Write stim subsection

src/thesis/chapters/3_fault_tolerant_qec.tex

@@ -1045,8 +1045,6 @@ circuit-level noise model to the same value, the physical error rate $p$.
 
 % Per-round LER
 
-\content{Introduce logical error rate}
-
 % TODO: Introduce the logical error rate
 Another aspect that is important to consider is the meaning of the
 logical error rate in the context of a \ac{qec} system with multiple
@@ -1101,20 +1099,35 @@ topic to our own work.
 \subsection{Stim}
 \label{subsec:Stim}
 
-As we noted in \autoref{subsec:Measurement Syndrome Matrix}, to
-obtain a measurement syndrome matrix we must propagate Pauli frames
+It is not immediately apparent how the \ac{dem} will look from looking
+at a code's \ac{pcm}, because it heavily depends on the exact circuit
+construction and choice of noise model.
+As we noted in \autoref{subsec:Measurement Syndrome Matrix}, we can
+obtain a measurement syndrome matrix by propagating Pauli frames
 through the circuit.
-\red{[This is where stim comes into play]}
+The standard choice of simulation tool used for this purpose is
+\emph{stim}%
+\footnote{https://github.com/quantumlib/Stim}
+\cite{gidney_stim_2021}, which is available as a Python 3
+pypi package.
+In fact, it was in this tool that the concept of the \ac{dem} was
+first introduced.
 
-\content{Circuit code heavily depends on the exact circuit construction}
-\content{Not easy to predict how errors at different locations
-propagate through the circuit an what detectors they affect}
+One capability of stim, and \acp{dem} in general, that we didn't go
+into detail about in this chapter is the merging of error mechanisms.
+Since \acp{dem} differentiate errors based on their effect on the
+measurements and not on their type and location, it is natural to
+group errors that have the same effect.
+This slightly lowers the computational complexity of decoding, as the
+number of resulting \acp{vn} is reduced.
 
-\content{Merging of error mechanisms}
+While stim is a useful tool for circuit simulation, it doesn't
+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}
+scheme in question.
 
-\content{Stim is were DEMs were first introduced}
-
-\content{Stim is a software package that generates DEMs from circuits}
-\content{The user still has to define the circuit themselves, and
-especially the detectors \cite[Sec~2.5]{derks_designing_2025}}
+\content{Introduce logical error rate}