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系統識別號 U0026-3107201315304700
論文名稱(中文) 高尺度量子資訊系統中量子過程解析之最佳化控制
論文名稱(英文) Quantum-Process-Tomography based Optimal Control for Large-Scale Quantum Information Processing
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) 蔡明諺
研究生(英文) Ming-Yen Tsai
學號 N96004400
學位類別 碩士
語文別 中文
論文頁數 164頁
口試委員 指導教授-黃吉川
口試委員-廖德祿
口試委員-李哲明
口試委員-陳俊良
口試委員-謝金源
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 本論文利用量子過程解析最佳化控制,設計高尺度量子邏輯閘,並將高可靠度量子邏輯閘組合成量子演算法。有別於一般最佳化控制理論,量子過程解析最佳化控制能以更客觀的方式來確保所有量子訊息的傳遞或儲存過程。我們以雙原子分子CO的物理特性-振動與轉動,建構出多層級量子系統,並利用糾纏回授演算法設計出最佳化控制電場,完成量子邏輯閘操作與量子演算法運算,成功模擬3個量子能階至14個量子能階的量子邏輯閘、3個量子能階至9個量子能階的量子搜尋演算法,以及8個量子能階的量子糾錯演算法。模擬結果量子邏輯閘的過程保真度在90%至99%之間,量子搜尋演算法其狀態保真度約在91%以上,而量子糾錯演算法的狀態保真度約在92%以上。本論文的研究方法與結果提供實現量子計算中,高尺度量子邏輯閘運算間,任意量子訊息的傳遞與儲存路徑。
英文摘要 In this thesis, we use the Quantum-Process-Tomography (QPT) based optimal control to design large scale and high reliable quantum logic gates. In addition, with these designed quantum logic gates, we theoretically demonstrated complex quantum algorithms for quantum computation. Compared with the usual optimal control theory, the QPT based optimal control provides an objective and reliable way to perform general quantum information tasks. To illustrate the power of our proposed scheme, we encode multi-level quantum information into the quantum states of CO molecule. Then, we use the entangled feedback algorithm to derive the optimal control electric field for the quantum gate and quantum algorithm operations. Here, we have simulated high-quality complex quantum logic gates up to fourteen levels, multi-object quantum search algorithms from three to nine elements, and the three-qubit quantum operation for the one-qubit quantum erro-correction code. The numerical results show that process fidelities of quantum logic gates are between 90% and 99%, whereas the state fidelities of the output of simulated quantum search algorithms and quantum erro-correction algorithms are better than 91% and 92%, respectively. The proposed scheme could pave the way for performing large scale quantum logic gates with arbitrary transferable and storable paths of quantum computation.
論文目次 中文摘要 ................................................I
Abstract .......................................II
致謝 ..............................................III
目錄 ................................................i
表目錄 ...............................................iv
圖目錄 ................................................v
符號說明 ..............................................xii
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 量子純態與量子混合態 ........................7
2-2 密度矩陣與密度算符運動方程式 ........................9
2-3 希爾伯特空間中的完備正交基底 .......................13
2-4 李維空間 .......................................16
2-5 量子李維動態方程式 ...............................18
2-6 量子力學的四大公設 ...............................18
2-7 量子保真度 ...............................20
第三章 量子邏輯電路與量子演算法 .......................21
3-1 量子邏輯電路 ...............................21
3-2 量子糾錯演算法 ...............................26
3-2-1 糾錯碼簡介 ...............................27
3-2-2 量子糾錯型態 ...............................28
3-2-3 Shor code ...............................31
3-3 量子搜尋演算法 ...............................33
3-3-1 古典的搜尋方法 ...............................33
3-3-2 Grover量子搜尋演算法 .......................34
第四章 量子過程解析與最佳化控制理論 .......................44
4-1 量子過程解析與量子過程保真度計算 ...............44
4-2 CO分子轉動-振動能階模型 .......................53
4-3 量子過程解析最佳化控制 .......................55
4-3-1 目標泛函確立 ...............................58
4-3-2 數值方法計算尤拉-拉格朗日方程式 ...............59
4-3-3 單調收斂糾纏回授演算法 .......................61
第五章 模擬結果分析與討論 ...............................64
5-1 硬體配置與運算資源 ...............................64
5-1-1 實驗室平台介紹 ...............................64
5-1-2 數值模擬計算所需運算資源 .......................66
5-2 量子搜尋演算法之數值模擬 .......................70
5-2-1 3個量子能階的搜尋演算法 .......................71
5-2-2 5個量子能階的搜尋演算法 .......................76
5-2-3 6個量子能階的搜尋演算法 .......................83
5-2-4 7個量子能階的搜尋演算法 .......................93
5-2-5 9個量子能階的搜尋演算法 ......................103
5-3 量子邏輯閘之數值模擬 ......................116
5-3-1 3個量子能階至14個量子能階的Idenity(I)邏輯閘 ......116
5-3-2 3個量子能階至14個量子能階的Fourier(F)邏輯閘 ......123
5-3-3 3個量子能階至14個量子能階的Toffoli(T)邏輯閘 ......138
5-4 量子糾錯演算法之數值模擬 ......................145
5-4-1 8個量子能階位元翻轉之量子糾錯演算法 ..............145
5-4-2 8個量子能階相位翻轉之量子糾錯演算法 ..............150
第六章 結論與未來展望 ..............................156
6-1 結論 ......................................156
6-2 未來展望 ......................................156
參考文獻 ..............................................159
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