Fix typos

src/thesis/chapters/3_fault_tolerant_qec.tex

@@ -20,7 +20,7 @@ introduces two new challenges \cite[Sec.~4]{gottesman_introduction_2009}:
     \item \ac{qec} systems are themselves partially implemented in
         quantum hardware. In addition to the errors we have
         originally introduced them for, these systems must
-        be able to acount for the fact they are implemented on noisy
+        be able to account for the fact they are implemented on noisy
         hardware themselves.
 \end{itemize}
 In the literature, both of these points are viewed under the umbrella
@@ -190,7 +190,7 @@ data qubits are possible \cite[Appendix~A]{gidney_new_2023}.
 This type of noise model is shown in \Cref{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.
+systems, as it does not account for errors during the syndrome extraction.
 
 %%%%%%%%%%%%%%%%
 \subsection{Depolarizing Channel}
@@ -230,7 +230,7 @@ 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
+It can, for example, be used to guide the design of fault-tolerant
 circuitry [DTTBE25, Sec. 4.2].
 
 %%%%%%%%%%%%%%%%
@@ -238,7 +238,7 @@ circuitry [DTTBE25, Sec. 4.2].
 \label{subsec:Circuit-Level Noise}
 
 The most general type of noise model is \emph{circuit-level noise}.
-Here we not only consider noise inbetween syndrome extraction rounds
+Here we not only consider noise between syndrome extraction rounds
 and at the measurements, but at each gate.
 Specifically, we allow arbitrary $n$-qubit Pauli errors after each
 $n$-qubit gate \cite[Def.~2.5]{derks_designing_2025}.
@@ -277,7 +277,8 @@ error locations.
 \section{Detector Error Models}
 \label{sec:Detector Error Models}
 
-\emph{Detector error models} (\acsp{dem}) constitue a standardized framework for
+\emph{Detector error models} (\acsp{dem}) constitute a standardized
+framework for
 passing information about a circuit used for \ac{qec} to a decoder.
 They are also useful as a theoretical tool to aid in the design of
 fault-tolerant \ac{qec} schemes.
@@ -439,7 +440,7 @@ circuit and each \ac{cn} corresponds to a syndrome measurement.
 % Mathematical definition
 
 We describe the circuit code using the \emph{measurement syndrome
-matrix} matrix $\bm{\Omega} \in \mathbb{F}_2^{M\times N}$, with
+matrix} $\bm{\Omega} \in \mathbb{F}_2^{M\times N}$, with
 \begin{align*}
     \Omega_{\ell,i} =
     \begin{cases}
@@ -824,7 +825,7 @@ For two detector matrices $\bm{D}_1$ and $\bm{D}_2$, as long as
 they describe the same set of possible measurement outcomes (under
 the absence of noise) and thus the same circuit.
 In fact, as long as \Cref{eq:kern_condition} holds, the detector
-error matrices we construct from them can distinguish between the
+error matrices constructed from them can distinguish between the
 same pairs of error sets \cite[Lemma~6]{derks_designing_2025}.
 To see this, we note that we can distinguish between two circuit
 error vectors $\bm{e}_1$ and $\bm{e}_2$ as long as they do not
@@ -1121,6 +1122,6 @@ include many utilities for building syndrome extraction circuitry automatically.
 The user has to define most, if not all, of the circuit manually,
 depending on the code in question.
 This is somewhat natural, as stim is meant first and foremost as a
-simulator, and circuit generation is contigent upon the \ac{qec}
+simulator, and circuit generation is contingent upon the \ac{qec}
 scheme in question.