diff --git a/src/thesis/chapters/3_fault_tolerant_qec.tex b/src/thesis/chapters/3_fault_tolerant_qec.tex index 2728f22..2efaf62 100644 --- a/src/thesis/chapters/3_fault_tolerant_qec.tex +++ b/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