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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 管希聖(Hsi-Sheng Goan) | |
| dc.contributor.author | Jung-Shen Tai | en |
| dc.contributor.author | 戴榮身 | zh_TW |
| dc.date.accessioned | 2021-05-16T16:22:11Z | - |
| dc.date.available | 2015-07-26 | |
| dc.date.available | 2021-05-16T16:22:11Z | - |
| dc.date.copyright | 2013-07-26 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-23 | |
| dc.identifier.citation | [1] L. Diosi, N. Gisin, and W. T. Strunz. Non-markovian quantum state diffusion.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6162 | - |
| dc.description.abstract | 在本論文中，我們結合由克羅托夫(V. Krotov)發展出來的最佳化控制理論(Optimal control theory)，以及精確推導(exactly derived)得到的主方程式(master equation)，以達成非馬可夫開放量子位元系統(non-Markovian open quantum bit system)中，單一量子位元邏輯閘(single-qubit quantum gate)的建構。我們發現，在適當的系統耗散條件之下，最佳化控制方法可以建構高精準度(fidelity)的量子邏輯閘。我們同時定義了一個重要的物理量: Imp ，用以量化在開放系統中，最佳化控制方法對邏輯閘失誤率(gate error)的修正。藉由Imp 的定義，我們可以找到一個理想的系統參數範圍，讓最佳化控制的效益最大化。 | zh_TW |
| dc.description.abstract | In this thesis, we apply the optimal control theory based on the Krotov’s method to an exactly derived master equation to find control pulses for single-qubit quantum gate operations under the influence of an non-Markovian environment. High fidelity quantum gates can be achieved for moderate qubit decaying parameters. An important quantity, improvement Imp, is defined to quantify the correction of gate errors due to
optimal control iteration for the open system. The desired range of parameters for mass improvement is found in which the effect of optimal control iteration is maximized. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-16T16:22:11Z (GMT). No. of bitstreams: 1 ntu-102-R00222021-1.pdf: 1535599 bytes, checksum: 4b1ea442aae10b7781882d00f404dbe7 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 論文口試委員審定書i
誌謝ii 中文摘要iii Abstract iv 1 Introduction 1 2 Non-Markovian Quantum State Diffusion 3 2.1 Overview[1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Formulation of Non-Markovian Quantum State Diffusion . . . . . . . . 5 2.2.1 Basic Properties of Coherent States . . . . . . . . . . . . . . . . 5 2.2.2 Bargmann States . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 Open Quantum Systems . . . . . . . . . . . . . . . . . . . . . . 10 2.2.4 Stochastic Schrodinger Equation . . . . . . . . . . . . . . . . . . 11 2.2.5 Convolution-less Formulation of Non-Markovian Quantum Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Spin-1/2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.1 Measurement-like Interaction (Pure Dephasing Model) . . . . . 17 2.3.2 Dissipative Model . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Optimal Control Theory 25 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Optimization Algorithm of a Global Method . . . . . . . . . . . . . . . 26 3.2.1 Control Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.2 Parameter function and the equivalent representation . . . . . . 26 3.2.3 An iterative algorithm . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.4 Construction of the parameter function and the improving algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.4.1 The sufficient conditions for local extremum . . . . . . 30 3.2.4.2 Realization of the iterative process . . . . . . . . . . . 33 3.2.5 Reduction of the parameter function . . . . . . . . . . . . . . . 34 3.2.5.1 Linear systems with concave criterion . . . . . . . . . . 34 3.2.5.2 Linear systems with quadratic criterion . . . . . . . . . 35 3.3 Optimization Algorithm of a gradient method . . . . . . . . . . . . . . 35 3.4 Application of OCT to Open Quantum Systems . . . . . . . . . . . . . 37 3.4.1 F(G(T)) first order in state . . . . . . . . . . . . . . . . . . . . 38 3.4.2 F(G(T)) second order in state . . . . . . . . . . . . . . . . . . . 40 3.5 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4 Optimal Control of Quantum Gates in Open Systems 43 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.1 Control problem . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.2 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2.3 Gate error and control update . . . . . . . . . . . . . . . . . . . 46 4.2.4 Range of control parameter . . . . . . . . . . . . . . . . . . . . 47 4.2.5 Initial guess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3.1 Lorentzian-like spectral density . . . . . . . . . . . . . . . . . . 49 4.3.2 Identity gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3.3 Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.4 Z-gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4 Ohmic spectral density . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.4.1 Identity gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.4.2 Z-gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.5 Environment suppression ability of optimal control . . . . . . . . . . . 61 4.5.1 Error correction due to phase shift . . . . . . . . . . . . . . . . 61 4.5.2 Conditions for mass improvement . . . . . . . . . . . . . . . . . 63 4.5.3 Suppression of dissipation . . . . . . . . . . . . . . . . . . . . . 68 5 Conclusion 70 A Lorentzian spectral density and cavity QED 72 B Fidelity in Closed and Open Systems 75 | |
| dc.language.iso | en | |
| dc.subject | Quantum gate | en |
| dc.subject | Optimal control | en |
| dc.subject | Exact solution | en |
| dc.subject | Non-Markovian | en |
| dc.subject | Open quantum system | en |
| dc.subject | Qubit | en |
| dc.title | 可精確解非馬可夫開放系統中之量子邏輯閘最佳化控制 | zh_TW |
| dc.title | Optimal Control of Quantum Gates in an Exactly Solvable Non-Markovian Open Quantum Bit System | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 胡崇德(Chong-Der Hu),蘇正耀(Zheng-Yao Su) | |
| dc.subject.keyword | 最佳化控制,精確解,非馬可夫,開放量子系統,量子位元,量子邏輯閘, | zh_TW |
| dc.subject.keyword | Optimal control,Exact solution,Non-Markovian,Open quantum system,Qubit,Quantum gate, | en |
| dc.relation.page | 80 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2013-07-24 | |
| 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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|---|---|---|---|
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