fixed some stuff as suggested by Simon
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@@ -96,7 +96,7 @@ integer states
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\begin{equation}
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\label{eq:ci}
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\ket{\psi} = \sum\limits_{i = 0}^{2^n - 1} c_i \ket{i} .
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\ket{\psi} = \sum\limits_{i = 0}^{2^n - 1} c_i \ket{i}
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\end{equation}
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with the normation condition
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@@ -176,13 +176,13 @@ The matrix representation of $CX$ and $CZ$ for two qbits is given by
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\begin{postulate}
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Let
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$$\ket{\psi} = \alpha\ket{\phi_1} \otimes \ket{1}_j + \beta\ket{\phi_0} \otimes \ket{0}_j$$
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\begin{equation}\ket{\psi} = \alpha\ket{\phi_1} \otimes \ket{1}_j + \beta\ket{\phi_0} \otimes \ket{0}_j\end{equation}
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be a $n$-qbit state
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where $\ket{1}_j, \ket{0}_j$ denote the $j$-th qbit state and $|\alpha|^2 + |\beta|^2 = 1$.
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Then the measurement of the $j$-th qbit will yield
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$$\ket{\phi_1} \otimes \ket{1}_j$$
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\begin{equation}\ket{\phi_1} \otimes \ket{1}_j\end{equation}
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with probability $|\alpha|^2$ and
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$$\ket{\phi_0} \otimes \ket{0}_j$$
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\begin{equation}\ket{\phi_0} \otimes \ket{0}_j\end{equation}
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with probability $|\beta|^2$ \cite{nielsen_chuang_2010}. This is called collapse of the wave function.
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\end{postulate}
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@@ -39,7 +39,8 @@
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\title{An Efficient Quantum Computing Simulator using a Graphical Description for Many-Qbit Systems \\
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\large Bachelor Thesis}
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\author[1]{Daniel Knüttel}
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\affil[1]{Institute I - Theoretical Physics, University of Regensburg}
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\affil[1]{Institute I - Theoretical Physics, University of Regensburg\\
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Supervised by Prof. Dr. Christoph Lehner}
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\date{10.04.2020}
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\begin{document}
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\maketitle
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