Add fault tolerance slide

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Andreas Tsouchlos 2026-01-30 17:50:19 +01:00
parent 95631f90cf
commit 90f421fbfe

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@ -27,7 +27,7 @@
\usetikzlibrary{spy, external, intersections, positioning}
% \ifdefined\ishandout\else
% \tikzexternalize
\tikzexternalize
% \fi
\usepackage{pgfplots}
@ -182,9 +182,9 @@
\item Quantum computers represent information through
correlations of qubits, not their values \\
directly \citereference{preskill_quantum_2018}
\item We want to not disturb the quantum state but need to
interact with the system $\rightarrow$ Protect the state
with \ac{qec}
\item Errors during quantum computation are inevitable
because quantum systems are fragile
\item We want to interact with the quantum state but not disturb it
\item We employ more physical qubits to introduce
redundancy and use the resulting \emph{physical} state to
represent the \emph{logical} state
@ -243,8 +243,8 @@
% much"
\begin{itemize}
\item As mentioned earlier, \ac{qec} is actually able to
protect the quantum state with all its correlations
\item \Ac{qec} is actually able to protect the quantum state
with all its correlations
\item We have to consider phase flip errors in addition to
bit flip errors \citereference{roffe_quantum_2019}
\vspace*{-10mm}
@ -345,13 +345,17 @@
\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%
\footnote {
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}
\vspace*{-10mm}
@ -372,7 +376,7 @@
% tex-fmt: off
\Qcircuit @C=1em @R=.7em {
& & \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 \\
\ket{0}_{\text{A}_1} & & \targ & \targ & \qw & \qw & \meter & \\
\ket{0}_{\text{A}_2} & & \qw & \qw & \targ & \targ & \meter &
@ -391,7 +395,6 @@
\addreferences
{nielsen_quantum_2010}
\stopreferences
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -405,23 +408,54 @@
\begin{frame}
\frametitle{Fault Tolerance}
\vspace*{-18mm}
\begin{itemize}
\item Quantum gates are faulty $\rightarrow$ we need QEC \\
But we do QEC with faulty gates $\rightarrow$ we need
fault tolerant QEC %
\footnote{
Designing fault-tolerant circuits using detector
error models - Gong et al, Section 4.1
}
\item We generally do multiple rounds of syndrome extraction
\item The Threshold theorem
\setcounter{footnote}{0}
\item Definition of fault tolerance \footnotemark
\item \red{Different approaches to fault tolerance?}
\item The quantum gates we use for syndrome extraction are
faulty themselves \\
$\rightarrow$ We need \emph{fault-tolerant} \ac{qec}
\citereference{roffe_quantum_2019}
\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
\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
\citereference{shor_fault-tolerant_1997})
\item We generally perform multiple rounds of syndrome extraction
\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}
% TODO: Where to we introduces the different kinds of noise models?
\begin{frame}
\frametitle{Noise models}