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系統識別號 U0026-1908201417293000
論文名稱(中文) 開放系統下量子邏輯閘之最佳化過程斷層掃瞄解析控制
論文名稱(英文) Optimal Quantum-Process-Tomography Control of Quantum Logic Gate In Open Systems
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 102
學期 2
出版年 103
研究生(中文) 莊矞棠
研究生(英文) Yu-Yang Zhuang
學號 n96011473
學位類別 碩士
語文別 中文
論文頁數 130頁
口試委員 指導教授-黃吉川
口試委員-李哲明
口試委員-陳俊良
口試委員-廖德祿
口試委員-謝金源
中文關鍵字 量子計算  量子最佳化控制  糾纏邏輯閘 
英文關鍵字 quantum computation  quantum information  nitrogen-vacancy center  entangling gates 
學科別分類
中文摘要 探討在封閉系統或開放系統環境下多量子位元的量子最佳化控制都是現今量子計算中重要的一環。隨著子系統數目的增加,在開放式環境的影響下系統複雜性隨之提高,而現今普遍用來檢測量子邏輯閘之最佳化控制優劣的工具並不夠嚴謹,隨著量子系統維度不斷地擴大,多量子位元系統的量子狀態保真度準確性將更加不客觀。本文以多個氮原子空缺中心為一個多體系統,來模擬量子邏輯閘控制最佳化的問題,並在動態過程中加入了馬可夫近似下的耗散影響,實現在開放系統之2至4個量子位元的糾纏邏輯閘操作。另外在4個氮原子空缺中心將2個空缺設定為假想環境,以這樣的模式完成非馬可夫動態過程下的邏輯閘操作。本論文以量子過程斷層解析搭配快速收斂疊代演算法模擬二量子位元、三量子位元與四量子位元的糾纏邏輯閘之操作。
英文摘要 The quantum optimal control of a multi-qubit system is one of central tasks of both quantum computation and quantum information. The complexity of particle interaction and environment coupling increases with the number of subsystems in open systems, as a detect tool to direct accurate logic gates, optimal control theory is popular, but it is lenient. In this paper, we construction physics model multi-systems on nitrogen-vacancy center, to simulate numerical computation of quantum logic gates of optimal control. We have presented faithful manipulations of quantum gates in Markovian approximation environments and then applied to the non-Markovian dynamics of independent qubits. The implementations of two-qubit, three-qubit and four-qubit, entangling gates by quantum process tomography optimal control technique.
論文目次 中文摘要 I
Abstract II
誌謝 VIII
目錄 X
表目錄 XIV
圖目錄 XV
符號說明 XXIII
第一章 緒論 1
1-1研究背景 1
1-2文獻回顧 2
1-3研究動機 4
1-4本文架構 7
第二章 量子資訊與密度矩陣理論 8
2-1 量子位元與量子邏輯閘 8
2-2 量子力學四大公設 11
2-2-1 公設1: 狀態空間表示 11
2-2-2 公設2: 動態演化 11
2-2-3 公設3: 量子量測 12
2-2-4 公設4: 複合系統 13
2-3 量子純態、混合態 13
2-4 量子糾纏 14
2-5 密度矩陣與動態方程式 15
2-6 希爾伯特空間與約化李維空間 18
2-7 量子保真度 20
第三章 開放式量子系統 21
3-1 Nitrogen-vacancy center物理模型 21
3-2 超級算符(Superoperator) 23
3-3 馬可夫近似下耗散 25
3-4 非馬可夫動態行為 32
第四章 量子過程斷層解析與最佳化控制理論 35
4-1 量子過程解析最佳化控制理論 35
4-1-1量子過程斷層掃描解析 35
4-1-2 修正型量子過程保真度計算 40
4-1-3目標泛函建立 43
4-1-4快速收斂疊代演算法 45
4-1-5尤拉-拉格朗日方程式之數值計算 48
第五章 模擬結果分析與討論 51
5-1 電腦設備介紹 51
5-2 最佳化控制理論之模擬分析 52
5-3 封閉系統下的最佳化控制分析 58
5-4 開放式系統下的最佳化控制分析 68
5-5 非馬可夫過程下的氮原子空缺中心系統 82
第六章 結論與未來展望 114
6-1 結論 114
6-2未來展望 115
參考文獻 116
附錄A 尤拉-拉格朗日方程式推導 126
附錄B 量子過程斷層掃描解析控制流程圖 130
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