diff --git a/src/thesis/chapters/4_decoding_under_dems.tex b/src/thesis/chapters/4_decoding_under_dems.tex index d08be46..e2ea8bd 100644 --- a/src/thesis/chapters/4_decoding_under_dems.tex +++ b/src/thesis/chapters/4_decoding_under_dems.tex @@ -72,7 +72,7 @@ problem into many smaller ones that can be solved more efficiently. % warm-start decoding. Or just go into warm-start decoding) We will start by briefly reviewing the existing work related to sliding-window decoding, -before focusing on one specific incarnation. +before focusing on one specific realization. We will then introduce a modification to the existing algorithm and perform numerical simulations to evaluate it. @@ -110,100 +110,6 @@ Each of these windows is then decoded separately. \subsection{Review of Existing Literature} \label{subsec:Review of Existing Literature} -% Description of the figure - -\Cref{fig:literature} gives an overview over the existing body of work -related to sliding-window decoding. -The papers \cite{huang_improved_2023} and \cite{huang_increasing_2024} are -lumped together, as they share the same content; -one is simply preprint published earlier. -We will only refer to \cite{huang_increasing_2024} in the following. -\cite{kang_quits_2025} is somewhat special in that the authors focus -more on the introduction of a new simluator framework they call -QUITS, rather than the performance of sliding-window decoding itself. -\cite{gong_toward_2024} and \cite{kang_quits_2025} have made their -software freely available online% -\footnote{ - https://github.com/mkangquantum/quits -}% -\footnote{ - https://github.com/gongaa/SlidingWindowDecoder -}. -A final thing to note is that \cite{dennis_topological_2002} never -explicitly mention sliding windows, they call their scheme -``overlapping recovery''. - -% Topological vs QLDPC - -Research has focused on two categories of \ac{qec} codes, topological -and \ac{qldpc} codes. -Most of the work on topological codes has treated surface codes, -with the exception of \cite{kuo_fault-tolerant_2024} where toric -codes were considered. -With regard to \ac{qldpc} codes, in \cite{huang_increasing_2024} -they examine \emph{hypergraph product} (\acs{hgp}) and -\emph{lifted-product} (\acs{lp}) codes. -HGP codes are constructed from the product of two classical codes, -while LP codes generalize this construction by additionally applying -a lift to reduce the qubit overhead. -In \cite{kang_quits_2025}, \emph{balanced product codes} (\acs{bpc}) -are additionally considered. -Finally, in \cite{gong_toward_2024} the authors explore \ac{bb} codes. - -% Sequential vs parallel - -After having divided the whole circuit into separate windows, the question -arises of how exactly to realize the decoding. -There are two main approaches, with differing mechanisms of reducing -the latency. -Some papers decode the sliding windows in a parallel fashion. -The benefit in this case is the option to more effectively utilize -classical hardware for decoding. -Others choose a sequential approach. -Here, decoding can start earlier, as there is no need to wait for the -syndrome measurements of all windows before beginning with the decoding. -With the exception of \cite{dennis_topological_2002}, literature -treating topological codes has mostly focused on parallel decoding -while literature treating \ac{qldpc} codes has wholely considered -sequential decoding. - -% Deep-dive into QLDPC methods - -\renewcommand{\arraystretch}{1.1} -\setlength{\tabcolsep}{12pt} -\begin{table}[t] - \centering - \caption{Experimental conditions for papers related to \ac{qldpc} codes.} - \vspace*{3mm} - \label{table:experimental_conditions} - \begin{tabular}{l|ccc} - % tex-fmt: off - Publication & Code & Noise Model & Decoder \\ \hline - \hspace{-2.5mm}\cite{huang_improved_2023},\cite{huang_increasing_2024} & \acs{hgp}, \acs{lp} & Phenomenological noise & \acs{bp} + \acs{osd} \\ - \hspace{-2.5mm}\cite{gong_toward_2024} & \acs{bb} & Circuit-level noise & \acs{bp} + \acs{gdg} \\ - \hspace{-2.5mm}\cite{kang_quits_2025} & \acs{hgp}, \acs{lp}, \acs{bpc} & Circuit-level noise & \acs{bp} + \ac{osd} - % tex-fmt: on - \end{tabular} -\end{table} - -For this work, the publications treating \ac{qldpc} codes are -especially interesting. -The experimental conditions for these are summarized in -\Cref{table:experimental_conditions}. -As we noted above, \ac{hgp} and \ac{lp} codes are considered in -\cite{huang_increasing_2024}, -\ac{hgp}, \ac{lp} and \ac{bpc} codes are considered in \cite{kang_quits_2025}, -and \ac{bb} codes are considered in \cite{gong_toward_2024}. -The employed noise models also differ; -\cite{huang_increasing_2024} use phenomenological noise, while -\cite{gong_toward_2024} and \cite{kang_quits_2025} use circuit-level noise. -Finally, \cite{gong_toward_2024} introduce their own variation of -\ac{bpgd}, \ac{bp} with \ac{gdg}, while \cite{huang_increasing_2024} -and \cite{kang_quits_2025} use \ac{bp} + \ac{osd}. -We would additionally like to note that only in -\cite{gong_toward_2024} and \cite{kang_quits_2025} do the authors -explicitly work with the \ac{dem} formalism. - \begin{figure}[t] \centering @@ -290,6 +196,103 @@ explicitly work with the \ac{dem} formalism. \label{fig:literature} \end{figure} +% Some general notes + +\Cref{fig:literature} gives an overview over the existing body of work +related to sliding-window decoding. +The papers \cite{huang_improved_2023} and \cite{huang_increasing_2024} are +lumped together, as they share the same content; +one is simply preprint published earlier. +We will only refer to \cite{huang_increasing_2024} in the following. +\cite{kang_quits_2025} is somewhat special in that the authors focus +more on the introduction of a new simluator framework they call +QUITS, rather than the performance of sliding-window decoding itself. +\cite{gong_toward_2024} and \cite{kang_quits_2025} have made their +software freely available online% +\footnote{ + https://github.com/mkangquantum/quits +}% +\footnote{ + https://github.com/gongaa/SlidingWindowDecoder +}. +A final thing to note is that \cite{dennis_topological_2002} never +explicitly mention sliding windows, they call their scheme +``overlapping recovery''. + +% Topological vs QLDPC + +Research has focused on two categories of \ac{qec} codes, topological +and \ac{qldpc} codes. +Most of the work on topological codes has treated surface codes, +with the exception of \cite{kuo_fault-tolerant_2024} where toric +codes were considered. +With regard to \ac{qldpc} codes, in \cite{huang_increasing_2024} +they examine \emph{hypergraph product} (\acs{hgp}) and +\emph{lifted-product} (\acs{lp}) codes. +HGP codes are constructed from the product of two classical codes, +while LP codes generalize this construction by additionally applying +a lift to reduce the qubit overhead. +In \cite{kang_quits_2025}, \emph{balanced product codes} (\acs{bpc}) +are additionally considered. +Like HGP codes, BPC codes are derived from a product construction, +but exploit an additional symmetry to yield fewer physical qubits for +the same code parameters. +Finally, in \cite{gong_toward_2024} the authors explore \ac{bb} codes. + +% Sequential vs parallel + +After having divided the whole circuit into separate windows, the question +arises of how exactly to realize the decoding. +There are two main approaches, with differing mechanisms of reducing +the latency. +Some papers decode the sliding windows in a parallel fashion. +The benefit in this case is the option to more effectively utilize +classical hardware for decoding. +Others choose a sequential approach. +Here, decoding can start earlier, as there is no need to wait for the +syndrome measurements of all windows before beginning with the decoding. +With the exception of \cite{dennis_topological_2002}, literature +treating topological codes has mostly focused on parallel decoding +while literature treating \ac{qldpc} codes has wholely considered +sequential decoding. + +% Deep-dive into QLDPC methods + +For this work, the publications treating \ac{qldpc} codes are +especially interesting. +The experimental conditions for these are summarized in +\Cref{table:experimental_conditions}. +As we noted above, \ac{hgp} and \ac{lp} codes are considered in +\cite{huang_increasing_2024}, +\ac{hgp}, \ac{lp} and \ac{bpc} codes are considered in \cite{kang_quits_2025}, +and \ac{bb} codes are considered in \cite{gong_toward_2024}. +The employed noise models also differ; +\cite{huang_increasing_2024} use phenomenological noise, while +\cite{gong_toward_2024} and \cite{kang_quits_2025} use circuit-level noise. +Finally, \cite{gong_toward_2024} introduce their own variation of +\ac{bpgd}, \ac{bp} with \ac{gdg}, while \cite{huang_increasing_2024} +and \cite{kang_quits_2025} use \ac{bp} + \ac{osd}. +We would additionally like to note that only in +\cite{gong_toward_2024} and \cite{kang_quits_2025} do the authors +explicitly work with the \ac{dem} formalism. + +\renewcommand{\arraystretch}{1.1} +\setlength{\tabcolsep}{12pt} +\begin{table}[t] + \centering + \caption{Experimental conditions for papers related to \ac{qldpc} codes.} + \vspace*{3mm} + \label{table:experimental_conditions} + \begin{tabular}{l|ccc} + % tex-fmt: off + Publication & Code & Noise Model & Decoder \\ \hline + \hspace{-2.5mm}\cite{huang_improved_2023},\cite{huang_increasing_2024} & \acs{hgp}, \acs{lp} & Phenomenological noise & \acs{bp} + \acs{osd} \\ + \hspace{-2.5mm}\cite{gong_toward_2024} & \acs{bb} & Circuit-level noise & \acs{bp} + \acs{gdg} \\ + \hspace{-2.5mm}\cite{kang_quits_2025} & \acs{hgp}, \acs{lp}, \acs{bpc} & Circuit-level noise & \acs{bp} + \ac{osd} + % tex-fmt: on + \end{tabular} +\end{table} + % \red{ % Existing work % \begin{itemize} @@ -381,12 +384,6 @@ error matrix is divided into overlapping windows. The algorithm detailed here follows \cite{kang_quits_2025}, whose work is in turn based on \cite{huang_increasing_2024}. -\red{ - \begin{itemize} - \item QUITS views sliding-window decoding more separately - \end{itemize} -} - \content{Possibly go into the fact that current sliding-window approaches don't differentiate clearly between the sliding-window part and the decoder part. This work aims to extend the @@ -394,9 +391,6 @@ work is in turn based on \cite{huang_increasing_2024}. different decoder parts. Combine this with QUITS modular structure for sliding window decoding} -We build on the approach taken by \cite{huang_increasing_2024} and -\cite{gong_toward_2024}. - % High-level overview of Sliding-Window decoding \content{Benefits of sliding-window decoding (lower latency due to @@ -427,7 +421,7 @@ with processing'' some VNs)} \content{4. Decode next window} \content{(?) Explicitly mention we don't reuse existing messages?} -\begin{figure}[H] +\begin{figure}[t] \centering \hspace*{-114mm}%