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midterm: Update bib file; Add input/internal/output error diagram

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Andreas Tsouchlos
2026-02-02 14:03:36 +01:00
parent d59b2e68d9
commit 1a613066e2
2 changed files with 331 additions and 71 deletions
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src/midterm_presentation/main.tex
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@@ -88,6 +88,21 @@
long=Calderbank Shor Steane
}
\DeclareAcronym{bb}{
short=BB,
long=bivariate bicycle
}
\DeclareAcronym{dem}{
short=DEM,
long=detector error model
}
\DeclareAcronym{bp}{
short=BP,
long=belief propagation
}
%
%
% Document body
@@ -226,7 +241,7 @@
\begin{frame}
\frametitle{Peculiarities of the Quantum Setting}
\vspace*{-5mm}
\vspace*{-18mm}
% Related interesting stuff
% - No cloning theorem -> Not replication of state, protection
@@ -244,48 +259,67 @@
% much"
\begin{itemize}
\item \Ac{qec} is actually able to protect the quantum state
with all its correlations
\item \Ac{qec} is actually able to protect the actual quantum state
\item Similar to bits and gates, quantum systems are built on
top of qubits and quantum gates
\item We have to consider phase flip errors in addition to
bit flip errors \citereference{roffe_quantum_2019}
\vspace*{-10mm}
\begin{figure}[H]
\centering
\begin{subfigure}{0.5\textwidth}
\centering
\end{itemize}
\begin{align*}
\ket{0} &\rightarrow \ket{1} \\
\ket{1} &\rightarrow \ket{0}
\end{align*}
\vspace*{-3mm}
\caption{Bit flip (X) error}
\end{subfigure}%
\begin{subfigure}{0.5\textwidth}
\centering
\begin{figure}[H]
\centering
\begin{subfigure}{0.32\textwidth}
\centering
\begin{align*}
\ket{0} &\rightarrow \phantom{-}\ket{0} \\
\ket{1} &\rightarrow -\ket{1}
\end{align*}
\begin{align*}
\ket{0} &\rightarrow \ket{1} \\
\ket{1} &\rightarrow \ket{0}
\end{align*}
\caption{Phase flip (Z) error}
\end{subfigure}
\end{figure}
\item \red{Introduce Y errors}
\caption{Bit flip (X) error}
\end{subfigure}%
\begin{subfigure}{0.32\textwidth}
\centering
\begin{align*}
\ket{0} &\rightarrow \phantom{-}\ket{0} \\
\ket{1} &\rightarrow -\ket{1}
\end{align*}
\caption{Phase flip (Z) error}
\end{subfigure}%
\begin{subfigure}{0.32\textwidth}
\centering
\begin{align*}
\ket{0} &\rightarrow \phantom{-j}\ket{1} \\
\ket{1} &\rightarrow -j\ket{0}
\end{align*}
\caption{Y error: Combination of X and Z}
\end{subfigure}
\end{figure}
\vspace*{-3mm}
\begin{itemize}
\item Measuring the qubits directly destroys superpositions
and entanglement \\
$\rightarrow$ We generally only work with the syndrome,
which we can measure \citereference{nielsen_quantum_2010}
\item We don't care about restoring the specific codeword,
only finding the coset it's in
\item Sometimes superposition permits multiple equivalent
solutions to the decoding problem (\emph{quantum
degeneracy}) \citereference{roffe_decoding_2020}
\end{itemize}
\vspace*{15mm}
\vspace*{7mm}
\addreferences
{nielsen_quantum_2010}
{roffe_quantum_2019}
{roffe_decoding_2020}
\stopreferences
\end{frame}
@@ -342,10 +376,6 @@
\begin{itemize}
\item We entangle the state with \emph{ancilla qubits} to
perform syndrome measurements \citereference{nielsen_quantum_2010}
\item \red{Implicitly introduce the concept of a quantum gate
by mentioning CNOT gates?}
\item \red{Mention that we can perform syndrome extraction
with just CNOTs and H? (and find citation)}
\item \red{Do I need to show what the syndrome extraction
circuitry for Z errors looks like?}
\item Example: The 3-qubit repetition code%
@@ -406,15 +436,47 @@
\begin{frame}
\frametitle{Fault Tolerance}
\vspace*{-10mm}
\vspace*{-15mm}
\begin{itemize}
\item The quantum gates we use for syndrome extraction are
faulty themselves \\
$\rightarrow$ We need \emph{fault-tolerant} \ac{qec}
\item A \ac{qec} procedure is said to be fault tolerant if it
can account for errors that occur at any location in the
circuit \citereference{roffe_quantum_2019}
\item A \ac{qec} procedure is said to be fault tolerant if,
in addition to correcting \emph{input errors}, the spread
of \emph{internal errors} is sufficiently limited
\citereference{derks_designing_2025}
\end{itemize}
\vspace*{3mm}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\node[rectangle, draw, fill=orange!20, minimum
height=3cm, minimum width=3.5cm, align=left] at (0,0)
(internal) {Internal\\ Errors};
\node[signal, draw, fill=blue!20, minimum height=3cm,
minimum width=4cm, align=left, signal pointer angle=140]
at (-3.7, 0) (input) {Input\\ Errors};
\node at (2.5,0) {\huge =};
\node[rectangle, draw, fill=red!20, minimum height=3cm,
minimum width=3.5cm, align=left] at (5,0) (output)
{Output\\ Errors};
\node[above] at (input.north) {\small Input State};
\node[above] at (internal.north) {\small QEC};
\node[above] at (output.north) {\small Output State};
\end{tikzpicture}
\end{figure}
\vspace*{3mm}
\begin{itemize}
\item We have to modify the syndrome extraction circuitry to
be fault tolerant (e.g., by using specially prepared
multi-qubit states for each ancilla
@@ -422,28 +484,11 @@
\item We generally perform multiple rounds of syndrome extraction
\end{itemize}
% \vspace*{1mm}
%
% \begin{figure}[H]
% \centering
% % tex-fmt: off
% \begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,q,q,n,n}]
% & \ctrl{3} & & & & & & \ctrl{5} & & & & \\
% \lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & \setwiretype{n}\ldots \\
% & & & & \ctrl{2} & & & & & & \ctrl{4} & \\
% \lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & & & & & & & \meter{} \\
% \lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & & & & & & & \meter{} \\
% & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} \\
% & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{}
% \end{quantikz}
% % tex-fmt: on
% \end{figure}
\vspace*{25mm}
\vspace*{10mm}
\addreferences
{roffe_quantum_2019}
{shor_fault-tolerant_1997}
{derks_designing_2025}
\stopreferences
\end{frame}
@@ -586,7 +631,7 @@
\end{frame}
\begin{frame}[fragile]
\frametitle{The Measurement Syndrome Matrix II}
\frametitle{The Measurement Syndromemani Matrix II}
\vspace*{-18mm}
@@ -923,15 +968,84 @@
\begin{frame}
\frametitle{The Detector Error Matrix II}
\vspace*{-17mm}
\begin{itemize}
\item \red{Highlight SC-LDPC like structure}
\item Visualization of general process \red{Deal with 3-qubit
state (somehow represent arbitrary qubit state)}
\end{itemize}
\vspace*{5mm}
\begin{figure}[H]
\centering
\tikzset{
gate/.style={
draw, %line width=1pt,
minimum height=2cm,
}
}
% tex-fmt: off
\begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}]
& \gate[3]{SE_1} & & \gate[3]{SE_2} & & \gate[3]{SE_3} & & \gate[3]{SE_4} & \\
\lstick{$\ket{\psi}$} & & & & & & & & & \setwiretype{n} & \ldots \\
& \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\
& \ctrl[wire=c]{0}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \\
& & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \\
& \gate[1]{\bm{D}_1} & & \gate[1]{\bm{D}_2} & & \gate[1]{\bm{D}_3} & & \gate[1]{\bm{D}_4} & \\
\end{quantikz}
% tex-fmt: on
\end{figure}
\begin{itemize}
\item E.g., for \ac{bb} codes, the resulting detector
error matrix under circuit-level noise has the form
\citereference{gong_toward_2024}
\end{itemize}
\vspace*{-15mm}
\begin{align*}
\bm{H} =
\begin{pmatrix}
\bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} & \bm{0}
& \bm{0} & \cdots \\
\bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & \bm{0}
& \bm{0} & \\
\bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & \bm{H}_0
& \bm{H}_1 & \\
\bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0}
& \bm{H}_2 & \\
\vdots & & & &
& & \ddots
\end{pmatrix}
\end{align*}
\vspace*{3mm}
\addreferences
{gong_toward_2024}
\stopreferences
\end{frame}
\begin{frame}[fragile]
\frametitle{Noise models}
\frametitle{Noise Model Types}
\vspace*{-7mm}
% Related interesting stuff
% - The difference between an n-qubit error and multiple
% simultaneous single-qubit errors is that in the n-qubit case,
% the errors can be correlated (e.g., XX more probable than XI)
\vspace*{-15mm}
\begin{itemize}
\item The noise model assigns a likelihood to the occurrence
of each error
\end{itemize}
\vspace*{7mm}
\begin{minipage}{0.60\textwidth}
\begin{itemize}
@@ -982,29 +1096,38 @@
\end{figure}
\end{minipage}
\vspace*{15mm}
\vspace*{10mm}
\addreferences
{derks_designing_2025}
{nielsen_quantum_2010}
{derks_designing_2025}
\stopreferences
\end{frame}
\begin{frame}
\frametitle{Challenges}
\frametitle{Decoding using Detector Error Models}
\begin{itemize}
\item \red{Multiple different errors are summarized
$\rightarrow$ short cycles \& degeneracy}
\footnote{
\texttt{
\red{https://www.math.cit.tum.de/fileadmin/w00ccg/math/\_my\_direct\_uploads/Dan\_Browne.pdf}
}
}
\\
\red{$\rightarrow$ We generally don't use "normal BP" (BP
+ OSD, BPGD, etc.)}
\item A \ac{dem} combines a detector error matrix and a noise model
\item The likelihoods of different error locations can be
used as priors for decoding
\vspace*{5mm}
\item Challenges
\begin{itemize}
\item Repeated syndrome measurements come with
increased decoding complexity
\citereference{gong_toward_2024}
\item Degeneracy and short cycles lead to degraded
performance of \ac{bp} \citereference{babar_fifteen_2015}
\end{itemize}
\end{itemize}
\vspace*{20mm}
\addreferences
{babar_fifteen_2015}
{gong_toward_2024}
\stopreferences{}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -1024,6 +1147,8 @@
\item Give overview of existing research
\item Explain exactly what they do in the main paper I am
basing my work on
\item \red{$\rightarrow$ We generally don't use "normal BP"
(BP + OSD, BPGD, etc.)}
\end{itemize}
\end{frame}