some work

thesis/Makefile

@@ -3,7 +3,8 @@ pdflatex=xelatex
 bibtex=bibtex 
 
 chapters = chapters/introduction.tex \
-		   chapters/naive_simulator.tex
+		   chapters/naive_simulator.tex \
+		   chapters/introduction_qc.tex
 
 all: main.pdf
 

thesis/chapters/naive_simulator.tex

@@ -1,3 +1,4 @@
+% vim: ft=tex
 \section{The naive Simulator}
 
 A quite big part of the simulations interesting for students and researchers is not
@@ -5,16 +6,17 @@ covered by stabilizer states and stabilizer circuits. In particular the
 phase estimation algorithm is essential for many applications. Being able to simulate
 such an algorithm is essential for education.
 
-\subsection{Core Design}
+\subsection{Simulator Core}
 
-The core of the simulator are states represented as numpy arrays \cite{numpy_array}
+Recalling \ref{ref:nqbitsystems} an arbitrary state $\ket{\psi}$ can be written as such:
-as a both fast, safe and handy storage. They can be modified and viewed without overhead
+
+$$ \ket{\psi} = \sum\limits_{i = 0}^{2^N - 1} c_i \ket{i} $$
+
+Which yields $2^N$ coefficients $c_i = \braket{\psi}{i}$. These coefficients are used to
+store the quantum mechanical state of the simulator and are stored in numpy arrays \cite{numpy_array}.
+They can be modified and viewed without overhead 
 using python and allow fast modification using so-called NumPy ufuncs\cite{numpy_ufunc}.
-All gates are implemented as NumPy ufuncs and map an $N$ qbit simulator state consisting 
+A simulator state also contains a classical state which is a length $N$ integer array containing
-of a $2^N$ dimensional quantum mechanical state and an $N$ dimensional classical state
+the measured classical bits with a default value of $-1$.
-to a new $2^N$ dimensional quantum mechanical state and an $N$ dimensional classical state.
-
-A $N$ qbit quantum mechanical state is the outer (kronecker) product of the $N$ single qbuit 
-state FIXME: source. The 
-
 
+The gates are implemented as NumPy ufuncs which allows 

thesis/main.tex

@@ -2,14 +2,19 @@
 \documentclass[a4paper,12pt]{scrartcl}
 \usepackage[utf8]{inputenc} 
 \usepackage{graphicx} 
-\usepackage{amssymb}
+\usepackage{amssymb, amsthm}
 \usepackage{setspace} 
 \usepackage{amsmath} 
 \usepackage{hyperref}
 \usepackage{geometry} 
 \usepackage{enumerate}
+\usepackage{physics}
+
 \geometry{left=2.5cm,right=2.5cm,top=2.5cm,bottom=2.5cm}
 
+\newtheorem{definition}{Definition}
+\newtheorem{postulate}{Postulate}
+
 \title{Development of an Extensible Quantum Computing
 Simulator with a Focus on Simulation in the Graph Formalism }
 \author{Daniel Knüttel} 
@@ -32,6 +37,8 @@ Simulator with a Focus on Simulation in the Graph Formalism }
 
 \include{chapters/introduction}
 
+\include{chapters/introduction_qc}
+
 \include{chapters/naive_simulator}
 
 %\backmatter