From 27f13c1db0977b6086547a1e4f32da3172394277 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Thu, 30 Apr 2026 14:05:32 +0200 Subject: [PATCH] Write chapter 4 intro --- src/thesis/acronyms.tex | 10 +++ src/thesis/chapters/3_fault_tolerant_qec.tex | 1 + src/thesis/chapters/4_decoding_under_dems.tex | 77 ++++++++++++++++++- .../chapters/5_conclusion_and_outlook.tex | 4 + src/thesis/main.tex | 2 +- 5 files changed, 91 insertions(+), 3 deletions(-) diff --git a/src/thesis/acronyms.tex b/src/thesis/acronyms.tex index abd52f5..997bbd6 100644 --- a/src/thesis/acronyms.tex +++ b/src/thesis/acronyms.tex @@ -28,6 +28,16 @@ long=normalized min-sum } +\DeclareAcronym{osd}{ + short=OSD, + long=ordered statistics decoding +} + +\DeclareAcronym{aed}{ + short=AED, + long=automorphism ensemble decoding +} + \DeclareAcronym{bsc}{ short=BSC, long=binary symetric channel diff --git a/src/thesis/chapters/3_fault_tolerant_qec.tex b/src/thesis/chapters/3_fault_tolerant_qec.tex index 56caa74..f0b5fea 100644 --- a/src/thesis/chapters/3_fault_tolerant_qec.tex +++ b/src/thesis/chapters/3_fault_tolerant_qec.tex @@ -1,4 +1,5 @@ \chapter{Fault-Tolerant Quantum Error Correction} +\label{ch:Fault tolerance} % Intro diff --git a/src/thesis/chapters/4_decoding_under_dems.tex b/src/thesis/chapters/4_decoding_under_dems.tex index 13a6dbb..5283bae 100644 --- a/src/thesis/chapters/4_decoding_under_dems.tex +++ b/src/thesis/chapters/4_decoding_under_dems.tex @@ -1,14 +1,87 @@ % TODO: Make all [H] -> [t] \chapter{Decoding under Detector Error Models} -% Intro +In \Cref{ch:Fundamentals} we introduced the fundamentals of classical +error correction, before moving on to quantum information science and +finally combining the two in \acf{qec}. +In \Cref{ch:Fault tolerance} we then turned to fault-tolerance, with +a focus on a specific way of implementing it, called \acfp{dem}. +In this chapter, we move on from the fundamental concepts and examine +how to apply them in practice. +Specifically, we concern ourselves with the practical aspects of decoding +under \acp{dem}. -\content{Intro} +We investigate decoding \acf{qldpc} codes under \acp{dem} in particular. +We focus on \ac{qldpc} codes, as they have emerged as leading +candidates for practical quantum error correction, offering the +ability to encode more logical qubits per physical qubit than surface +codes while maintaining favorable threshold properties +\cite[Sec.~1]{bravyi_high-threshold_2024}. +Because of this, the decoding algorithms we consider will all be +related to \acf{bp} in some way. +Our aim is to build a fault-tolerant \ac{qec} system that works well +even under consideration of circuit-level noise. +We must overcome two main challenges to achieve this. + +First, recall the problems related to degeneracy, which is inherent +to quantum codes. +Because multiple minimum-weight codewords exist, the \ac{bp} +algorithm becomes uncertain of the direction to proceed in. +Additionally, the commutativity conditions of the stabilizers +necessitate the existence of short cycles. +These two aspects together lead to substantial convergence problems +of \ac{bp} for quantum codes, when it is used on it's own. + +Second, the consideration of circuit-level noise introduces many more +error locations into the circuit. +Using \acp{dem}, we construct a new circuit code and model each of +these error locations as a new \acf{vn}. +We also perform multiple rounds of syndrome measuremetns, +exacerbating the problem. +This leads to a massively increased computational complexity and +latency of the decoding process. +In our experiments using the $\llbracket 144,12,12 \rrbracket$ +\acf{bb} code with $12$ syndrome measurement rounds, for example, the +number of \acp{vn} was increased from $144$ to $9504$, and the +number of \acfp{cn} was increased from $72$ to $1008$. + +The first problem is not inherent to \acp{dem} or fault-tolerance, +but rather quantum codes in general. +Many different approaches to solving it exist, usually centered +around somehow modifying \ac{bp}. +The most popular approach by far is combining a few initial +iterations of \ac{bp} with a second decoding algorithm, \ac{osd} +\cite{roffe_decoding_2020}. +Other approaches exist, such as \ac{aed} +\cite{koutsioumpas_automorphism_2025}, were multiple variations of +the code are decoded simultaneously to increase the chances of convergence. +Here, we will focus on the \acf{bpgd} algorithm +\cite{yao_belief_2024} we already introduced in \Cref{ch:Fundamentals}, +for reasons that will become clear later in the chapter. + +The second problem is inherent to decoding using \acp{dem}. +This is an area that has been less studied. +As we saw in \Cref{sec:Quantum Error Correction}, for \ac{qec}, +latency is the main constraint, not raw computational complexity, +and reducing latency is the main goal of the existing literature. +This is generally done using windowing approaches; either +sliding-window based, where the latency is reduced due an earlier +start to the decoding process \cite{kuo_fault-tolerant_2024}% +\cite{huang_improved_2023}\cite{huang_increasing_2024}\cite{gong_toward_2024}, +or by decoding multiple windows in parallel +\cite{skoric_parallel_2023}\cite{tan_scalable_2023}. +This work is based on the sliding-window method. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Sliding-Window Decoding} \label{sec:Sliding-Window Decoding} +\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 + sliding-window part in a general fashion that is compatible with many +different decoder parts.} + % Intro \content{Callback to previous chapter} diff --git a/src/thesis/chapters/5_conclusion_and_outlook.tex b/src/thesis/chapters/5_conclusion_and_outlook.tex index e72e0bd..f88fc24 100644 --- a/src/thesis/chapters/5_conclusion_and_outlook.tex +++ b/src/thesis/chapters/5_conclusion_and_outlook.tex @@ -1 +1,5 @@ \chapter{Conclusion and Outlook} + +\content{\textbf{Ideas for further research}} +\content{Softer way of decimating VNs} + diff --git a/src/thesis/main.tex b/src/thesis/main.tex index d767888..ffad638 100644 --- a/src/thesis/main.tex +++ b/src/thesis/main.tex @@ -51,7 +51,7 @@ % \newcommand{\red}[1]{\textcolor{red}{#1}} -\newcommand{\content}[1]{\noindent\indent\red{[#1]}\\} +\newcommand{\content}[1]{\noindent\indent\red{[#1]\\}} \newcommand{\figwidth}{10cm} \newcommand{\figheight}{7.5cm}