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EMU I-REP >
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Theses (Master's and Ph.D) – Mathematics >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/11129/3588
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| Title: | Quantum Error Correction Methods |
| Authors: | Rıza, Mustafa
Alizadeh, Yashar
Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics |
| Keywords: | Mathematics
Applied Mathematics and Computer Science
Quantum computers - Error - correcting codes (Information theory)
QEC
Coding theory
Stabilizer formalism
CSS codes
Fault-tolerant quantum computing
Threshold condition |
| Issue Date: | Sep-2016 |
| Publisher: | Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) |
| 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. |
| 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
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 |
| 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. |
| URI: | http://hdl.handle.net/11129/3588 |
| Appears in Collections: | Theses (Master's and Ph.D) – Mathematics
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