系統識別號 U0026-1708201616484400
論文名稱(中文) 量子多位元退相干控制
論文名稱(英文) Decoherence Control of Multiple Quantum Bits
校院名稱 成功大學
系所名稱(中) 航空太空工程學系
系所名稱(英) Department of Aeronautics & Astronautics
學年度 104
學期 2
出版年 105
研究生(中文) 劉士豪
研究生(英文) Shih-Hao Liu
學號 P46034309
學位類別 碩士
語文別 中文
論文頁數 97頁
口試委員 指導教授-楊憲東
中文關鍵字 量子控制  Lyapunov控制  Liouville方程式  退相干控制  Lindblad方程式 
英文關鍵字 Quantum Control  Lyapunov Control  Liouville Equation  Decoherence Control  Lindblad Equation 
中文摘要 本論文的目的是利用『單一磁場控制多電子』之技術,探討在外界環境的影響下,多位元量子電腦的可實現性。電子在糾纏時會互相傳遞量子訊息,這有助於不同量子狀態間之轉換(即不同位元間之切換),但量子糾纏的時間本就非常短暫,開放性環境的干擾又進一步抑制了量子糾纏的強度。因此如何讓量子糾纏的時間拉長,不受外界環境的干擾,是量子電腦極待解決的問題。本論文考慮開放性系統所造成的退相干效應,並透過量子控制的引入,延緩退相干的發生。
英文摘要 This thesis considers the technique of controlling multiple quantum bits by a single magnetic field under the influence of external environment. Quantum entanglement is the essential feature of a quantum computer, which helps electrons to transfer information between different quantum bits and accelerates the switch between them. However, a real quantum computer operates in open systems and is vulnerable to external disturbances so as to lose its entangling behavior eventually, a phenomenon called decoherence. The presence of decoherence is the bottleneck of realizing quantum computer. This thesis focuses on the decoherence effect caused by open systems and proposes the means of quantum control to suppress and/or delay its occurrence.
To date, the research on suppressing decoherence by quantum control is limited to a 2-electron (2-qubit) system. The thesis extends the existing results to consider the suppression of decoherence for general n-qubit systems. The decoherent effect is described by the Lindblad equation and the main contribution of the thesis is to express this abstract operator equation in terms of a dynamic model described by matrix differential equations, which then can be solved easily by Matlab. The established quantum dynamic model allows us to investigate quantitatively the adverse effect on qubit transfer by decoherence. Based on the proposed quantum model, we derive robust quantum control by Lyapunov approach to suppress decoherence in order to maintain the strength and duration of entanglement for general n-qubit systems.
論文目次 中文摘要 i
Decoherence Control of Multiple Quantum Bits ii
誌謝 vi
目錄 vii
圖目錄 ix
表目錄 xii
符號表 xiii
第 1 章 緒論 1
1.1 背景及文獻回顧 1
1.2 研究目標 5
1.3 各章簡述 6
第 2 章 多電子自旋退相干模型的建構 9
2.1 相干態的保持 9
2.2 Hilbert空間內的退相干模型 11
2.3 Liouville空間內的退相干模型 15
第 3 章 退相干控制 19
3.1 以Lyapunov理論建立量子控制律 19
3.2 多粒子自旋退相干控制的漸進穩定性分析 24
3.3 Trace Distance 28
第 4 章 不同類型多粒子自旋控制 32
4.1 多粒子狀態驅動模型建立 32
4.2 單粒子狀態驅動 33
4.3 雙粒子狀態驅動 44
第 5 章 同類型多粒子自旋控制 53
5.1 自由Hamiltonian環境的選取 53
5.2 雙電子狀態驅動 55
5.2.1 糾纏熵(Entanglement Entropy) 69
5.3 多電子狀態驅動 70
5.3.1 n個電子狀態驅動 70
5.3.2 三電子狀態驅動 71
5.3.3 四電子狀態驅動 76
第 6 章 結論 80
6.1 結果與討論 80
6.2 未來研究方向 81
參考文獻 82
附錄 A Lindblad形式的退相干矩陣 85
附錄 B 任意n階的Liouville退相干算符形式 86
附錄 C 觀測算符P的構造與收斂分析 92
附錄 D 量子退相干矩陣的特性 95
參考文獻 [1]A.A. Budini, Open quantum system approach to single-molecule spectroscopy, Physical Review A, 79 (4), p. 043804, 2009.
[2]B. Hwang, H.S. Goan, Optimal control for non-Markovian open quantum systems, Physical Review A, 85 (3), p. 032321, 2012.
[3]B. Vacchini, HP Breuer, Exact master equations for the non-Markovian decay of a qubit, Physical Review A, 81 (4), p. 042103, 2010.
[4]B.M. Escher, G. Bensky, J. Clausen, G. Kurizki, Optimized control of quantum state transfer from noisy to quiet qubits, Journal of Physics B: Atomic, Molecular and Optical Physics, 44 (15), p. 154015, 2011.
[5]C. Altafini, Feedback stabilization of isospectral control systems on complex flag manifolds: application to quantum ensembles, IEEE Transactions on Automatic Control, 52, pp. 2019-2028, 2007.
[6]C. Anastopoulos, S. Shresta, B.L. Hu, Non-Markovian entanglement dynamics of two qubits interacting with a common electromagnetic field, Quantum information processing, 8 (6), pp. 549-563, 2009.
[7]C. Meier, D. Tannor, Non-Markovian evolution of the density operator in the presence of strong laser filed, Journal of Chemical Physics, 111(8), pp.3365-3376, 1999.
[8]D. D’Alessandro, Constructive decomposition of the controllability Lie algebra for quantum systems, IEEE Transactions on Automatic Control, 55, pp.1416-1421, 2010.
[9]D. Dong, C. Chen, T. Tarn, A. Pechen, H. Rabitz, Incoherent control of quantum systems with wavefunction-controllable subspaces via quantum reinforcement learning. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 38, pp.957-962, 2008.
[10]D. Dong, I. Petersen, Controllability of quantum systems with switching control, International Journal of Control, 84, pp.37-46, 2010.
[11]E. Vaz, J. Kyriakidis, Transient dynamics of confined charges in quantum dots in the sequential tunneling regime, Physical Review B, 81 (8), p. 085315, 2010.
[12]H. Huebl, F. Hoehne, B. Grolik, A.R. Stegner, M. Stutzmann, M.S. Brandt, Spin echoes in the charge transport through phosphorus donors in silicon, Physical Review Letters, 100 (17), p. 177602, 2008.
[13]H.J. Carmichael, An Open Systems Approach to Quantum Optics, Spring-Verlag, Berlin, pp. 5-38, 1993.
[14]H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, Oxford University Press, Oxford, pp.1524-1652, 2002.
[15]J. Coron, A. Grigoriu, C. Lefter, G. Turinici, Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling, New Journal of Physics, 11, p.105034, 2009.
[16]J. Pillo, S. Maniscalco,L. Harkonen,K. A. Suominen, Non-Markovian quantum jumps, Physical Review Letters, 100, p.180402, 2008.
[17]J. Wilkie, Y. Wong, Sufficient conditions for positivity of non-Markovian master equation with Hermitian generators, Journal of Physics A: Mathematical and Theorectical, 42, p.015006, 2009.
[18]K. Beauchard, J. Coron, M. Mirrahimi, P. Rouchon, Implicit Lyapunov control of finite dimensional Schrödinger equations, Systems and Control Letters, 56, pp. 388-395, 2007.
[19]M. Zhang, B.Q. Ou, H.Y. Dai, D.W. Hu, Control decoherence by quantum generalized measurement, Acta Automatica Sinica, 34 (4), pp. 433–437, 2008.
[20]M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, pp. 5-44, 2000.
[21]P. Gross, D. Neuhauser, H Rabitz, Optimal control of unimolecular reactions in the collisional regime, Journal of Chemical Physics, 94, p.1158, 1991.
[22]P. Haikka, S. Maniscalco, Non-Markovian dynamics of a damped driven two-state system, Physical Review A, 81 (5), p. 052103, 2010.
[23]P. Rebentrost, I. Serban, T. Schulte-Herbrüggen, F.K. Wilhelm, Optimal control of a qubit coupled to a non-Markovian environment, Physical Review Letters, 102 (9), p. 090401, 2009.
[24]P.C. Assis, Jr., R.P. de Souza, P.C. da Silva, L.R. da Silva, L.S. Lucena, and E.K. Lenzi, Non-Markovian Fokker-Planck equation: solutions and first passage time distribution, Physical Review E, 73(3), p.032101, 2006.
[25]Q.J. Tong, J.H. An, H.G. Luo, C.H. Oh, Decoherence suppression of a dissipative qubit by the non-Markovian effect, Journal of Physics B: Atomic, Molecular and Optical Physics, 43 (15), p. 155501, 2010.
[26]S. Baldi, G. Battistelli, E. Mosca, P. Tesi, Multi-model unfalsified adaptive switching supervisory control, Automatica, 46, 249-259, 2010.
[27]S. Cong, Y.Y. Zhang, Superposition state preparation based on Lyapunov stability theorem in quantum systems, Journal of University of Science and Technology of China, 38 (7), pp. 821–827, 2008.
[28]S. Maniscalco, F. Petruccione, Non-Markovian dynamics of a qubit, Physical Review A, 73 (1), p. 012111, 2006.
[29]S. Maniscalco, S. Olivares, M.G.A. Paris, Entanglement oscillations in non-Markovian quantum channels, Physical Review A, 75 (6), p. 062119,2007.
[30]S.B. Xue, R.B. Wu, W.M. Zhang, J. Zhang, C.W. Li, T.J. Tarn, Decoherence suppression via non-Markovian coherent feedback control, Physical Review A, 86 (5), p. 052304, 2012.
[31]T. Ho, H. Rabitz, Accelerated monotonic convergence of optimal control over quantum dynamics, Physical Review E, 82, p.26703, 2010.
[32]W. Cui, Z.R. Xi, Y Pan, Optimal decoherence control in non-Markovian open dissipative quantum systems, Physical Review A, 77 (3), p. 032117, 2008.
[33]W. Cui, Z.R. Xi, Y. Pan, Controlled population transfer for quantum computing in non-Markovian noise environment, Proceeding of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, IEEE, Shanghai, China, pp. 2504–2509, 2009.
[34]W. Strunz, T. Yu, Convolutionless non-Markovian master equation and quantum trajectories: Brownian motion, Physical Review A, 69, p.052115, 2004.
[35]Y. Dong, J. Sun, On hybrid control of a class of stochastic non-linear Markovian switching systems, Automatica, 44, pp.990-995, 2008.
[36]Y. Mo, R. Xu, P. Cui, Y. Yan, Correlation and response functions with non-Markovian dissipation: a reduced Liouville-space theory, The Journal of Chemical Physics, 122, p.084115, 2005.
[37]Y. Ohtsuki, Non-Markovian effects on quantum optimal control of dissipative wave packet dynamics, The Journal of Chemical Physics, 119(2), pp.661-671, 2003.
[38]Y.H. Ji, L. Xu, Entanglement decoherence of coupled superconductor qubits entangled states in non-Markovian environment, Chinese Journal of Quantum Electronics, 28 (1), pp. 58–64, 2011.
[40]陳宗海、董道毅、張陳斌,量子控制導論,中國科學技術大學出版社,中國,pp. 107-192,2005。
[43]叢爽、匡森,糾纏態的探測與製備:雙自旋系統的糾纏態製備,載於量子系統控制理論與方法,中國科學技術大學出版社,中國,pp. 281-291,2013。
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