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