Quantum Error Correction Methods

EMU I-REP

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dc.contributor.advisor Rıza, Mustafa
dc.contributor.author Alizadeh, Yashar
dc.date.accessioned 2018-04-12T07:58:49Z
dc.date.available 2018-04-12T07:58:49Z
dc.date.issued 2016-09
dc.date.submitted 2016-09
dc.identifier.citation Alizadeh, Yashar. (2016). Quantum Error Correction Methods . Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. en_US
dc.identifier.uri http://hdl.handle.net/11129/3588
dc.description Master of Science in Applied Mathematics and Computer Science. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2016. Supervisor: Assist. Prof. Dr. Mustafa Rıza. en_US
dc.description.abstract This study surveys the mathematical structure of a quantum error correcting codes and the way they are developed through certain stages of error correction. In particular, the families of Calderbank-Shor-Steane codes (CSS) and the stabilizer codes are discussed and through elaborative examples it will be shown that the CSS codes are in the family of the stabilizer codes. Since the study of the CSS codes depends on a firm knowledge of classical coding theory, a rigorous mathematical review of the linear codes is done separately. Analysing the structure of the stabilizer formalism is highly depended on the effective use of some group theoretic notions. This structure is discussed in more detail and examples will be given. As the ultimate application of the quantum error correction the rules of the fault-tolerant quantum computing is explored and finding the threshold condition of an example will be done. Keywords: QEC, Coding theory, Stabilizer formalism, CSS codes, Fault-tolerant quantum computing, Threshold condition en_US
dc.description.abstract OZ : Bu c¸alıs¸ma kuantum hata d¨uzeltimin kodlarının matematiksel yapısını ve belli hata d¨uzeltilim evrelerinden nasıl gec¸ti˘gini incelemektedir. ¨ozellikle, Calderbank-Shor- Steane (CSS) kod ailesi ve stabilizat¨or kodları ele alınarak, ve ayrıca ayrıntılı ¨ornekler ile CSS kodları stabilizat¨or kodlar ailesinden oldu˘gunu g¨osterilmektedir. CSS kodları klasik kodlama teorisine dayandı˘gı ic¸in, matematiksel ayrıntılı bir s¸ekilde lineer kodlar g¨ozden gec¸irilmis¸tir. Stabilizat¨or bic¸imcili˘gin str¨ukt¨ur¨un¨un analizi gurup teorisi tabanında yapılmıs¸tır. Bu bic¸imcilik detaylı s¸ekilde tartıs¸ılacaktır ve ¨orneklerle desteklenecektir. Kuantum hata d¨uzeltimi kurallarının en uc¸ uygulaması kusura dayanıklı kuantum hesaplamaları incelenmis¸tir ve bir ¨ornekte es¸ik seviyesinin nasıl bulundu˘gu g¨osterilecektir. Anahtar Kelimeler:Kuantum Hata D¨uzeltme, Kodlama teorisi, Stabiliz¨or bic¸imcili˘gi, CSS kodları, hata d¨uzeltimi kuantum hesaplamalar, es¸ik seviyesi s¸artı en_US
dc.language.iso eng en_US
dc.publisher Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) en_US
dc.rights info:eu-repo/semantics/openAccess en_US
dc.subject Mathematics en_US
dc.subject Applied Mathematics and Computer Science en_US
dc.subject Quantum computers - Error - correcting codes (Information theory) en_US
dc.subject QEC en_US
dc.subject Coding theory en_US
dc.subject Stabilizer formalism en_US
dc.subject CSS codes en_US
dc.subject Fault-tolerant quantum computing en_US
dc.subject Threshold condition en_US
dc.title Quantum Error Correction Methods en_US
dc.type masterThesis en_US
dc.contributor.department Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics en_US


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