fixed some stuff as suggested by Simon

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2020-03-27 15:38:43 +01:00
parent 798793bdf5
commit 361167f5de
13 changed files with 20 additions and 19 deletions

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@@ -96,7 +96,7 @@ integer states
\begin{equation}
\label{eq:ci}
\ket{\psi} = \sum\limits_{i = 0}^{2^n - 1} c_i \ket{i} .
\ket{\psi} = \sum\limits_{i = 0}^{2^n - 1} c_i \ket{i}
\end{equation}
with the normation condition
@@ -176,13 +176,13 @@ The matrix representation of $CX$ and $CZ$ for two qbits is given by
\begin{postulate}
Let
$$\ket{\psi} = \alpha\ket{\phi_1} \otimes \ket{1}_j + \beta\ket{\phi_0} \otimes \ket{0}_j$$
\begin{equation}\ket{\psi} = \alpha\ket{\phi_1} \otimes \ket{1}_j + \beta\ket{\phi_0} \otimes \ket{0}_j\end{equation}
be a $n$-qbit state
where $\ket{1}_j, \ket{0}_j$ denote the $j$-th qbit state and $|\alpha|^2 + |\beta|^2 = 1$.
Then the measurement of the $j$-th qbit will yield
$$\ket{\phi_1} \otimes \ket{1}_j$$
\begin{equation}\ket{\phi_1} \otimes \ket{1}_j\end{equation}
with probability $|\alpha|^2$ and
$$\ket{\phi_0} \otimes \ket{0}_j$$
\begin{equation}\ket{\phi_0} \otimes \ket{0}_j\end{equation}
with probability $|\beta|^2$ \cite{nielsen_chuang_2010}. This is called collapse of the wave function.
\end{postulate}

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@@ -39,7 +39,8 @@
\title{An Efficient Quantum Computing Simulator using a Graphical Description for Many-Qbit Systems \\
\large Bachelor Thesis}
\author[1]{Daniel Knüttel}
\affil[1]{Institute I - Theoretical Physics, University of Regensburg}
\affil[1]{Institute I - Theoretical Physics, University of Regensburg\\
Supervised by Prof. Dr. Christoph Lehner}
\date{10.04.2020}
\begin{document}
\maketitle