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系統識別號 U0026-1608201211070000
論文名稱(中文) 量子演算法之量子過程解析最佳化控制理論研究
論文名稱(英文) Scheme for Implementing Quantum Algorithm via Quantum Process Tomography Optimal Control Theorem
校院名稱 成功大學
系所名稱(中) 工程科學系碩博士班
系所名稱(英) Department of Engineering Science
學年度 100
學期 2
出版年 101
研究生(中文) 傅及昌
研究生(英文) Chi-Chang Fu
學號 N96991047
學位類別 碩士
語文別 中文
論文頁數 174頁
口試委員 指導教授-黃吉川
口試委員-李哲明
口試委員-謝金源
口試委員-陳俊良
口試委員-廖德祿
中文關鍵字 量子控制  量子資訊  量子計算 
英文關鍵字 Quantum control  Quantum Information  Quantum computation 
學科別分類
中文摘要 在本論文中,我們提出量子過程解析最佳化控制理論,並以CO雙原子分子振動和轉動的量子態建構量子位元系統,模擬2個量子位元和3個量子位元的多伊奇-喬茲薩(Deutsch-Jozsa)和量子搜尋演算法;其中我們以快速收斂疊代演算法,計算出最佳化控制雷射場,完成量子演算法的運算;其模擬的量子演算法的保真度均在93% 以上;本論文所提出之研究方法與結果,提供了量子電腦設計與實驗的理論基礎。
英文摘要 In this thesis, we propose the quantum process tomography optimal control theory for quantum computation. To illustrate the power of our proposed scheme, we take the vibrational and rotational states of CO molecule for example to construct single-, two-, and three-qubit quantum system. Moreover, we utilize the two-, and three-qubit quantum system to simulate the Deutsch-Jozsa and quantum search algorithms. Here, we use the entangled feedback algorithm to derive the optimal control laser field for the quantum algorithms operations. The fidelities of simulated quantum algorithms are better than 93%. The proposed scheme can provide a basis for the design and implementation of quantum computers.
論文目次 中文摘要 I
Abstract II
致謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
符號說明 XIV
第一章 緒論 1
1-1研究背景 1
1-2文獻回顧 3
1-3研究動機 5
1-4本文組織架構 6
第二章 量子資訊與密度矩陣理論 7
2-1 量子位元和量子邏輯閘 7
2-2 量子純態和量子混合態 11
2-3 密度矩陣 12
2-4 密度矩陣運動方程式 14
2-5 希爾伯特空間中的完備正交基底 15
2-6 約化李維空間 17
2-6-1 李維空間基底表示 17
2-6-2 量子李維方程式 19
2-7 量子保真度計算 20
第三章 量子演算法 21
3-1 古典計算問題 21
3-2 量子平行運算 24
3-3 量子多伊奇-喬茲薩演算法 25
3-3-1 2個量子位元多伊奇-喬茲薩演算法數值計算 27
3-3-2 3個量子位元多伊奇-喬茲薩演算法數值計算 30
3-4 量子搜尋演算法 38
第四章 量子過程解析最佳化控制理論 46
4-1 量子過程解析與量子過程保真度計算 46
4-2 CO分子轉動-振動能階模型 50
4-3 量子過程解析最佳化控制 53
4-3-1 建立目標泛函 55
4-3-2 快速收斂疊代演算法 57
4-3-3 數值方法計算尤拉-拉格朗日方程式 60
4-4 最佳化控制理論與量子過程解析最佳化控制方法比較 62
第五章 模擬結果分析與討論 67
5-1 量子邏輯閘之數值模擬 67
5-2 2個量子位元的多伊奇-喬茲薩演算法之數值模擬 77
5-3 3個量子位元的多伊奇-喬茲薩演算法之數值模擬 87
5-4 2個量子位元的搜尋演算法之數值模擬 105
5-4-1 4個量子態取1個量子態之搜尋演算法數值模擬 107
5-4-2 4個量子態取2個量子態之搜尋演算法數值模擬 110
5-5 3個量子位元的搜尋演算法之數值模擬 116
5-5-1 8個量子態取1個量子態之搜尋演算法數值模擬 118
5-5-2 8個量子態取2個量子態之搜尋演算法數值模擬 124
5-5-3 8個量子態取3個量子態之搜尋演算法數值模擬 127
5-5-4 8個量子態取4個量子態之搜尋演算法數值模擬 133
5-6 多伊奇-喬茲薩演算法模擬結果分析 140
5-7 量子搜尋演算法模擬結果分析 142
第六章 結論與未來展望 145
6-1 結論 145
6-2 未來展望 146
參考文獻 148
附錄A 尤拉-拉格朗日方程式推導 154
附錄B 時間演化算符推導與數值計算 157
附錄B-1 時間演化算符推導 157
附錄B-2 時間演化算符數值方法 161
附錄B-3 時間演化算符之電場數值計算 162
附錄C 快速收斂疊代演算法證明 165
附錄D 單位換算表 174
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