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Add fault tolerance slide

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Andreas Tsouchlos 2026-01-30 17:50:19 +01:00
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1 changed files with 58 additions and 24 deletions
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src/midterm_presentation/main.tex
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@ -27,7 +27,7 @@
\usetikzlibrary{spy, external, intersections, positioning} \usetikzlibrary{spy, external, intersections, positioning}
% \ifdefined\ishandout\else % \ifdefined\ishandout\else
% \tikzexternalize \tikzexternalize
% \fi % \fi
\usepackage{pgfplots} \usepackage{pgfplots}
@ -182,9 +182,9 @@
\item Quantum computers represent information through \item Quantum computers represent information through
correlations of qubits, not their values \\ correlations of qubits, not their values \\
directly \citereference{preskill_quantum_2018} directly \citereference{preskill_quantum_2018}
\item We want to not disturb the quantum state but need to \item Errors during quantum computation are inevitable
interact with the system $\rightarrow$ Protect the state because quantum systems are fragile
with \ac{qec} \item We want to interact with the quantum state but not disturb it
\item We employ more physical qubits to introduce \item We employ more physical qubits to introduce
redundancy and use the resulting \emph{physical} state to redundancy and use the resulting \emph{physical} state to
represent the \emph{logical} state represent the \emph{logical} state
@ -243,8 +243,8 @@
% much" % much"
\begin{itemize} \begin{itemize}
\item As mentioned earlier, \ac{qec} is actually able to \item \Ac{qec} is actually able to protect the quantum state
protect the quantum state with all its correlations with all its correlations
\item We have to consider phase flip errors in addition to \item We have to consider phase flip errors in addition to
bit flip errors \citereference{roffe_quantum_2019} bit flip errors \citereference{roffe_quantum_2019}
\vspace*{-10mm} \vspace*{-10mm}
@ -345,13 +345,17 @@
\begin{itemize} \begin{itemize}
\item We entangle the state with \emph{ancilla qubits} to \item We entangle the state with \emph{ancilla qubits} to
perform syndrome measurements \citereference{nielsen_quantum_2010} 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% \item Example: The 3-qubit repetition code%
\footnote { \footnote {
Note that, for simplicity, this chosen example is a Note that, for simplicity, this chosen example is a
code that is not only able to correct X errors (bit flips) code that is only able to correct X errors (bit flips)
} % } %
\red{Do I need to show what the syndrome extraction
circuitry for Z errors looks like?}
\end{itemize} \end{itemize}
\vspace*{-10mm} \vspace*{-10mm}
@ -372,7 +376,7 @@
% tex-fmt: off % tex-fmt: off
\Qcircuit @C=1em @R=.7em { \Qcircuit @C=1em @R=.7em {
& & \ctrl{3} & \qw & \qw & \qw & \qw & \qw \\ & & \ctrl{3} & \qw & \qw & \qw & \qw & \qw \\
\ket{\psi}_\text{L} & & \qw & \ctrl{2} & \ctrl{3} & \qw & \qw & \qw \\ \ket{\psi} & & \qw & \ctrl{2} & \ctrl{3} & \qw & \qw & \qw \\
& & \qw & \qw & \qw & \ctrl{2} & \qw & \qw \\ & & \qw & \qw & \qw & \ctrl{2} & \qw & \qw \\
\ket{0}_{\text{A}_1} & & \targ & \targ & \qw & \qw & \meter & \\ \ket{0}_{\text{A}_1} & & \targ & \targ & \qw & \qw & \meter & \\
\ket{0}_{\text{A}_2} & & \qw & \qw & \targ & \targ & \meter & \ket{0}_{\text{A}_2} & & \qw & \qw & \targ & \targ & \meter &
@ -391,7 +395,6 @@
\addreferences \addreferences
{nielsen_quantum_2010} {nielsen_quantum_2010}
\stopreferences \stopreferences
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -405,23 +408,54 @@
\begin{frame} \begin{frame}
\frametitle{Fault Tolerance} \frametitle{Fault Tolerance}
\vspace*{-18mm}
\begin{itemize} \begin{itemize}
\item Quantum gates are faulty $\rightarrow$ we need QEC \\ \item The quantum gates we use for syndrome extraction are
But we do QEC with faulty gates $\rightarrow$ we need faulty themselves \\
fault tolerant QEC % $\rightarrow$ We need \emph{fault-tolerant} \ac{qec}
\footnote{ \citereference{roffe_quantum_2019}
Designing fault-tolerant circuits using detector \item A \ac{qec} procedure is said to be fault tolerant if it
error models - Gong et al, Section 4.1 can account for errors that occur at any location in the circuit
} \item We have to modify the syndrome extraction circuitry to
\item We generally do multiple rounds of syndrome extraction be fault tolerant (e.g., by using specially prepared
\item The Threshold theorem multi-qubit states for each ancilla
\setcounter{footnote}{0} \citereference{shor_fault-tolerant_1997})
\item Definition of fault tolerance \footnotemark \item We generally perform multiple rounds of syndrome extraction
\item \red{Different approaches to fault tolerance?}
\end{itemize} \end{itemize}
\vspace*{-3mm}
\begin{figure}[H]
\centering
\scalebox{0.6}{
\mbox{
% tex-fmt: off
\Qcircuit @C=1em @R=.7em {
& & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \qw & \qw & \qw & \qw & \qw \\
\ket{\psi} & & \qw & \ctrl{2} & \ctrl{3} & \qw & \qw & \qw & \qw & \ctrl{4} & \ctrl{5} & \qw & \qw & \qw \\
& & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \qw & \qw \\
\ket{0}_{\text{A}_1} & & \targ & \targ & \qw & \qw & \meter & & & & & & & \\
\ket{0}_{\text{A}_2} & & \qw & \qw & \targ & \targ & \meter & & & & & & & \\
& & & & & & \ket{0}_{\text{A}_3} & & \targ & \targ & \qw & \qw & \meter & \\
& & & & & & \ket{0}_{\text{A}_4} & & \qw & \qw & \targ & \targ & \meter & & \cdots
}
% tex-fmt: on
}
}
\caption{Multiple rounds of syndrome measurements for the
3-qubit repetition code}
\end{figure}
% \vspace*{-2mm}
\addreferences
{roffe_quantum_2019}
{shor_fault-tolerant_1997}
\stopreferences
\end{frame} \end{frame}
% TODO: Where to we introduces the different kinds of noise models?
\begin{frame} \begin{frame}
\frametitle{Noise models} \frametitle{Noise models}