.005 & -0.006 \\ 
3\e{-4} & 4\e{-4} & -0.052 & -0.002 \\ 
-2\e{-4} & -3\e{-4} & -4\e{-5} & -0.052
 \end{array}\!\!\right) $
 \\ \hline
Gy & $ \left(\!\!\begin{array}{cccc}
2\e{-5} & -5\e{-5} & -2\e{-5} & 3\e{-5} \\ 
2\e{-4} & -0.052 & 0.007 & 5\e{-4} \\ 
3\e{-4} & 0.001 & -0.05 & 0.001 \\ 
2\e{-4} & -7\e{-6} & -0.004 & -0.053
 \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}
1 \\ 
0.949 \\ 
0.946e^{i0.00} \\ 
0.946e^{-i0.00}
 \end{array} $
 $\pm$ $ \begin{array}{c}
0.001 \\ 
0.013 \\ 
0.009e^{i0.68} \\ 
0.009e^{i0.68}
 \end{array} $
 & $ \begin{array}{c}
0.999 \\ 
-0.024 \\ 
0.011 \\ 
0.023
 \end{array} $
 & $ \begin{array}{c}
0.004 \\ 
-0.934 \\ 
0.149 \\ 
0.325
 \end{array} $
 & $ \begin{array}{c} 0.051 \\ \pm 0.013 \end{array} $ & $ \begin{array}{c} 0.054 \\ \pm 0.007 \end{array} $ \\ \hline
Gx & $ \begin{array}{c}
0.949e^{i1.57} \\ 
0.949e^{-i1.57} \\ 
1 \\ 
0.951
 \end{array} $
 $\pm$ $ \begin{array}{c}
0.003e^{i0.72} \\ 
0.003e^{i0.72} \\ 
0.001 \\ 
0.004
 \end{array} $
 & $ \begin{array}{c}
1 \\ 
0.008 \\ 
-2\e{-5} \\ 
2\e{-4}
 \end{array} $
 & $ \begin{array}{c}
0.001 \\ 
-1 \\ 
2\e{-5} \\ 
-3\e{-4}
 \end{array} $
 & $ \begin{array}{c} 0.049 \\ \pm 0.004 \end{array} $ & $ \begin{array}{c} 0.051 \\ \pm 0.002 \end{array} $ \\ \hline
Gy & $ \begin{array}{c}
1 \\ 
0.951 \\ 
0.949e^{i1.57} \\ 
0.949e^{-i1.57}
 \end{array} $
 $\pm$ $ \begin{array}{c}
0.001 \\ 
0.004 \\ 
0.003e^{i0.79} \\ 
0.003e^{i0.79}
 \end{array} $
 & $ \begin{array}{c}
1 \\ 
-8\e{-6} \\ 
0.007 \\ 
-2\e{-4}
 \end{array} $
 & $ \begin{array}{c}
-5\e{-4} \\ 
0.005 \\ 
-1 \\ 
0.001
 \end{array} $
 & $ \begin{array}{c} 0.049 \\ \pm 0.004 \end{array} $ & $ \begin{array}{c} 0.051 \\ \pm 0.002 \end{array} $ \\ \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 & $ \begin{array}{c}(0.001 \\ \pm 0.002)\pi \end{array} $ &  & $ \begin{array}{c}(0.117 \\ \pm 0.336)\pi \end{array} $ & $ \begin{array}{c}(0.549 \\ \pm 0.426)\pi \end{array} $ \\ \hline
Gx & $ \begin{array}{c}(0.5 \\ \pm 0.001)\pi \end{array} $ & $ \begin{array}{c}(0.117 \\ \pm 0.336)\pi \end{array} $ &  & $ \begin{array}{c}(0.502 \\ \pm 0.001)\pi \end{array} $ \\ \hline
Gy & $ \begin{array}{c}(0.5 \\ \pm 0.001)\pi \end{array} $ & $ \begin{array}{c}(0.549 \\ \pm 0.426)\pi \end{array} $ & $ \begin{array}{c}(0.502 \\ \pm 0.001)\pi \end{array} $ &  \\ \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|c|}
\hline
Gate & Superoperator (Pauli basis) & 95\% C.I. $\nicefrac{1}{2}$-width \\ \hline
Gi & $ \left(\!\!\begin{array}{cccc}
1 & 3\e{-4} & 3\e{-4} & 7\e{-5} \\ 
-0.001 & 0.945 & -0.006 & -0.009 \\ 
0.001 & 0.001 & 0.947 & 0.004 \\ 
0.001 & 2\e{-5} & 0.001 & 0.949
 \end{array}\!\!\right) $
 & $ \left(\!\!\begin{array}{cccc}
0.001 & 0.002 & 0.002 & 0.001 \\ 
0.002 & 0.004 & 0.004 & 0.004 \\ 
0.002 & 0.004 & 0.004 & 0.004 \\ 
0.002 & 0.004 & 0.004 & 0.004
 \end{array}\!\!\right) $
 \\ \hline
Gx & $ \left(\!\!\begin{array}{cccc}
1 & 7\e{-5} & 4\e{-5} & 4\e{-5} \\ 
4\e{-4} & 0.951 & -0.005 & -0.005 \\ 
2\e{-4} & 3\e{-4} & 4\e{-5} & -0.949 \\ 
3\e{-4} & 3\e{-4} & 0.949 & -0.002
 \end{array}\!\!\right) $
 & $ \left(\!\!\begin{array}{cccc}
0.001 & 0.001 & 0.004 & 0.004 \\ 
0.002 & 0.004 & 0.001 & 0.002 \\ 
0.001 & 0.003 & 0.003 & 0.002 \\ 
0.001 & 0.003 & 0.002 & 0.003
 \end{array}\!\!\right) $
 \\ \hline
Gy & $ \left(\!\!\begin{array}{cccc}
1 & -5\e{-5} & -2\e{-5} & 3\e{-5} \\ 
2\e{-4} & -9\e{-6} & -0.004 & 0.949 \\ 
3\e{-4} & 0.001 & 0.951 & 0.001 \\ 
-2\e{-4} & -0.949 & -0.006 & -4\e{-4}
 \end{array}\!\!\right) $
 & $ \left(\!\!\begin{array}{cccc}
0.001 & 0.001 & 0.001 & 0.001 \\ 
0.001 & 0.003 & 0.001 & 0.002 \\ 
0.002 & 0.003 & 0.004 & 0.003 \\ 
0.001 & 0.002 & 0.002 & 0.002
 \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|c|}
\hline
Operator & Matrix & Hilbert-Schmidt vector (Pauli basis) & 95\% C.I. $\nicefrac{1}{2}$-width \\ \hline
$\rho_{0}$ & $ \left(\!\!\begin{array}{cc}
0.99 & 0.001e^{-i0.13} \\ 
0.001e^{i0.13} & 0.01
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.707 \\ 
0.002 \\ 
2\e{-4} \\ 
0.693
 \end{array} $
 & $ \begin{array}{c}
0.003 \\ 
0.004 \\ 
0.005 \\ 
0.004
 \end{array} $
 \\ \hline
$E_{0}$ & $ \left(\!\!\begin{array}{cc}
0.083 & 0.002e^{i1.84} \\ 
0.002e^{-i1.84} & 0.918
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.708 \\ 
-0.001 \\ 
-0.002 \\ 
-0.591
 \end{array} $
 & $ \begin{array}{c}
0.001 \\ 
0.003 \\ 
0.004 \\ 
0.004
 \end{array} $
 \\ \hline
\end{tabular}

\\
\vspace{2em}
\\
\begin{tabular}[l]{|c|c|c|}
\hline
 & $E_{0}$ & $E_C$ \\ \hline
$\rho_{0}$ & $ \begin{array}{c} 0.091 \\ \pm 0.004 \end{array} $ & $ \begin{array}{c} 0.909 \\ \pm 0.006 \end{array} $ \\ \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}
0.96 & 0.001e^{-i1.80} & 0.002e^{-i1.48} & 0.002e^{i1.40} \\ 
0.001e^{i1.80} & 0.012 & 0.001e^{-i2.93} & 0.002e^{i3.12} \\ 
0.002e^{i1.48} & 0.001e^{i2.93} & 0.013 & 0.001e^{i0.28} \\ 
0.002e^{-i1.40} & 0.002e^{-i3.12} & 0.001e^{-i0.28} & 0.014
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.011 \\ 
0.013 \\ 
0.017 \\ 
0.96
 \end{array} $
 $\pm$ $ \begin{array}{c}
0.002 \\ 
0.002 \\ 
0.002 \\ 
0.002
 \end{array} $
 \\ \hline
Gx & $ \left(\!\!\begin{array}{cccc}
0.487 & 0.475e^{i1.57} & 0.001e^{-i1.53} & 0.001e^{i1.51} \\ 
0.475e^{-i1.57} & 0.488 & 0.001e^{-i3.10} & 0.001e^{i3.11} \\ 
0.001e^{i1.53} & 0.001e^{i3.10} & 0.013 & 8\e{-5}e^{-i1.71} \\ 
0.001e^{-i1.51} & 0.001e^{-i3.11} & 8\e{-5}e^{i1.71} & 0.012
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.011 \\ 
0.013 \\ 
0.014 \\ 
0.962
 \end{array} $
 $\pm$ $ \begin{array}{c}
0.001 \\ 
0.001 \\ 
0.001 \\ 
0.002
 \end{array} $
 \\ \hline
Gy & $ \left(\!\!\begin{array}{cccc}
0.488 & 0.002e^{-i1.55} & 0.474e^{i1.57} & 0.001e^{i1.60} \\ 
0.002e^{i1.55} & 0.012 & 0.001e^{i3.07} & 1\e{-4}e^{i2.22} \\ 
0.474e^{-i1.57} & 0.001e^{-i3.07} & 0.488 & 0.001e^{-i3.08} \\ 
0.001e^{-i1.60} & 1\e{-4}e^{-i2.22} & 0.001e^{i3.08} & 0.012
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.011 \\ 
0.012 \\ 
0.015 \\ 
0.962
 \end{array} $
 $\pm$ $ \begin{array}{c}
0.001 \\ 
0.001 \\ 
0.001 \\ 
0.002
 \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 & Matrix & Hilbert-Schmidt vector (Pauli basis) \\ \hline
$\rho_{0}$ & $ \left(\!\!\begin{array}{cc}
1 & 0 \\ 
0 & 0
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.707 \\ 
0 \\ 
0 \\ 
0.707
 \end{array} $
 \\ \hline
$E_{0}$ & $ \left(\!\!\begin{array}{cc}
0 & 0 \\ 
0 & 1
 \end{array}\!\!\right) $
 & $ \begin{array}{c}
0.707 \\ 
0 \\ 
0 \\ 
-0.707
 \end{array} $
 \\ \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}
0.003 & 0 \\ 
0.02 & 0 \\ 
0.663 & 1 \\ 
0.679 & 1 \\ 
0.747 & 1 \\ 
3.007 & 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}
\includegraphics[width=4.00in,height=2.50in,keepaspectratio]{slidesB_files/directLongSeqGSTChi2Boxes.pdf}
\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}
\includegraphics[width=4.00in,height=2.50in,keepaspectratio]{slidesB_files/directLongSeqGSTDeviationBoxes.pdf}
\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}
\includegraphics[width=4.00in,height=2.50in,keepaspectratio]{slidesB_files/smallEigvalErrRateBoxes.pdf}
\caption{Extrapolated from the smallest magnitude eigenvalue of the direct GST gate matrix.}
\end{center}
\end{figure}

\end{frame}
}{}

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

\begin{frame}
\frametitle{Iteration 1 ($L=1$): $\chi^2$ values}
\begin{figure}
\begin{center}
\includegraphics[width=1.60in,height=1.09in,keepaspectratio]{slidesB_files/L1_Chi2Boxes.pdf}
\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Iteration 2 ($L=2$): $\chi^2$ values}
\begin{figure}
\begin{center}
\includegraphics[width=2.40in,height=1.09in,keepaspectratio]{slidesB_files/L2_Chi2Boxes.pdf}
\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Iteration 3 ($L=4$): $\chi^2$ values}
\begin{figure}
\begin{center}
\includegraphics[width=3.20in,height=2.73in,keepaspectratio]{slidesB_files/L3_Chi2Boxes.pdf}
\end{center}
\end{figure}
\end{frame}

}{}


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

\begin{frame}
\frametitle{Whack-a-$\chi^2$-mole plot for $\mathrm{Gx}^{8}$}\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesB_files/whackGxMoleBoxes.pdf}
\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Whack-a-$\chi^2$-mole plot for $\mathrm{Gy}^{8}$}\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesB_files/whackGyMoleBoxes.pdf}
\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Whack-a-$\chi^2$-mole plot for $\mathrm{Gi}^{8}$}\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesB_files/whackGiMoleBoxes.pdf}
\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Summed whack-a-$\chi^2$-mole plot for $\mathrm{Gx}^{8}$}\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesB_files/whackGxMoleBoxesSummed.pdf}
\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Summed whack-a-$\chi^2$-mole plot for $\mathrm{Gy}^{8}$}\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesB_files/whackGyMoleBoxesSummed.pdf}
\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Summed whack-a-$\chi^2$-mole plot for $\mathrm{Gi}^{8}$}\begin{figure}
\begin{center}
\includegraphics[width=4.00in,height=3.00in,keepaspectratio]{slidesB_files/whackGiMoleBoxesSummed.pdf}
\end{center}
\end{figure}
\end{frame}

}{}

\end{document}