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