diff --git a/src/midterm_presentation/main.tex b/src/midterm_presentation/main.tex index d36bc70..722e1f4 100644 --- a/src/midterm_presentation/main.tex +++ b/src/midterm_presentation/main.tex @@ -431,36 +431,47 @@ \item Example: The 3-qubit repetition code for $\X$ errors \end{itemize} - \vspace*{-5mm} - - \begin{align*} - \bm{H} = - \begin{pmatrix} - 1 & 1 & 0 \\ - 0 & 1 & 1 - \end{pmatrix} - \end{align*} + \vspace*{5mm} \begin{figure}[H] - % \newcommand{\anyerrgate}{\gate[style={fill=red!20}]{\mathcal{E}_\text{XYZ}}} - \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}}} - \centering - % tex-fmt: off - \begin{quantikz}%[row sep=4mm, column sep=4mm] - & \ctrl{3} & & & & & \\ - \lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & \\ - & & & & \ctrl{2} & & \\ - \lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ - \lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} - \end{quantikz} - % tex-fmt: on - % \caption{Circuit-level noise model for the 3-qubit repetition code} + \hspace*{-25mm} + \begin{subfigure}{0.4\textwidth} + \centering + \begin{align*} + \bm{H} = + \begin{pmatrix} + 1 & 1 & 0 \\ + 0 & 1 & 1 + \end{pmatrix} + \end{align*} + + % \newcommand{\anyerrgate}{\gate[style={fill=red!20}]{\mathcal{E}_\text{XYZ}}} + \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}}} + + \centering + % tex-fmt: off + \begin{quantikz}%[row sep=4mm, column sep=4mm] + & \ctrl{3} & & & & & \\ + \lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & \\ + & & & & \ctrl{2} & & \\ + \lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ + \lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} + \end{quantikz} + % tex-fmt: on + \end{subfigure}% + \begin{subfigure}{0.15\textwidth} + \centering + \begin{align*} + \bm{H} \bm{y}^\text{T} = \bm{s} + \end{align*} + \vspace*{-5mm} + \end{subfigure} \end{figure} - \vspace*{5mm} + \vspace*{10mm} \addreferences {nielsen_quantum_2010} @@ -1115,8 +1126,6 @@ \vspace*{-17mm} \begin{itemize} - \item \schlagwort{Detector error matrix} $\bm{H}$ contains - modified error patterns \citereference{derks_designing_2025} \item Repetition of errors mitigated by XORing measurements \end{itemize} @@ -1171,19 +1180,21 @@ \begin{minipage}{0.6\textwidth} \newcommand\cc{\cellcolor{blue!20}} - \begin{align*} - \bm{H} = - % tex-fmt: off - \left(\begin{array}{ccccccccccccccc} - 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ - 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ - \cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ - \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ - \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 \\ - \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1 - \end{array}\right) - % tex-fmt: on - \end{align*} + \visible<3->{ + \begin{align*} + \bm{H} = + % tex-fmt: off + \left(\begin{array}{ccccccccccccccc} + 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ + \cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & \cc{0} & 1 & 1 & 0 & 1 & 0 \\ + \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{0} & \cc{1} & 0 & 1 & 1 & 0 & 1 + \end{array}\right) + % tex-fmt: on + \end{align*} + } \end{minipage} \vspace*{5mm} @@ -1192,6 +1203,8 @@ \begin{itemize} \item A detector is a parity constraint on a set of measurement outcomes + \item The \schlagwort{detector error matrix} $\bm{H}$ contains + modified error patterns \citereference{derks_designing_2025} \end{itemize} } @@ -1328,16 +1341,20 @@ \fill[kit-blue!60] ($(path picture bounding box.south west)+(0,0)$) -- ($(path picture bounding box.north west)+(0,0)$) -- - ($(path picture bounding box.north west)+(0.34,0)$) -- cycle; + ($(path picture bounding box.north + west)+(0.34,0)$) -- cycle; \fill[kit-orange!60] ($(path picture bounding box.north east)+(0,0)$) -- ($(path picture bounding box.south east)+(0,0)$) -- - ($(path picture bounding box.south east)+(-0.34,0)$) -- cycle; + ($(path picture bounding box.south + east)+(-0.34,0)$) -- cycle; \fill[kit-red!60] ($(path picture bounding box.north east)+(0,0)$) -- - ($(path picture bounding box.south east)+(-0.34,0)$) -- + ($(path picture bounding box.south + east)+(-0.34,0)$) -- ($(path picture bounding box.south west)+(0,0)$) -- - ($(path picture bounding box.north west)+(0.34,0)$) -- cycle; + ($(path picture bounding box.north + west)+(0.34,0)$) -- cycle; } }]{\phantom{1}}} @@ -1394,23 +1411,41 @@ % - Babar et al. use the SPA % - A lot of publications use Roffe's ldpc package -> min-sum + \vspace*{-10mm} + \begin{itemize} - \item A \ac{dem} combines a detector error matrix and a noise model - \item When employing \ac{bp}, the syndrome-based variant must - be used \citereference{babar_fifteen_2015} - \item The likelihoods of different error locations can be - used as priors for decoding - \vspace*{5mm} - \item Challenges - \begin{itemize} - \item Repeated syndrome measurements come with - increased decoding complexity - \citereference{gong_toward_2024} - \item Degeneracy and short cycles lead to degraded - performance of \ac{bp} \citereference{babar_fifteen_2015} - \end{itemize} + \item A \schlagwort{\acl{dem}} (DEM) combines a detector error + matrix and a noise model + \visible<2->{ + \item Tanner graph of detector error matrix of \ac{bb} code + \citereference{koutsioumpas_automorphism_2025} + } \end{itemize} + \vspace*{5mm} + + \visible<2->{ + \begin{figure}[H] + \centering + + \includegraphics[scale=5,angle=90]{res/stergios_tanner_graph} + \end{figure} + } + + \visible<3->{ + \begin{itemize} + \item Challenges + \begin{itemize} + \item Repeated syndrome measurements lead to + increased decoding complexity + \citereference{gong_toward_2024} + \item Degeneracy and short cycles lead to degraded + performance of \ac{bp} + \citereference{babar_fifteen_2015} + \end{itemize} + \end{itemize} + } + \vspace*{20mm} \addreferences @@ -1481,6 +1516,8 @@ \ac{bp} with guided decimation \end{itemize} + \vspace*{5mm} + \begin{figure} \begin{subfigure}[b]{0.5\textwidth} \newcommand{\pz}{\phantom{\bm{0}}} @@ -1559,8 +1596,6 @@ \end{subfigure}% \end{figure} - \vspace*{3mm} - \visible<2->{ \begin{itemize} \item However, no passing of soft information between windows diff --git a/src/midterm_presentation/res/stergios_tanner_graph.png b/src/midterm_presentation/res/stergios_tanner_graph.png new file mode 100644 index 0000000..89c5649 Binary files /dev/null and b/src/midterm_presentation/res/stergios_tanner_graph.png differ