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