請用此 Handle URI 來引用此文件：
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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 管希聖(Hsi-Sheng Goan) | |
| dc.contributor.author | Yi Chou | en |
| dc.contributor.author | 周宜 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:09:11Z | - |
| dc.date.available | 2015-08-09 | |
| dc.date.copyright | 2013-08-09 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-08-01 | |
| dc.identifier.citation | [1] Presentation file of viatcheslav dobrovitski: downloaded from
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61673 | - |
| dc.description.abstract | 量子邏輯閘（Quantum Gate）能驅使一系列完備的量子態基底作期望的轉換，並且是實現量子計算在真實物理上的基本
元件之一。 許多量子裝置被考慮用來實現量子計算的執行。，其中有鑽石中氮原子空缺中心（Nitrogen-Vacancy Center）的自旋（Spin），其相干性（Coherence）是很長的時間，即使在室溫下也可完成量子操作。所以，它成為可信賴在實際上執行量子計算的候選之一。然而與環境耦合所造成的去相干性（Decoherence）妨礙實現高精確度（Fidelity）的量子邏輯閘,故如何去克服其去相干性是現今主要的課題之一。最佳化控制方法（Optimal Control Method）是其中一個有效地抑止去相干性的工具，並且完成高精準度的量子邏輯閘。在本論文中，我們先介紹科羅多夫的最佳化控制方法（ Krotov Optimization Method）,它是一個最有效率且恆定的計算方法用於求解最佳化控制問題。再來，我們會呈現含時變外加控制的非馬可夫開放系統(Non-Markovian Open Quantum System)的主運動方程（Quantum Master Equation）。接著利用科羅多夫的最佳化控制方法來實行鑽石中氮原子空缺中心量子邏輯閘，我們得到的控制脈衝可實現高精準度X-gate，Z-gate以及CNOT-gate,其誤差約為10^{-4}。 | zh_TW |
| dc.description.abstract | The ability to steer a complete set of basis quantum states towards a desired transformation, often referred to as a quantum gate, is one of the essentiality for physical implementation of quantum computing. Many quantum devices are considered and implemented to realize quantum gates. The spin of a nitrogen-vacancy (NV) center in diamond has long coherence times and reliability of quantum operations even at room temperature. Therefore, it becomes a promising candidate for a practical implementation of quantum computing. One of the key challenges now is to overcome the decoherence induced by the uncontrolled couplings to the surrounding environment, preventing high-fidelity gate performance. Optimal control method is one of the effective strategy to dynamically suppress decoherence and to achieve the high-fidelity quantum gates. In this thesis, we first introduce the Krotov optimization method which is one of the most effective and universal computation methods for solving optimal control problems. Then we present the quantum master equation approach for non-Markovian open quantum systems with time-dependent external control. The Krotov based optimal method is then used to implement quantum logical gates for spins of a NV center in diamond, interacting with nearby noise qubits and a Non-Markovian bath. We find the control pulses to achieve high-fidelity X,Z and CNOT gates with errors about 10^{-4} for the NV center. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T13:09:11Z (GMT). No. of bitstreams: 1 ntu-102-R00222008-1.pdf: 2442908 bytes, checksum: 7e5898722f049409e0b4e3723bba0dc5 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 致謝i
中文摘要ii Abstract iii Contents iv List of Figures vii 1 Introduction 1 2 Krotov method of optimization 4 2.1 Description of problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Definition of utility constructs . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Iterative algorithm to improve the objective . . . . . . . . . . . . . . . . 6 2.3.1 An iterative algorithm of Krotov method . . . . . . . . . . . . . 6 2.3.2 Monotonically convergence of Krotov method . . . . . . . . . . 7 2.4 Construction of . to first order in x . . . . . . . . . . . . . . . . . . . . . 8 2.5 Example of Krotov method . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5.2 A linear problem . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 The dynamics of open quantum system 13 3.1 Master equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.1.1 Density matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.1.2 Derivation of the master equation . . . . . . . . . . . . . . . . . 14 3.1.3 Born and Markov Approximation . . . . . . . . . . . . . . . . . 16 3.2 Technique of auxiliary density matrices . . . . . . . . . . . . . . . . . . 19 3.2.1 Model and noise spectrum . . . . . . . . . . . . . . . . . . . . . 19 3.2.2 Time-nonlocal master equation . . . . . . . . . . . . . . . . . . . 21 3.2.3 Time-local Master equation . . . . . . . . . . . . . . . . . . . . 23 4 Optimal control for quantum gate 26 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 The closed composite-system . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2.1 The model system . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2.2 The measure of gate error . . . . . . . . . . . . . . . . . . . . . 29 4.2.3 Optimal control . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.4 The case of one noise qubit . . . . . . . . . . . . . . . . . . . . . 33 4.2.5 The case of two noise qubits . . . . . . . . . . . . . . . . . . . . 34 4.3 The open composite-system . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.1 The model system . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.2 Modified measure of gate error . . . . . . . . . . . . . . . . . . . 38 4.3.3 The result of optimal control . . . . . . . . . . . . . . . . . . . . 39 5 The nitrogen-vacancy center in diamond 42 5.1 Decoherence of an NV spin caused by the spin bath . . . . . . . . . . . . 42 5.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.1.2 Model system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.1.3 Simulation of the decoherence . . . . . . . . . . . . . . . . . . . 45 5.2 Single-qubit gates with the NV center . . . . . . . . . . . . . . . . . . . 48 5.2.1 Closed composite-system . . . . . . . . . . . . . . . . . . . . . . 48 5.2.2 Optimal control for single-qubit gates . . . . . . . . . . . . . . . 49 5.2.3 Discussion of performing Z-gate and X-gate . . . . . . . . . . . . 50 5.3 Two-qubit gate with a NV center in diamond . . . . . . . . . . . . . . . 53 5.3.1 Open Composite-system . . . . . . . . . . . . . . . . . . . . . . 53 5.3.2 Radio frequency π pulse . . . . . . . . . . . . . . . . . . . . . . 55 5.3.3 Optimal control for CNOT gate . . . . . . . . . . . . . . . . . . 57 5.3.4 Result and discussion . . . . . . . . . . . . . . . . . . . . . . . . 58 6 Conclusion 66 Appendix A: The explicit form of dK/dU 68 Bibliography 71 | |
| dc.language.iso | en | |
| dc.subject | 非馬可夫開放系統 | zh_TW |
| dc.subject | 最佳化控制 | zh_TW |
| dc.subject | 科羅多夫 | zh_TW |
| dc.subject | 量子邏輯閘 | zh_TW |
| dc.subject | 氮原子空缺中心 | zh_TW |
| dc.subject | 去相干性 | zh_TW |
| dc.subject | Krotov | en |
| dc.subject | Non-Markovian Open Quantum System | en |
| dc.subject | Decoherence | en |
| dc.subject | Nitrogen-Vacancy Center | en |
| dc.subject | Quantum Gate | en |
| dc.subject | Optimal Control Method | en |
| dc.title | 鑽石中氮原子空缺中心量子邏輯閘的最佳化控制 | zh_TW |
| dc.title | Optimal Control of Quantum Gates for the NV-center in Diamond | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡政達(Jeng-Da Chai),周忠憲(Chung-Hsien Chou) | |
| dc.subject.keyword | 最佳化控制,科羅多夫,量子邏輯閘,氮原子空缺中心,去相干性,非馬可夫開放系統, | zh_TW |
| dc.subject.keyword | Optimal Control Method,Krotov,Quantum Gate,Nitrogen-Vacancy Center,Decoherence,Non-Markovian Open Quantum System, | en |
| dc.relation.page | 77 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-08-01 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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