diff --git a/src/midterm_presentation/main.tex b/src/midterm_presentation/main.tex index 81d87c1..c08ba00 100644 --- a/src/midterm_presentation/main.tex +++ b/src/midterm_presentation/main.tex @@ -49,10 +49,11 @@ \usepackage{braket} \usepackage{quantikz} \usepackage{nicematrix} +\usepackage{xpatch} \title{Fault Tolerant Quantum Error Correction} \subtitle{Master's Thesis Midterm Presentation} -\author[Tsouchlos]{Andreas Tsouchlos} +\author[Andreas]{Andreas Tsouchlos} \date[]{} \DeclareFieldFormat{note}{} @@ -77,6 +78,14 @@ \newcommand{\Y}{\textcolor{kit-red}{\bm{Y}}} \newcommand{\I}{\bm{I}} +\xpatchcmd{\fullwire} +{\arrow[arrows,start anchor=#2startone,end anchor=#2endone] +{#1}\arrow[arrows,start anchor=#2starttwo,end anchor=#2endtwo,#4] {#1}} +{\arrow[arrows,start anchor=#2startone,end anchor=#2endone,#4] +{#1}\arrow[arrows,start anchor=#2starttwo,end anchor=#2endtwo,#4] {#1}} +{\typeout{Successfully patched fullwire for classical wires}} +{\typeout{Failed to patch fullwire for classical wires}} + % % % Acronyms @@ -120,7 +129,7 @@ \DeclareAcronym{scldpc}{ short=SC-LDPC, - long=spatially - coupled low - density parity - check + long=spatially-coupled low-density parity-check } % @@ -819,7 +828,7 @@ \hspace*{-75mm} \scalebox{0.85}{ \parbox{.5\linewidth}{% - \vspace*{22.5mm} + \vspace*{22.6mm} \begin{gather*} \bm{\Omega} = \left( @@ -1100,34 +1109,46 @@ \end{frame} % TODO: Journal not showing for derks_designing_2025 -\begin{frame} +\begin{frame}[fragile] \frametitle{The Detector Error Matrix I} \vspace*{-17mm} \begin{itemize} - \item A detector is a parity constraint on a set of - measurement outcomes \citereference{derks_designing_2025} - \item Each column of the \schlagwort{detector error matrix} $\bm{H}$ - corresponds to a detector pattern an error produces - \item We can mitigate the propagation of errors into - subsequent rounds by XORing the measurements, i.e., - defining detectors appropriately; this is equivalent to - row additions + \item \schlagwort{Detector error matrix} $\bm{H}$ contains + modified error patterns + \item Repetition of errors mitigated by XORing measurements \end{itemize} \begin{minipage}{0.5\textwidth} \begin{figure}[H] + \newcommand{\redwire}[1]{ + \wire[r][#1][style={draw=red, line width=2pt, double}]{q} + } + \newcommand{\inwire}{ + \wire[l][1][style={draw=red, line width=2pt}]{q} + } + \newcommand{\redtarg}{ + \targ[style={draw=red,line width=2pt}]{}% + \setwiretype{n}% + } + \newcommand{\redctrl}[1]{ + \ctrl[style={draw=red,fill=red, line width=2pt}]{0}% + \wire[d][#1][style={draw=red, line width=2pt, double}]{q} + } + \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}} + \newcommand{\redgate}[1]{\gate[style={draw=red,fill=red!20}]{\textcolor{red}{#1}}} + \centering % tex-fmt: off \begin{quantikz}[row sep=4mm, column sep=4mm, wire types={n,n,n,n,n,n}] - & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & \ctrl[vertical wire=c]{2} & & \gate{D_1} \\ - & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & & \ctrl[vertical wire=c]{2} & \gate{D_2} \\ - & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & \ctrl[vertical wire=c]{2} & & \targ{} & & \gate{D_3} \\ - & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & \ctrl[vertical wire=c]{2} & & \targ{} & \gate{D_4} \\ - & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & \targ{} & & & & \gate{D_5} \\ - & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & \targ{} & & & \gate{D_6} + & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & \ctrl[vertical wire=c]{2} & & \gate{D_1} \\ + & \meter{}\wire[l][1]{q}\wire[r][1]{c} & \setwiretype{c} & & & & \ctrl[vertical wire=c]{2} & \gate{D_2} \\ + & \redmeter{}\inwire\redwire{6} & & \redctrl{2} & & \targ{} & & \redgate{D_3} \\ + & \redmeter{}\inwire\redwire{6} & & & \redctrl{2} & & \targ{} & \redgate{D_4} \\ + & \redmeter{}\inwire\redwire{2} & & \redtarg\wire[r][4]{c} & & & & \gate{D_5} \\ + & \redmeter{}\inwire\redwire{3} & & & \redtarg\wire[r][3]{c} & & & \gate{D_6} \end{quantikz} % tex-fmt: on \end{figure} @@ -1150,6 +1171,11 @@ \end{align*} \end{minipage} + \begin{itemize} + \item A detector is a parity constraint on a set of + measurement outcomes \citereference{derks_designing_2025} + \end{itemize} + \vspace*{5mm} \addreferences @@ -1168,7 +1194,7 @@ % qubit state)} \end{itemize} - \vspace*{5mm} + \vspace*{2mm} \begin{figure}[H] \centering @@ -1182,7 +1208,7 @@ % tex-fmt: off \begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}] - & \gate[3]{SE_1} & & \gate[3]{SE_2} & & \gate[3]{SE_3} & & \gate[3]{SE_4} & \\ + & \gate[3]{\text{SE}_1} & & \gate[3]{\text{SE}_2} & & \gate[3]{\text{SE}_3} & & \gate[3]{\text{SE}_4} & \\ \lstick{$\ket{\psi}$} & & & & & & & & & \setwiretype{n} & \ldots \\ & \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\ & \ctrl[wire=c]{0}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \\ @@ -1193,30 +1219,24 @@ \end{figure} \begin{itemize} - \item E.g., for \ac{bb} codes, the resulting detector - error matrix under circuit-level noise has the form + \item E.g., for \ac{bb} codes under circuit-level noise \citereference{gong_toward_2024} \end{itemize} - \vspace*{-15mm} + \vspace*{-4mm} \begin{align*} \bm{H} = \begin{pmatrix} - \bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} & \bm{0} - & \bm{0} & \cdots \\ - \bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & \bm{0} - & \bm{0} & \\ - \bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & \bm{H}_0 - & \bm{H}_1 & \\ - \bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0} - & \bm{H}_2 & \\ - \vdots & & & & - & & \ddots + \bm{H}_0 & \bm{H}_1 & & & & & \\ + & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & & & \\ + & & & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & \\ + & & & & & \bm{H}_2 & \\ + & & & & & & & \ddots \end{pmatrix} \end{align*} - \vspace*{3mm} + \vspace*{5mm} \addreferences {gong_toward_2024} @@ -1348,17 +1368,15 @@ \vspace*{-18mm} \begin{itemize} - \item Many window-based approaches exist to combat the - decoding complexity + \item Decoding complexity addressed with window-based approaches \begin{itemize} - \item Parallel decoding of syndromes - \citereference{skoric_parallel_2023} - \item Using sliding windows + \item Parallel decoding \citereference{skoric_parallel_2023} + \item Sliding windows \citereference{huang_improved_2023} \citereference{gong_toward_2024} \end{itemize} - \item To deal with the degraded \ac{bp} performance, it is - usually modified or extended + \item Degraded \ac{bp} performance addressed with + modification or extension \begin{itemize} \item \Ac{osd} post-processing \citereference{roffe_decoding_2020} @@ -1388,48 +1406,16 @@ \begin{frame}[fragile] \frametitle{Sliding-Window Decoding} - \vspace*{-18mm} + \vspace*{-15mm} \begin{itemize} - \item The sliding window approach taken in - \citereference{gong_toward_2024} resembles a \ac{scldpc} - code decoder - \item However, they don't pass soft information between - windows (only update of syndrome based on hard decision - in previous window) + \item Approach taken in \citereference{gong_toward_2024} + resembles \acf{scldpc} code + \item They try \ac{bp} + \ac{osd} and a modification of + \ac{bp} with guided decimation \end{itemize} - \vspace*{-8mm} - \begin{figure} - \begin{subfigure}[b]{0.5\textwidth} - \begin{gather*} - \begin{pmatrix} - \bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} & - \bm{0} & \bm{0} \\ - \bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & - \bm{0} & \bm{0} \\ - \bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & - \bm{H}_0 & \bm{H}_1 - \end{pmatrix} - \begin{pmatrix} - \hat{\bm{e}}_0 \\ - \vdots \\ - \hat{\bm{e}}_5 - \end{pmatrix} - = - \begin{pmatrix} - \bm{s}_1 \\ - \bm{s}_2 \\ - \bm{s}_3 - \end{pmatrix} \\[5mm] - \bm{s}_2' = \bm{s}_2 + \bm{H}_2 \hat{\bm{e}}_1 - \end{gather*} - - \vspace*{2mm} - - \caption{Equations for the decoding of the first window} - \end{subfigure}% \begin{subfigure}[b]{0.5\textwidth} \newcommand{\pz}{\phantom{\bm{0}}} \[ @@ -1477,14 +1463,45 @@ \caption{Visualization of sliding window procedure} \end{subfigure}% + \begin{subfigure}[b]{0.5\textwidth} + \begin{gather*} + \begin{pmatrix} + \bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} & + \bm{0} & \bm{0} \\ + \bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & + \bm{0} & \bm{0} \\ + \bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & + \bm{H}_0 & \bm{H}_1 + \end{pmatrix} + \begin{pmatrix} + \hat{\bm{e}}_0 \\ + \vdots \\ + \hat{\bm{e}}_5 + \end{pmatrix} + = + \begin{pmatrix} + \bm{s}_1 \\ + \bm{s}_2 \\ + \bm{s}_3 + \end{pmatrix} \\[5mm] + \bm{s}_2' = \bm{s}_2 + \bm{H}_2 \hat{\bm{e}}_1 + \end{gather*} + + \vspace*{2mm} + + \caption{Equations for the decoding of the first window} + \end{subfigure}% \end{figure} - \begin{itemize} - \item They try \ac{bp} + \ac{osd} and a modification of - \ac{bp} with guided decimation - \end{itemize} + \vspace*{3mm} - \vspace*{5mm} + \visible<2->{ + \begin{itemize} + \item However, no passing of soft information between windows + \end{itemize} + } + + \vspace*{8mm} \addreferences {gong_toward_2024} @@ -1492,34 +1509,44 @@ \end{frame} %%%%%%%%%%%%%%%% -\subsection{Proposed Research} -\label{subsec:Proposed Research} +\subsection{Future Work} +\label{subsec:Future Work} \begin{frame} - \frametitle{Proposed Research} + \frametitle{Future Work} - \vspace*{-5mm} + \vspace*{-15mm} \begin{itemize} + \item Completed work + \begin{itemize} + \item Review of literature on fault-tolerant \ac{qec} + \item Identification of research gap + \end{itemize} + \vspace*{7mm} \item Research gap \begin{itemize} \item Existing literature into circuit-level noise - fails to properly consider the \ac{scldpc} like - structure of the detector error matrix + fails to properly consider \ac{scldpc}-like + structure \end{itemize} \vspace*{7mm} - \item Proposed Methodology - \begin{itemize} - \item Adapt modified guided decimation decoder from - \citereference{gong_toward_2024} to pass soft information - \item Investigate performance of different - modifications of \ac{bp} for "inner decoder" - (e.g., quaternary neural \ac{bp} - \citereference{miao_quaternary_2025}) - \end{itemize} + \visible<2->{ + \item Future directions + \begin{itemize} + \item Adapt modified guided decimation decoder from + \citereference{gong_toward_2024} to pass soft + information + \item Investigate performance of different + modifications of \ac{bp} for "inner decoder" + (e.g., quaternary neural \ac{bp} + \citereference{miao_quaternary_2025}) + \item \ldots + \end{itemize} + } \end{itemize} - \vspace*{15mm} + \vspace*{10mm} \addreferences {gong_toward_2024} @@ -1536,18 +1563,6 @@ \subsection{The Code and Other Parameters} \label{subsec:The Code and Other Parameters} -% TODO: I have to mention somewhere that I am interested in decoder -% design specifically -\begin{frame} - \frametitle{Memory and Stability experiments} - - \begin{itemize} - \item \red{What is a memory experiment? Communications Engineering - view (what are my inputs and outpus? What do I expect?)} - \item \red{What is a stability experiment?} - \end{itemize} -\end{frame} - \begin{frame} \frametitle{Noise Models and Figures of Merit} @@ -1579,34 +1594,23 @@ \label{subsec:Proposed Methodology} \begin{frame} - \frametitle{Proposed Simulation Methodology} + \frametitle{Conclusion} - \begin{itemize} - \item \red{Noise model} - \item \red{Memory or stability experiment} - \item \red{Figure of merit: Footprint plot} - \item \red{Comparison with BB code also simulated by - \citereference{gong_toward_2024}} - \item \red{Comparison with surface code} - \end{itemize} - - \vspace*{15mm} - - \addreferences - {gong_toward_2024} - \stopreferences -\end{frame} - -\begin{frame}[t] - \frametitle{Questions} + \vspace*{-15mm} \begin{minipage}[c]{0.65\textwidth} - \centering - - \LARGE Thank you for your attention!\\ Any questions? + \begin{itemize} + \item \red{Noise model} + \item \red{Memory or stability experiment} + \item \red{Figure of merit: Footprint plot} + \item \red{Comparison with BB code also simulated by + \citereference{gong_toward_2024}} + \item \red{Comparison with surface code} + \end{itemize} \end{minipage}% \begin{minipage}[c]{0.35\textwidth} \centering + \pause \begin{figure}[H] \centering @@ -1616,7 +1620,6 @@ \end{tikzpicture} \end{figure} \end{minipage} - \end{frame} \appendix