32 lines
1.9 KiB
TeX
32 lines
1.9 KiB
TeX
% vim: ft=tex
|
|
\chapter{Introduction}
|
|
|
|
Quantum computing has been a rapidly growing field over the last years with
|
|
many companies and institutions working on building and using quantum computers
|
|
\cite{ibmq}\cite{intelqc}\cite{microsoftqc}\cite{dwavesys}\cite{lrzqc}\cite{heise25_18}.
|
|
One important topic in this research is quantum error correction
|
|
\cite{nielsen_chuang_2010}\cite{gottesman2009}\cite{gottesman1997}\cite{shor1995}
|
|
that will allow the execution of arbitrarily long quantum circuits \cite{nielsen_chuang_2010}. One
|
|
important class of quantum error correction strategies are stabilizer codes
|
|
\cite{gottesman2009}\cite{gottesman1997} that can be simulated exponentially
|
|
faster than general quantum circuits
|
|
\cite{gottesman_aaronson2008}\cite{CHP}\cite{andersbriegel2005}.
|
|
|
|
One particularly efficient way to simulate stabilizer states is the graphical
|
|
representation \cite{andersbriegel2005} that has been studied extensively in
|
|
the context of both quantum error correction and quantum information theory
|
|
\cite{schlingenmann2001}\cite{dahlberg_ea2019}\cite{vandennest_ea2004}\cite{hein_eisert_briegel2008}.
|
|
This paper describes the development of a quantum computing simulator
|
|
using both the usual dense state vector representation for a general state
|
|
and a graphical representation for stabilizer states. After giving some introduction
|
|
to quantum computing some basic properties of stabilizer states and their
|
|
dynamics are elucidated. Using this the graphical representation is introduced
|
|
and some operations on the graphical states are explained. Following is
|
|
a chapter describing the implementation of these techniques and some performance
|
|
analysis.
|
|
|
|
Being able to simulate large stabilizer states is particularly interesting for
|
|
exploring quantum error correction strategies as fault tolerant quantum computing
|
|
requires several layers of encoding - so called concatenated codes \cite{nielsen_chuang_2010} -
|
|
that require many physical qbits to encode one logical qbit.
|