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Quantum Algorithms Using Quantum Fourier Transform : 양자 푸리에 변환을 이용한 양자 알고리즘
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이훈희 | - |
| dc.contributor.author | 이두영 | - |
| dc.date.accessioned | 2018-12-03T01:50:26Z | - |
| dc.date.available | 2018-12-03T01:50:26Z | - |
| dc.date.issued | 2018-08 | - |
| dc.identifier.other | 000000153090 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/144068 | - |
| dc.description | 학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수학과, 2018. 8. 이훈희. | - |
| dc.description.abstract | In this thesis, we study quantum algorithms, espectially using the quan-
tum Fourier transform. At rst, we introduce quantum Fourier transform on groups and using this, we study how to solve problems with quantum algorithms. | - |
| dc.description.tableofcontents | 1 Introduction 1
2 Preliminaries 3 2.1 Basic Representation Theory . . . . . . . . . . . . . . . . . 3 2.2 Basic Quantum Mechanics . . . . . . . . . . . . . . . . . . . 5 3 Quantum Fourier Transform 8 3.1 Quantum Fourier Transform on Z=NZ . . . . . . . . . . . . 8 3.2 Quantum Fourier Transform on a Finite Abelian Group . . 10 3.3 Quantum Fourier Transform on a General Group . . . . . . 11 4 Quantum Algorithms 13 4.1 Phase Estimation . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Period Finding . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.3 Period Finding on Z . . . . . . . . . . . . . . . . . . . . . . 17 4.4 Period Finding Using Phase Estimation . . . . . . . . . . . 21 4.5 Order Finding . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.6 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.7 Discrete Logarithm . . . . . . . . . . . . . . . . . . . . . . . 26 4.8 Discrete Logarithm Using Phase Estimation . . . . . . . . . 27 5 Hidden Subgroup Problem 30 5.1 Abelian Hidden Subgroup Problem . . . . . . . . . . . . . . 30 5.2 Normal Hidden Subgroup Problem . . . . . . . . . . . . . . 34 5.3 Hidden Subgroup Problem on the Dihedral Group DN . . . 37 Bibliography 43 국문초록 45 | - |
| dc.format | application/pdf | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | ko | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject.ddc | 510 | - |
| dc.title | Quantum Algorithms Using Quantum Fourier Transform | - |
| dc.title.alternative | 양자 푸리에 변환을 이용한 양자 알고리즘 | - |
| dc.type | Thesis | - |
| dc.description.degree | Master | - |
| dc.contributor.affiliation | 자연과학대학 수학과 | - |
| dc.date.awarded | 2018-08 | - |
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