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Daniel Knüttel 2019-10-16 07:37:49 +02:00
parent 3519606f64
commit 37cb33b5b4
3 changed files with 22 additions and 12 deletions
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3
thesis/Makefile
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@ -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

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thesis/chapters/naive_simulator.tex
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@ -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}
as a both fast, safe and handy storage. They can be modified and viewed without overhead
Recalling \ref{ref:nqbitsystems} an arbitrary state $\ket{\psi}$ can be written as such:
$$ \ket{\psi} = \sum\limits_{i = 0}^{2^N - 1} c_i \ket{i} $$
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
of a $2^N$ dimensional quantum mechanical state and an $N$ dimensional classical state
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
A simulator state also contains a classical state which is a length $N$ integer array containing
the measured classical bits with a default value of $-1$.
The gates are implemented as NumPy ufuncs which allows

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thesis/main.tex
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@ -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