109 lines
3.0 KiB
TeX
109 lines
3.0 KiB
TeX
\documentclass[10pt]{beamer}
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\usepackage[utf8]{inputenc}
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\usepackage{graphicx}
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\usepackage{amssymb, amsthm}
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\usepackage{setspace}
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\usepackage{amsmath}
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\usepackage{hyperref}
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\usepackage{geometry}
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\usepackage{enumerate}
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\usepackage{physics}
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\usepackage{listings}
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%\usepackage{struktex}
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\usepackage{qcircuit}
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\newtheorem{definition}{Definition}
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\newtheorem{postulate}{Postulate}
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\newtheorem{corrolary}{Corrolary}
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\newtheorem{lemma}{Lemma}
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\newtheorem{theorem}{Theorem}
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\usetheme[progressbar=frametitle]{metropolis}
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\setbeamercolor{background canvas}{bg=white!20}
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\title{An Efficient Quantum Computing Simulator using a Graphical Description for Many-Qbit Systems}
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\subtitle{Simulation in the Stabilizer Formalism}
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\author{Daniel Knüttel}
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\date{21.02.2020}
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\institute{Universität Regensburg}
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\titlegraphic{\small\center Universität Regensburg\\
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Faculty of the Institute of Theoretical Physics
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\vspace{-11mm}\flushright\includegraphics[height=1.0cm]{logo.png}}
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%\logo{\includegraphics[width=1cm]{logo.png}\hfill}
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%\newcommand{\nologo}{\setbeamertemplate{logo}{}} % command to set the logo to nothing
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%\newcommand{\congress}{Faculty of the Institute of Theoretical Physics}
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%% footer
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\makeatletter
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\setbeamertemplate{footline}
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{
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%\leavevmode%
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\hbox{%
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\begin{beamercolorbox}[wd=.9\paperwidth,ht=2.25ex,dp=1ex,left]{Faculty of the Institute of Theoretical Physics}%
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\end{beamercolorbox}%
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\begin{beamercolorbox}[wd=.1\paperwidth,ht=2.25ex,dp=1ex,right]{Faculty of the Institute of Theoretical Physics}%
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\insertframenumber{} / \inserttotalframenumber\hspace*{2ex}
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\end{beamercolorbox}}%
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}
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\makeatother
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\begin{document}
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\maketitle
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\section{Introduction}
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{
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\begin{frame}{Motivation}
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\begin{itemize}
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\item Some (physical) problems are classically hard to solve.
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\item The quantum simulator: Mapping a hard problem to quantum hardware that can simulate this specific problem.
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\item The (universal) quantum computer: able to simulate any unitary transformation on the system.
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\end{itemize}
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\end{frame}
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}
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{
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\begin{frame}{Quantum Errors and Quantum Error Correction}
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\begin{itemize}
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\item Quantum systems at non-zero temperature often have dephasing effects and a finite population lifetime (relaxation).
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\item Fault tolerant QC needs a way to correct for those errors.
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\item Several strategies exist one important class of quantum error correction codes are \textbf{stabilizer codes}.
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\end{itemize}
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\end{frame}
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}
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\section{Binary Quantum Computing}
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{
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\begin{frame}{Qbits}
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\begin{definition}
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A qbit is a two-level quantum mechanical system $\ket{0}, \ket{1}$ with $\braket{0}{1} = 0$.
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In the following $Z = \sigma_Z, X = \sigma_X, Y = \sigma_Y, I = \id$ will be used.
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\end{definition}
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Where $Z\ket{0} = +1\ket{0}$ and $Z\ket{1} = -1\ket{1}$.
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\begin{postulate}
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A $n$-qbit system is the tensor product of the single-qbit systems.
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\end{postulate}
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\end{frame}
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}
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\end{document}
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