Polish second paragraphs of noise model subsecions

src/thesis/chapters/3_fault_tolerant_qec.tex

@@ -178,9 +178,10 @@ We visualize the different types of noise models in
 The simplest type of noise model is \emph{bit-flip} noise.
 This corresponds to the classical \ac{bsc}, i.e., only $X$ errors on the
 data qubits are possible \cite[Appendix~A]{gidney_new_2023}.
+This type of noise model is shown in \autoref{subfig:bit_flip}.
+
 Note that we cannot use bit-flip noise to develop fault-tolerant
 systems, as it doesnt't account for errors during the syndrome extraction.
-This type of noise model is shown in \autoref{subfig:bit_flip}.
 
 %%%%%%%%%%%%%%%%
 \subsection{Depolarizing Channel}
@@ -193,12 +194,12 @@ errors, we obtain the \emph{depolarizing channel}
 It is well-suited for modeling memory experiments, where data qubits
 are stored idly for some period of time and errors accumulate due to
 decoherence.
-Bit-flip noise and the depolarizing channel are sometimes referred to
-as \emph{code capacity noise models}.
 
 While the depolarizing channel is still not suited for the design and
 simulation of fault-tolerant systems, it is already complex enough to
 be used to gauge the suitability of a code for the \ac{qec} problem.
+Bit-flip noise and the depolarizing channel are sometimes referred to
+as \emph{code capacity noise models}.
 
 %%%%%%%%%%%%%%%%
 \subsection{Phenomenological Noise}
@@ -210,17 +211,18 @@ Here, we consider multiple rounds of syndrome measurements with a
 depolarizing channel before each round.
 Additionally, we allow for measurement errors by having $X$ error
 locations right before each measurement \cite[Appendix~A]{gidney_new_2023}.
-Note that it is enough to only consider $X$ errors at this point,
+Note that it is enough to only consider $X$ errors at these points,
 since that is the only type of error directly affecting the
 measurement outcomes.
 This model is depicted in \autoref{subfig:phenomenological}.
 
 While not fully capturing all possible error mechanisms,
-phenomenological noise is already \ldots .
-Additionally, there are applications were the consideration of
-phenomenological noise is enough.
-It can, for example, be used for \ldots \red{the design of
-fault-tolerant circuitry} \cite[Sec.~4.2]{derks_designing_2025}.
+phenomenological noise is already a significant step beyond the code
+capacity noise models.
+Additionally, there are applications where the
+consideration of phenomenological noise is enough.
+It can, for example, be used for guiding the design of fault-tolerant
+circuitry [DTTBE25, Sec. 4.2].
 
 %%%%%%%%%%%%%%%%
 \subsection{Circuit-Level Noise}
@@ -238,6 +240,9 @@ This type of noise model is shown in \autoref{subfig:circuit_level}.
 While phenomenological noise is useful for some design aspects of
 fault tolerant circuitry, for simulations, circuit-level noise should
 always be used \cite[Sec.~4.2]{derks_designing_2025}.
+Note that this introduces new challenges during the decoding process,
+as the decoding complexity is increased considerably due to the many
+error locations.
 
 \begin{figure}[t]
     \centering