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系統識別號 U0026-0812200915404817
論文名稱(中文) 量子邏輯運算閘之最佳化控制研究
論文名稱(英文) Scheme for Implementing Quantum Logic Gate via Optimal Quantum 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 98
學期 2
出版年 98
研究生(中文) 何儀輝
研究生(英文) Yi-Huei He
電子信箱 n9696146@mail.ncku.edu.tw
學號 n9696146
學位類別 碩士
語文別 中文
論文頁數 140頁
口試委員 指導教授-黃吉川
口試委員-謝金源
口試委員-林振森
口試委員-廖德祿
口試委員-陳俊良
中文關鍵字 量子控制  量子資訊  量子計算 
英文關鍵字 Quantum computation  Quantum Information  Quantum control 
學科別分類
中文摘要 本文將以雙原子分子C12O16內部振動和轉動運動行為來建1-qubit和2-qubits基本量子閘，從基於量子最佳化控制方案，控制分子系統在不同能階的躍遷，數值模擬找出一組量子閘作用的最佳輸入雷射場，其最佳化控制採用密度矩陣和劉維-馮·諾伊曼方程式描述多體量子系綜動力學演化，並結合投影算符將系統分為主要狀態和殘餘狀態兩個子空間，以提高演算法效率，模擬結果量子閘保真度和平均轉移機率均有96% 以上良率，提供實現量子計算中量子邏輯閘運算後量子訊息傳遞和儲存的路徑。
英文摘要 The motion behaviors of internal rovibration of a diatomic molecule are applied to build the elementary quantum gates encode one qubit and two qubits in this research. The molecular system we chose was carbon monoxide (C12O16). We used the optimal control theory to examined an optimization gate laser pulse numerically to control molecular system transition of different energy state. The controlled quantum systems are described with the probability-density-matrix based on Liouville–von Neumann equation. Projection operators were used to improve efficiency, and the states of the quantum system are decomposed into two sub-spaces, namely the ‘main state’ space and the ‘remaining state’ space. The numerical results show high gate fidelity and average transition probability over 96% to promise that it's reachable to perform transferable and storable paths of quantum information via distinguishably quantum logic gates.
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 IX
第一章 緒論 1
1-1研究背景 1
1-2文獻回顧 5
1-3研究動機 9
1-4本文組織架構 10
第二章 量子統計力學與密度矩陣理論 12
2-1 量子統計力學 13
2-1-1 量子純態和量子混合態 14
2-1-2 密度矩陣 16
2-1-3 可觀測物理期望值 20
2-1-4 劉維爾-馮•諾伊曼方程式 22
2-2 約化劉維空間 24
2-2-1 劉維空間基底表示 24
2-2-2 可觀測物理期望值 27
2-2-3 劉維爾-馮•諾伊曼方程式 28
2-3 量子資訊基礎 32
2-3-1 量子位和量子邏輯閘 33
2-3-2 量子糾纏態 38
第三章 量子最佳化控制計劃 40
3-1 雙原子分子控制系統 41
3-1-1 轉振光譜能階解析解 42
3-1-2角動量耦合和Winger 3-j符號 45
3-1-3 狀態基底和相互作用哈密頓量 49
3-1-4 系統可控制性和可觀測性 52
3-2 量子最佳化控制 56
3-2-1 目標泛函確立 58
3-2-2 歐拉-拉格朗日方程式 60
3-2-3 單調收斂糾纏回授演算法 66
3-2-4 對稱分離算符實現么正演化算符 69
第四章 數值實現多維度量子封閉系統控制 75
4-1 投影算符法 76
4-2 控制場設計 83
4-3 數值模擬 91
第五章 結論與展望 107
5-1 結論 107
5-2 未來展望 108
參考文獻 110
附錄A-1 么正時間演化算符推導 122
附錄A-2 么正時間演化算符的數值方法 127
附錄B Morse能階 128
附錄C 數值演算李代數程式 134
附錄D 單位換算表 136
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