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系統識別號 U0026-3107201310591000
論文名稱(中文) 耗散系統中量子邏輯閘最佳化控制之研究
論文名稱(英文) Quantum optimal control of quantum logical gate in dissipation systems
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 101
學期 2
出版年 102
研究生(中文) 倪峻傑
研究生(英文) Chun-Chieh Ni
學號 N96004442
學位類別 碩士
語文別 中文
論文頁數 131頁
口試委員 指導教授-黃吉川
口試委員-李哲明
口試委員-廖德祿
口試委員-陳俊良
口試委員-謝金源
中文關鍵字 量子資訊  量子控制  量子計算  量子糾纏邏輯閘 
英文關鍵字 Quantum information  Quantum control  Quantum computing  Quantum entangling gates 
學科別分類
中文摘要 量子狀態保真度已被廣泛地用來判別模擬的量子邏輯閘與理想量子邏輯閘間的相似性;然而如同本論文所顯示,對於設計高可靠度量子邏輯閘而言,透過量子狀態保真度來探討是不夠客觀的。在此本論文以量子過程解析最佳化控制理論結合開放式系統,針對整個量子過程進行剖析,解決了量子狀態保真度客觀性的不足,並設計高可靠度的量子邏輯閘。我們以快速收斂糾纏回授演算法為出發,探討1量子位元CO分子轉振能階系統於開放式環境中,系統如何受到影響,而後利用自旋系統在開放式環境中實現2與3量子位元系統之糾纏邏輯閘,模擬結果顯示量子過程解析保真度均能高達97%以上。最後利用基因演算法以脈衝雷射之電場為出發,實現1量子位元CO分子轉振能階系統NOT與Hadamard量子邏輯閘,模擬結果顯示量子過程解保真度均高達97%以上。
英文摘要 Quantum state fidelity has been widely used to indicate whether simulated quantum gate is close to an ideal one. However, as shown in the thesis, it is not objective enough to show the similarity between real and ideal quantum gates. In order to avoid this shortcoming, we apply quantum process fidelity for designing reliable and faithful quantum logic gates. In this thesis, we design high reliable quantum logic gates in open quantum systems with quantum process tomography. Firstly, we take the ro-vibratoinal states of CO molecule to discuss how the systems were influenced by environment in one qubit quantum open system. Sequentially, the quantum entangling logic gates were simulated in open spin systems, the result also shows that the quantum process fidelities can achieve up to 97%. Finally, we use genetic algorithm to realize NOT and Hadamard quantum logic gates in CO molecule quantum systems and both of quantum process fidelities can be better than 97%. The proposed scheme can provide a basis for 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 本文架構 .........................6
第二章 量子資訊與密度矩陣理論 .........7
2-1 量子位元與量子邏輯閘 .........7
2-2 量子純態、混合態與糾纏態 .........12
2-3 密度矩陣與密度算符運動方程式 .........14
2-4 希爾伯特空間(Hilbert Space)........16
2-5 約化李維空間(Liouville Space).....18
2-6 量子力學四大公設 .................21
2-7 量子保真度 .................23
2-7-1 量子狀態保真度 .................23
2-7-2 量子過程保真度 .................23
2-7-3 量子狀態保真度與量子過程保真度比較.....24
第三章 開放式量子耗散系統 .................25
3-1 超級算符(Superoperator) .........25
3-2 量子耗散通道 .................27
3-2-1 Depolarizing channel .........27
3-2-2 Phasing-damping channel .........30
3-2-3 Amplitude-damping channel........32
3-3 馬可夫過程耗散方程 .................33
第四章 最佳化控制理論 .................35
4-1 CO分子轉動-振動能階模型 .........35
4-2 Nitrogen-vacancy center .........40
4-3 量子過程解析最佳化控制理論 .........43
4-3-1 量子過程解析與量子過程保真度計算......43
4-3-2 目標泛涵建立 .................47
4-3-3 快速收斂疊代演算法 .................48
4-3-4 數值方法計算尤拉-拉格朗日方程式.......51
4-4 基因演算法 .................53
第五章 模擬結果分析與討論 .................58
5-1 CO分子能階耗散系統 .................58
5-1-1 對角線項耗散 .................58
5-1-2 非對角線項耗散 .................79
5-1-3 馬可夫過程近似耗散 .................95
5-2 自旋物理系統 .................107
5-3 基因演算法量子邏輯閘實現.............117
5-4 改善方法建議 .................120
第六章 結論與未來展望 .................121
6-1 結論 .........................121
6-2 未來展望 .........................122
參考文獻 .........................123
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