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U not SU

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Daniel Knüttel 2020-03-16 13:16:33 +01:00
parent edaa8ac4a4
commit 8e27775b0e
2 changed files with 3 additions and 3 deletions
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4
thesis/chapters/quantum_computing.tex
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@ -14,8 +14,8 @@
are used in these cases.
\end{definition}
A gate acting on a qbit is a unitary operator $G \in SU(2)$. One can show that
$\forall G \in SU(2)$ $G$ can be approximated arbitrarily good as a product of unitary generator matrices
A gate acting on a qbit is a unitary operator $G \in U(2)$. One can show that
$\forall G \in U(2)$ $G$ can be approximated arbitrarily good as a product of unitary generator matrices
\cite[Chapter 4.3]{kaye_ea2007}\cite[Chapter 2]{marquezino_ea_2019};
common choices for the generators are $ X, H, R_{\phi}$ or $Z, H, R_{\phi}$ with
\label{ref:singleqbitgates}

2
thesis/chapters/stabilizer.tex
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@ -172,7 +172,7 @@ a set of stabilizers.
\begin{definition}
For $n$ qbits
\begin{equation}
C_n := \left\{U \in SU(2^n) \middle| \forall p \in P_n: UpU^\dagger \in P_n \right\}
C_n := \left\{U \in U(2^n) \middle| \forall p \in P_n: UpU^\dagger \in P_n \right\}
\end{equation}
is called the Clifford group. $C_1 =: C_L$ is called the local Clifford