diff --git a/thesis/chapters/quantum_computing.tex b/thesis/chapters/quantum_computing.tex index 99963d2..3a33796 100644 --- a/thesis/chapters/quantum_computing.tex +++ b/thesis/chapters/quantum_computing.tex @@ -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} diff --git a/thesis/chapters/stabilizer.tex b/thesis/chapters/stabilizer.tex index d66388d..56aefd7 100644 --- a/thesis/chapters/stabilizer.tex +++ b/thesis/chapters/stabilizer.tex @@ -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