Incorporate Jonathan's corrections to the introduction

src/thesis/chapters/1_introduction.tex

@@ -17,7 +17,7 @@ factorization \cite{shor_algorithms_1994}.
 
 Similar to the way classical computers are built from bits and gates,
 quantum computers are built from \emph{qubits} and \emph{quantum gates}.
-Because of quantum entanglement, it is not enough to consider the
+Because of quantum entanglement, it does not suffice to consider the
 qubits individually, we also have to consider correlations between them.
 For a system of $n$ qubits, this makes the state space grow with
 $2^n$ instead of linearly with $n$, as would be the case for a classical system
@@ -30,12 +30,11 @@ what provides them with their power \cite[Sec.~2.1]{roffe_decoding_2020}.
 Realizing algorithms that leverage these quantum-mechanical effects
 requires hardware that can execute long quantum computations reliably.
 This poses a problem, because the qubits making up current devices
-are difficult to sufficiently isolate from their environment
+consistently interact with their environment \cite[Sec.~1]{roffe_quantum_2019}.
-\cite[Sec.~1]{roffe_quantum_2019}.
+This interaction acts as a continuous small-scale measurement, an
-Their interaction with the environment acts as a continuous small-scale
+effect we call \emph{decoherence} of the stored quantum state, which
-measurement, an effect we call \emph{decoherence} of the stored quantum
+results in errors on the qubits.
-state.
+Decoherence is the reason large systems do not exhibit visible quantum
-Decoherence is the reason large systems don't exhibit visible quantum
 properties at human scales \cite[Sec.~1]{gottesman_stabilizer_1997}.
 
 % Intro to QEC
@@ -45,8 +44,8 @@ It addresses the issue by encoding the information of $k$
 \emph{logical qubits} into a larger number $n>k$ of \emph{physical
 qubits}, in close analogy to classical channel coding
 \cite[Sec.~1]{roffe_quantum_2019}.
-The redundancy introduced this way can then be used to restore
+The redundancy introduced this way can then be used to detect and
-the quantum state, should it be disturbed.
+correct a corrupted the quantum state.
 The quantum setting imposes some important constraints that do not exist in the
 classical case, however \cite[Sec.~2.4]{roffe_quantum_2019}:
 \begin{itemize}
@@ -54,7 +53,7 @@ classical case, however \cite[Sec.~2.4]{roffe_quantum_2019}:
     \item In addition to the bit-flip errors we know from the
         classical setting, qubits are subject to \emph{phase-flips}.
     \item We are not allowed to directly measure the encoded qubits,
-        as that would disturb their quantum states.
+        as that would collapse their quantum states.
 \end{itemize}
 We can deal with the first constraint by not duplicating information, instead
 spreading the quantum state across the physical qubits
@@ -74,8 +73,8 @@ subsequent decoding process on the measured syndrome.
 
 Another difference between \ac{qec} and classical channel coding is
 the resource constraints.
-For \ac{qec}, low latency matters more than low overall computational
+For \ac{qec}, achieving low latency matters more than having a low
-complexity, due to the backlog problem
+overall computational complexity, due to the backlog problem
 \cite[Sec.~II.G.3.]{terhal_quantum_2015}: Certain gates turn
 single-qubit errors into multi-qubit ones, so errors must be
 corrected beforehand.
@@ -83,7 +82,7 @@ A \ac{qec} system that is too slow accumulates a backlog at these points,
 causing exponential slowdown.
 
 Several code constructions have been proposed for \ac{qec} codes over the years.
-Topological codes such as surface codes have been the industry
+Topological codes, such as surface codes, have been the industry
 standard for experimental applications for a long time
 \cite[Sec.~I]{koutsioumpas_colour_2025}, due to their
 reliance on only local connections between qubits
@@ -116,15 +115,15 @@ focusing only on the relationship between possible errors
 and their effects on the syndrome \cite[Sec.~1.4.3]{higgott_practical_2024}.
 A \emph{detector error matrix} is generated from the circuit, which is
 used for decoding instead of the original check matrix.
-Decoding under a \ac{dem} poses a challenge with respect to the
+The detector error matrix is much larger than the
-latency constraint.
-This is because the detector error matrix is much larger than the
 check matrix of the underlying code, since it needs to represent many
 more error locations.
 For example, in our experiments using the $\llbracket 144,12,12
 \rrbracket$ \ac{bb} code with $12$ syndrome measurement rounds, the
 number of \acp{vn} grew from $144$ to $9504$ and the number of
 \acp{cn} grew from $72$ to $1008$.
+Therefore, decoding under a \ac{dem} poses a challenge with respect to the
+latency constraint.
 
 To keep the latency of \ac{dem} decoding manageable, one approach is
 \emph{sliding-window decoding}.
@@ -154,7 +153,7 @@ We propose \emph{warm-start sliding-window decoding}, in which the
 \ac{bp} messages from the overlap region of the previous window are
 reused to initialize \ac{bp} in the current window in place of the
 standard cold-start initialization.
-We formulate the warm start first for plain \ac{bp} and then for
+We formulate the warm start for standard \ac{bp} and for
 \ac{bpgd}, a variant of \ac{bp} with better convergence properties
 for \ac{qec} codes.
 The decoders are evaluated by Monte Carlo simulation on the
@@ -166,6 +165,7 @@ low-latency operation.
 
 % Outline of the Thesis
 
+This thesis is structured as follows:
 \Cref{ch:Fundamentals} reviews the fundamentals of classical and
 quantum error correction.
 On the classical side, it covers binary linear block codes,

src/thesis/main.tex

@@ -123,6 +123,11 @@
 % \listoftables
 % \include{abbreviations}
 
+% \cleardoublepage
+% \phantomsection
+% \addcontentsline{toc}{chapter}{List of Abbreviations}
+% \printacronyms
+
 \bibliography{lib/cel-thesis/IEEEabrv,src/thesis/bibliography}
 
 \end{document}