進階搜尋


下載電子全文  
系統識別號 U0026-2101201513391200
論文名稱(中文) 整合最佳化控制及基因演算法設計量子邏輯閘
論文名稱(英文) Scheme for Designing Quantum Logic Gate via Integrated Optimal Control and Genetic Algorithm
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 103
學期 1
出版年 104
研究生(中文) 彭崑祐
研究生(英文) Kun-You Peng
學號 N96011499
學位類別 碩士
語文別 中文
論文頁數 106頁
口試委員 指導教授-黃吉川
口試委員-廖德祿
口試委員-謝金源
口試委員-林振森
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 在本論文中,主要是探討雙原子分子C^12 O^16系統是否可經脈衝雷射整形模擬實驗中,來達到量子計算與量子邏輯閘操作的可行性,在模擬實驗中常用於控制電場有下列兩種演算法,其一為最佳化演算法在時域下以提供最大的靈活度的方式,在頻率位置和電場振幅的排列組合中求取脈衝雷射電場,不過此電場常被質疑是否能在實際的實驗中調製出來,其二為基因演算法則是啟發式搜尋法,其主要在離散的頻域下和適當的雷射脈衝的波形範圍內進行搜尋雷射電場,但由於量子位元(qubit)逐漸往上提升,會造成搜尋發散而導致無法收斂,故此論文將兩個方法的結合,首先利用最佳化控制理論求出該量子邏輯閘的初始電場,再選取其重要頻率位置做保留,然後將電場以染色體形式做編碼和實驗參數調整之後,將其當作基因演算法初始雷射電場,最後經過基因演算法不斷演化達到最佳化可行性脈衝雷射電場,而這電場可以使在模擬實驗中完成量子邏輯閘操作。最後本論文有成功模擬1個量子位元NOT與Hadamard量子邏輯閘、2個量子位元CNOT量子邏輯閘和3個量子位元Toffoli量子邏輯閘。
英文摘要 In this thesis, we focus on diatomic molecular system (C^12 O^16) whether through laser pulse shaping simulation experiment to achieve quantum computation and the feasibility of quantum logic gate operations. The simulation often used two algorithms to control the electric field. One is optimal algorithm which can seek the laser pulse electric field used by the permutations between the frequency location and electric field amplitude through the greatest flexibility in the time domain, but it’s often doubt whether this electric field can be modulated in the actual experiment. Two is genetic algorithm which is a heuristic search method, the main task is search laser electric field within appropriate range of laser pulse waveform in the discrete frequency domain, due to the quantum bit (qubit) gradually raise up will cause search result divergence which led to non-convergence. Therefore, this project will be a combination of two methods which is the integrated optimal control and genetic algorithm to overcome these problems. At first, use the optimal control theory to obtain the initial electric field of the quantum logic gates and select the important frequency position to make reservations, then use by chromosomes form to encoding electric field and adjusting experimental parameter. Let it be initial electric field in genetic algorithm, and after evolving to achieve optimal feasibility pulsed laser electric field. Finally, this thesis has successfully simulated one qubit Hadamard and NOT gates, two qubit CNOT gate and three qubit Toffoli gate.
論文目次 中文摘要 I
AbstractII
誌謝 VI
目錄 VII
表目錄 X
圖目錄 XI
符號說明 XIV
第一章 緒論 1
1-1 研究背景 1
1-2 文獻回顧 4
1-3 研究動機 7
1-4 本文架構 8
第二章 量子控制與資訊理論 9
2-1何謂量子控制 10
2-2量子位元與量子邏輯閘 11
2-3量子純態、混合態與糾纏態 16
2-4密度矩陣與密度算符運動方程式 18
2-5希爾伯特空間(Hilbert Space) 20
2-6約化李維空間(Liouville Space) 22
2-7量子力學四大公設 25
2-8量子過程解析 27
2-9量子保真度 29
第三章 量子最佳化控制與飛秒雷射脈衝 31
3-1 CO分子轉動-振動能階模型 31
3-2量子最佳化控制理論 35
3-2-1量子最佳化控制 35
3-2-2目標泛函確立 37
3-2-3數值方法計算尤拉-拉格朗日方程式 38
3-2-4單調收斂糾纏回授演算法 40
3-3飛秒脈衝雷射概述 44
3-4飛秒脈衝雷射整形 46
3-4-1 4-f脈衝整形裝置 47
3-4-2 LC-SLM的色散補償原理 49
3-4-3脈衝雷射整形應用於量子控制 51
第四章 整合最佳化控制及基因演算法 53
4-1基因演算法的起源 53
4-2基因遺傳演算法定義與架構 55
4-2-1基因遺傳演算法定義 55
4-2-2因遺傳演算法的架構 58
4-3利用基因演算法求解最佳化電場 64
4-4整合最佳化控制及基因演算法 68
第五章 模擬結果與分析 73
5-1 一個量子位元邏輯閘之模擬 73
5-1-1 NOT量子邏輯閘 73
5-1-2 Hadamard量子邏輯閘 78
5-2 二個量子位元CNOT量子邏輯閘之模擬 84
5-3三個量子位元Toffoli量子邏輯閘之模擬 90
第六章 結論與未來展望 99
6-1結論 99
6-2未來展望 100
參考文獻 101
參考文獻 [1] R. R. Schaller, "Moore's law: past, present and future," Spectrum, IEEE, vol. 34, pp. 52-59, 1997.
[2] D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature, vol. 390, pp. 575-579, 1997.
[3] A. K. Ekert, "Quantum cryptography based on Bell’s theorem," Physical review letters, vol. 67, p. 661, 1991.
[4] P. W. Shor and J. Preskill, "Simple proof of security of the BB84 quantum key distribution protocol," Physical Review Letters, vol. 85, p. 441, 2000.
[5] R. P. Feynman, "Quantum mechanical computers," Foundations of physics, vol. 16, pp. 507-531, 1986.
[6] S. Shi and H. Rabitz, "Quantum mechanical optimal control of physical observables in microsystems," The Journal of chemical physics, vol. 92, pp. 364-376, 1990.
[7] R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Physical Review Letters, vol. 68, p. 1500, 1992.
[8] E. Potter, J. Herek, S. Pedersen, Q. Liu, and A. Zewail, "Femtosecond laser control of a chemical reaction," Nature, vol. 355, pp. 66-68, 1992.
[9] L. Zhu, V. Kleiman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, "Coherent laser control of the product distribution obtained in the photoexcitation of HI," SCIENCE-NEW YORK THEN WASHINGTON-, pp. 77-77, 1995.
[10] A. Shnitman, I. Sofer, I. Golub, A. Yogev, M. Shapiro, Z. Chen, et al., "Experimental Observation of Laser Control: Electronic Branching in the Photodissociation of N a 2," Physical review letters, vol. 76, p. 2886, 1996.
[11] C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, "Feedback quantum control of molecular electronic population transfer," Chemical Physics Letters, vol. 280, pp. 151-158, 1997.
[12] A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, et al., "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science, vol. 282, pp. 919-922, 1998.
[13] J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, "Adaptive feedback control of ultrafast semiconductor nonlinearities," Applied Physics Letters, vol. 77, pp. 924-926, 2000.
[14] S. M. Hurley and A. W. Castleman, "Keeping reactions under quantum control," Science, vol. 292, pp. 648-649, 2001.
[15] J. I. Cirac and P. Zoller, "Quantum computations with cold trapped ions," Physical review letters, vol. 74, p. 4091, 1995.
[16] J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, "Geometric quantum computation using nuclear magnetic resonance," Nature, vol. 403, pp. 869-871, 2000.
[17] D. Loss and D. P. DiVincenzo, "Quantum computation with quantum dots," Physical Review A, vol. 57, p. 120, 1998.
[18] X. Xu, Y. Wu, B. Sun, Q. Huang, J. Cheng, D. Steel, et al., "Fast spin state initialization in a singly charged InAs-GaAs quantum dot by optical cooling," Physical review letters, vol. 99, p. 097401, 2007.
[19] B. E. Kane, "A silicon-based nuclear spin quantum computer," nature, vol. 393, pp. 133-137, 1998.
[20] V. Smelyanskiy, A. Petukhov, and V. Osipov, "Quantum computing on long-lived donor states of Li in Si," Physical Review B, vol. 72, p. 081304, 2005.
[21] D. R. Glenn §, D. A. Lidar, and V. A. Apkarian, "Quantum logic gates in iodine vapor using time–frequency resolved coherent anti-Stokes raman scattering: a theoretical study," Molecular Physics, vol. 104, pp. 1249-1266, 2006.
[22] S. Suzuki, K. Mishima, and K. Yamashita, "Ab initio study of optimal control of ammonia molecular vibrational wavepackets: Towards molecular quantum computing," Chemical physics letters, vol. 410, pp. 358-364, 2005.
[23] B. Zhou, R. Tao, S.-Q. Shen, and J.-Q. Liang, "Quantum computing of molecular magnet Mn 12," Physical Review A, vol. 66, p. 010301, 2002.
[24] J. Roslund and H. Rabitz, "Gradient algorithm applied to laboratory quantum control," Physical Review A, vol. 79, p. 053417, 2009.
[25] B. Amstrup, G. J. Toth, G. Szabo, H. Rabitz, and A. Loerincz, "Genetic algorithm with migration on topology conserving maps for optimal control of quantum systems," The Journal of Physical Chemistry, vol. 99, pp. 5206-5213, 1995.
[26] M. Tsubouchi, A. Khramov, and T. Momose, "Rovibrational wave-packet manipulation using shaped midinfrared femtosecond pulses," Physical Review A, vol. 77, p. 023405, 2008.
[27] M. Tsubouchi and T. Momose, "Rovibrational wave-packet manipulation using shaped midinfrared femtosecond pulses toward quantum computation: Optimization of pulse shape by a genetic algorithm," Physical Review A, vol. 77, p. 052326, 2008.
[28] J.-L. Chen, C.-M. Li, C.-C. Hwang, and Y.-H. Ho, "The operations of quantum logic gates with pure and mixed initial states," The Journal of chemical physics, vol. 134, p. 134103, 2011.
[29] R. R. Zaari and A. Brown, "Quantum gate operations using midinfrared binary shaped pulses on the rovibrational states of carbon monoxide," The Journal of chemical physics, vol. 132, p. 014307, 2010.
[30] R. R. Zaari and A. Brown, "Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations," The Journal of chemical physics, vol. 135, p. 044317, 2011.
[31] R. R. Zaari and A. Brown, "Effect of laser pulse shaping parameters on the fidelity of quantum logic gates," The Journal of chemical physics, vol. 137, p. 104306, 2012.
[32] D. Shyshlov and D. Babikov, "Complexity and simplicity of optimal control theory pulses shaped for controlling vibrational qubits," The Journal of chemical physics, vol. 137, p. 194318, 2012.
[33] T. Schulte-Herbrüggen, A. Spörl, N. Khaneja, and S. Glaser, "Optimal control for generating quantum gates in open dissipative systems," Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 44, p. 154013, 2011.
[34] H.-G. Duan and X.-T. Liang, "Entanglement detection for bipartite systems with continuous variables in non-Markovian baths," Physical Review A, vol. 83, p. 032316, 2011.
[35] M. Hu, "State transfer in dissipative and dephasing environments," The European Physical Journal D-Atomic, Molecular, Optical and Plasma Physics, vol. 59, pp. 497-507, 2010.
[36] P. Busch, T. Heinonen, and P. Lahti, "Heisenberg's uncertainty principle," Physics Reports, vol. 452, pp. 155-176, 2007.
[37] M. N. Wilson, "Superconducting magnets," 1983.
[38] C. Rose-Petruck, R. Jimenez, T. Guo, A. Cavalleri, C. W. Siders, F. Rksi, et al., "Picosecond–milliångström lattice dynamics measured by ultrafast X-ray diffraction," Nature, vol. 398, pp. 310-312, 1999.
[39] A. Imamog, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, et al., "Quantum information processing using quantum dot spins and cavity QED," Physical Review Letters, vol. 83, p. 4204, 1999.
[40] J. Zúñiga, A. Bastida, and A. Requena, "The Rotating Morse–Pekeris Oscillator Revisited," Journal of Chemical Education, vol. 85, p. 1675, 2008.
[41] A. G. Butkovskiy and Y. I. Samoilenko, Control of quantum-mechanical processes and systems: Kluwer, 1990.
[42] R. Stanton, "Hellmann‐Feynman Theorem and Correlation Energies," The Journal of Chemical Physics, vol. 36, pp. 1298-1300, 1962.
[43] T. H. Maiman, "Stimulated optical radiation in ruby," 1960.
[44] R. Fork, B. Greene, and C. Shank, "Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking," Applied Physics Letters, vol. 38, pp. 671-672, 1981.
[45] D. E. Spence, P. N. Kean, and W. Sibbett, "60-fsec pulse generation from a self-mode-locked Ti: sapphire laser," Optics letters, vol. 16, pp. 42-44, 1991.
[46] F. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. Haus, C. Heine, et al., "Design and fabrication of double-chirped mirrors," Optics letters, vol. 22, pp. 831-833, 1997.
[47] D. Zeidler, "Coherent control of molecular dynamics with shaped femtosecond pulses," lmu, 2002.
[48] A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Review of scientific instruments, vol. 71, pp. 1929-1960, 2000.
[49] A. M. Weiner, D. E. Leaird, J. Patel, and J. Wullert, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," Quantum Electronics, IEEE Journal of, vol. 28, pp. 908-920, 1992.
[50] P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, "Femtosecond quantum control of molecular dynamics in the condensed phase," Physical Chemistry Chemical Physics, vol. 9, pp. 2470-2497, 2007.
[51] J. H. Holland, Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence: U Michigan Press, 1975.
[52] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning: Addison-Wesley Longman Publishing Co., Inc., 1989.
[53] L. Davis, Handbook of genetic algorithms vol. 115: Van Nostrand Reinhold New York, 1991.
[54] C. Kane and M. Schoenauer, "Genetic operators for two-dimentional shape optimization," in Artificial Evolution, 1996, pp. 355-369.
[55] S. Woon, O. Querin, and G. Steven, "Structural application of a shape optimization method based on a genetic algorithm," Structural and Multidisciplinary Optimization, vol. 22, pp. 57-64, 2001.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2015-02-16起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2015-02-16起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw