量子系统控制场设计方法研究
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摘要
寻找有效的量子系统控制场设计方法在量子控制理论以及实践中占有关键的地位,对量子信息、量子物理、化学选键、纳米及微生物技术等领域的发展具有重要的指导意义。但是由于量子系统本身的一些特性,对一般的高维复杂量子系统的控制场设计依然是很困难的,目前还没一种普适的量子控制场的设计方法,还需要广大的科研工作者付出不懈的努力。在这一背景下,本论文重点研究了量子位系统的控制场开环设计、封闭量子系统一般混合态的量子Lyapunov设计以及开放量子系统的控制场设计等问题。具体内容包含一下几个方面：
1、研究Lyapunov控制场设计技术在封闭量子系统中的应用问题。首先,利用相互作用图景变换将量子系统的动力学方程变换为齐次双线性方程,在此基础上设计Lyapunov控制律实现封闭量子系统一般混合态的控制；其次,针对目前Lyapunov方法普遍存在的收敛性问题,证明了一定条件下Lyapunov方法收敛的充分必要条件。利用量子状态的相干向量表示,设计Lyapunov函数的虚拟观测量算符,在保证控制律的稳定性的基础上,从Barblat引理出发,获得量子系统最大状态不变集的结构,通过分析最大不变集中状态的动力学稳定性,证明一定条件下量子Lyapunov方法收敛的充分必要条件；第三,针对量子系统在Lyapunov控制律作用下无法收敛到给定的目标状态的情况,利用李群分解技术对量子Lyapunov方法进行改进,提出量子跃迁路径规划策略,实现到目标状态的控制,并证明了该策略的收敛性；最后,通过数值仿真实验检验了相应的分析以及所提策略的正确性。
2、针对量子位系统进行控制场设计。首先,基于单量子位系统状态的Bloch球表示,从几何的角度设计控制场实现单量子位任意纯态之间的演化；其次,对于双量子位系统,根据绝热通道技术来设计控制脉冲,并利用不同脉冲之间的相干相位来制备不同的状态,分析并总结出了相干相位与制备的状态之间的近似关系；第三,从各个基本控制脉冲的物理意义出发,根据系统控制哈密顿量与能级跃迁结构之间的关系着手,针对多量子位系统设计控制脉冲序列,实现布居数的相干转移;第四,进行系统数值仿真实验对所设计的控制场进行检验。
3、研究开放量子系统控制场的设计问题。首先,从最简单的情况出发,研究外加控制场对粒子间相互作用引起的纯度以及相干性变化产生的影响,并设计控制场保持被控粒子的纯度以及消除粒子纯度的波动；第二,提出将系统粒子与辅助粒子间的相互作用作为控制手段,引入局部非幺正作用,并设计相互作用强度变化以对系统粒子的纯度和相干性进行补偿,以及抵消系统粒子的消相干过程；最后,进行系统数值仿真实验,验证了所设计控制场的有效性。
4、定义了一种弱测量算符的结构,并给出其参数需要满足的充分条件。分析弱测量对不同量子系统状态演化的影响,并讨论其在开放量子系统耗散及消相干控制问题中的应用。
The studies of control fields design methods for quantum systems is a critical issue in quantum control theory and practice, it can greatly promotes many developing domains such as quantum information, quantum physics, bond selective chemistry, nanometer and microbial techniques. However, due to the properties of quantum systems themselves, it is difficult to design control fields for generic high-dimension and complex quantum systems. By now, there is no universal control fields design method for quantum systems, so an untiring endeavor of the scholars in various domains is still needed. Under such a background, this thesis studies the control fields design methods for quantum systems including the open loop control design, quantum Lyapunov methods for closed quantum systems with generic mixed states, the control design for open quantum systems and so on. The main contents are as follows:
1. The Lyapunov based methods for quantum systems are researched. At first, the dynamical equation of the quantum system is transferred into a homogeneous bilinear one in the interaction picture, so it becomes a homogeneous bilinear equation. Based on this, the Lyapunov control law is designed to achieve the generic mixed states control for closed quantum systems described in the interaction picture. The next, aiming at the convergence problem universally exists in the quantum Lyapunov methods at present, the sufficient and necessary conditions are proved under certain assumptions. The observable operator in the Lyapunov function is constructed using the coherent vector presentation of quantum states to guarantee the stability the control law. Based on this, the largest invariant set of the controlled system is deduced utilizing the Barblat lemma. The sufficient and necessary conditions are proved through the analyzing of the dynamical stabilities of the states in the largest invariant set. Then, for the situation that the system can't converge to the given target state, the Lie group decomposition technology is utilized to improve the quantum Lyapunov methods, and a strategy called transition path programming is proposed to accomplish the control task, the convergence of the proposed strategy is also proved; at last, system numerical simulation experiments are done to verify the validity of the analysis and the strategy proposed.
2. Control fields for cubit systems are designed. Firstly, based on the Bloch sphere presentation of a single qubit state, control fields are designed from the viewpoint of the geometry to achieve an arbitrary pure state of a single qubit. Secondly, adiabatic passage technology is used to design control fields for two-qubit systems, the coherence phase between control pulses is utilized to prepare different quantum states, the relationship between the coherence phase and the states prepared are analyzed and an approximate equation is summarized. Thirdly, utilizing the physical meanings of the basic control pulses and the relation between the system control Hamiltonians and the energy level structure, control pulse sequences are designed to accomplish the population transfer of multi-qubit systems. And fourthly, system numerical simulations are done to verify the validity of the control pulses.
3. Control fields design methods for open quantum systems are studied. For the simplest case, the impact of external control fields on the purity and coherence variety due to the interaction between particles is studied, and control fields are designed to preserve the particle purity and eliminate the purity fluctuations. A new control method is proposed, in which local non-unitary operations are induced by an assistant system and its interactions with the priori system. By controlling the interactions between the two systems, the purity and coherence of the priori system are compensated, and the decoherence effect is counteracted. All the designs are verified by numerical simulation experiments.
4. A kind of weak measurement operators is defined. A sufficient condition of the parameters is given. The impact of weak measurements on different quantum systems are analyzed, and the applications of such measurements in dissipation and decoherence control for open quantum systems are also discussed.
1、研究Lyapunov控制场设计技术在封闭量子系统中的应用问题。首先,利用相互作用图景变换将量子系统的动力学方程变换为齐次双线性方程,在此基础上设计Lyapunov控制律实现封闭量子系统一般混合态的控制；其次,针对目前Lyapunov方法普遍存在的收敛性问题,证明了一定条件下Lyapunov方法收敛的充分必要条件。利用量子状态的相干向量表示,设计Lyapunov函数的虚拟观测量算符,在保证控制律的稳定性的基础上,从Barblat引理出发,获得量子系统最大状态不变集的结构,通过分析最大不变集中状态的动力学稳定性,证明一定条件下量子Lyapunov方法收敛的充分必要条件；第三,针对量子系统在Lyapunov控制律作用下无法收敛到给定的目标状态的情况,利用李群分解技术对量子Lyapunov方法进行改进,提出量子跃迁路径规划策略,实现到目标状态的控制,并证明了该策略的收敛性；最后,通过数值仿真实验检验了相应的分析以及所提策略的正确性。
2、针对量子位系统进行控制场设计。首先,基于单量子位系统状态的Bloch球表示,从几何的角度设计控制场实现单量子位任意纯态之间的演化；其次,对于双量子位系统,根据绝热通道技术来设计控制脉冲,并利用不同脉冲之间的相干相位来制备不同的状态,分析并总结出了相干相位与制备的状态之间的近似关系；第三,从各个基本控制脉冲的物理意义出发,根据系统控制哈密顿量与能级跃迁结构之间的关系着手,针对多量子位系统设计控制脉冲序列,实现布居数的相干转移;第四,进行系统数值仿真实验对所设计的控制场进行检验。
3、研究开放量子系统控制场的设计问题。首先,从最简单的情况出发,研究外加控制场对粒子间相互作用引起的纯度以及相干性变化产生的影响,并设计控制场保持被控粒子的纯度以及消除粒子纯度的波动；第二,提出将系统粒子与辅助粒子间的相互作用作为控制手段,引入局部非幺正作用,并设计相互作用强度变化以对系统粒子的纯度和相干性进行补偿,以及抵消系统粒子的消相干过程；最后,进行系统数值仿真实验,验证了所设计控制场的有效性。
4、定义了一种弱测量算符的结构,并给出其参数需要满足的充分条件。分析弱测量对不同量子系统状态演化的影响,并讨论其在开放量子系统耗散及消相干控制问题中的应用。
The studies of control fields design methods for quantum systems is a critical issue in quantum control theory and practice, it can greatly promotes many developing domains such as quantum information, quantum physics, bond selective chemistry, nanometer and microbial techniques. However, due to the properties of quantum systems themselves, it is difficult to design control fields for generic high-dimension and complex quantum systems. By now, there is no universal control fields design method for quantum systems, so an untiring endeavor of the scholars in various domains is still needed. Under such a background, this thesis studies the control fields design methods for quantum systems including the open loop control design, quantum Lyapunov methods for closed quantum systems with generic mixed states, the control design for open quantum systems and so on. The main contents are as follows:
1. The Lyapunov based methods for quantum systems are researched. At first, the dynamical equation of the quantum system is transferred into a homogeneous bilinear one in the interaction picture, so it becomes a homogeneous bilinear equation. Based on this, the Lyapunov control law is designed to achieve the generic mixed states control for closed quantum systems described in the interaction picture. The next, aiming at the convergence problem universally exists in the quantum Lyapunov methods at present, the sufficient and necessary conditions are proved under certain assumptions. The observable operator in the Lyapunov function is constructed using the coherent vector presentation of quantum states to guarantee the stability the control law. Based on this, the largest invariant set of the controlled system is deduced utilizing the Barblat lemma. The sufficient and necessary conditions are proved through the analyzing of the dynamical stabilities of the states in the largest invariant set. Then, for the situation that the system can't converge to the given target state, the Lie group decomposition technology is utilized to improve the quantum Lyapunov methods, and a strategy called transition path programming is proposed to accomplish the control task, the convergence of the proposed strategy is also proved; at last, system numerical simulation experiments are done to verify the validity of the analysis and the strategy proposed.
2. Control fields for cubit systems are designed. Firstly, based on the Bloch sphere presentation of a single qubit state, control fields are designed from the viewpoint of the geometry to achieve an arbitrary pure state of a single qubit. Secondly, adiabatic passage technology is used to design control fields for two-qubit systems, the coherence phase between control pulses is utilized to prepare different quantum states, the relationship between the coherence phase and the states prepared are analyzed and an approximate equation is summarized. Thirdly, utilizing the physical meanings of the basic control pulses and the relation between the system control Hamiltonians and the energy level structure, control pulse sequences are designed to accomplish the population transfer of multi-qubit systems. And fourthly, system numerical simulations are done to verify the validity of the control pulses.
3. Control fields design methods for open quantum systems are studied. For the simplest case, the impact of external control fields on the purity and coherence variety due to the interaction between particles is studied, and control fields are designed to preserve the particle purity and eliminate the purity fluctuations. A new control method is proposed, in which local non-unitary operations are induced by an assistant system and its interactions with the priori system. By controlling the interactions between the two systems, the purity and coherence of the priori system are compensated, and the decoherence effect is counteracted. All the designs are verified by numerical simulation experiments.
4. A kind of weak measurement operators is defined. A sufficient condition of the parameters is given. The impact of weak measurements on different quantum systems are analyzed, and the applications of such measurements in dissipation and decoherence control for open quantum systems are also discussed.
引文
陈代展.2002.量子控制——一个全新的学科领域[J].控制与决策,17(5)：513-516.
陈宗海,董道毅,张陈斌.2005.量子控制导论[M].合肥：中国科学技术大学出版社.
丛爽,郑毅松,姬北辰等.2003a.量子系统控制发展综述[J].量子电子学报,20(1)：1-9.
从爽,郑毅松.2003b.量子力学系统控制的基础及现状[J].自动化博览,20(1)：41-44.
从爽.2006.量子力学系统控制导论[M].北京：科学出版社.
丛爽,东宁.2006.量子力学系统与双线性系统可控性关系的对比研究[J].量子电子学报,23：83-92.
从爽,杨洁,楼越升.2007.基于马尔科夫决策的量子系统状态布居数转移最短路径的决策[C].中国控制与决策学术年会论文集,东北大学出版社,367-370.
从爽,楼越升.2008a.开放量子系统中消相干及其控制策略[J].量子电子学报,25(6)：665-669.
丛爽,楼越升.2008b.利用相位的自旋1／2量子系统的相干控制[J].控制理论与应用,25(2)：187-192.
东宁,从爽.2005.量子系统中幺正演化矩阵分解办法的对比[C].第二十四届中国控制会议论文集.
董道毅,陈宗海,陈春林.2004a.量子控制系统模型的比较研究[C].系统仿真技术及应用,6：29-34.
董道毅,陈宗海.2004b.量子控制系统的建模与仿真研究[C].Proc. WCICA 2004, IEEEPress,276-279.
匡森.2007.基于Lyapunov和最优控制理论的量子系统控制方法的研究[D].[博士].合肥：中国科学技术大学.
楼越升,从爽.2007.基于Bloch球的量子系统状态演化的轨迹控制[C].第26届中国控制会议论文集,6：576-580.
叶怀安.1991.时变与泛函[M].合肥：中国科学技术大学出版社.
张永德.2006.量子信息物理原理[M].北京：科学出版社.
曾谨言.2000.量子力学[M].第三版.北京：科学出版社.
Albertini F, D'Alessandro D.2003. Notions of controllability for bilinear multilevel quantum systems [J]. IEEE Trans. Automat. Contr.,48:1399-1403.
Aliki R.2005. A unified picture of decoherence control [OL]. arXiv:quant-ph/0501109v2,1-14.
Altafini C.2003. Controllability properties for finite dimensional quantum Markovian master equations [J]. J. Math. Phys.,44(6):2357-2372.
Altafini C.2005. Feedback stabilization of quantum ensembles:a global convergence analysis on complex flag manifold [OL]. arXiv:quant-ph/0506268vl.
Altafini C.2007a.Feedback control of spin systems[J].Quantum Information Processing,6(1):9-36.
Altafini C.2007b.Feedback stabilization of isospectrol control systems on complex flag manifolds: Application to quantum ensembles [J]. IEEE Trans. Automat. Contr.,52(11):2019-2028.
Ardeen CJB, Yakovlev VV, Wilson KR et al.1997. Feedback quantum control of molecular electronic population transfer [J]. Chem. Phys. Lett.,280:151.
Armen MA, Au JK, Stockton JK et al.2002. Adaptive homodyne measurement of optical phase [J]. Phys. Rev. Lett.,89(13):133602.
Armstrong JA, Courtens E.1968. Solution of a pi-pulse problem [J]. J. Quantum Electronics,4(6): 411-419.
Assion A, Baumert T, Bergt M et al.1998. Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses [J]. Science,282:919-922.
Audretsch J, Diosi L, Konrad T.2002. Evolution of qubit under the influence of a succession of weak measurements with unitary feedback [J]. Phys. Rev. A,66:022310-022320.
Bardeen CJ, Yakovlev VV, Squier JA et al.1998. Quantum control of population transfer in green fluorescent protein by using chirped femtosecond pulses [J]. J. Am. Chem. Soc., 120(50):13023-13027.
Bartels RA, Backus S, Zeek E et al.2000. Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays [J]. Nature,406:164-166.
Bartels RA.2002. Coherent control of atoms and molecules [D]. [Ph. D.]. The University of Michigan.
Beauchard K, Coron JM, Mirrahimi M et al.2007. Implicit Lyapunov control of finite dimensional Schrodinger equations [J]. Systems & Control Letters,56:388-395.
Bennett CH, Divincenzo DP, Fuchs C A et al.1999. Quantum nonlocality without entanglement [J]. Phys. Rev. A,59(2):1070-1090.
Bennett CH, Divincenzo DP.2000. Quantum information and computation [J]. Nature,404: 247-252.
Bergmann K, Theuer H, Shore B.1998. Coherent population transfer among quantum states [J]. Rev. Mod. Phys.,70:1003.
Bergt M, Brixner T, Kiefer B et al.1999. Controlling the femtochemistry of Fe(Co)5 [J]. J. Phys. Chem. A,103(49):10381-10389.
Berman GP, Doolen GD, Lopez GV et al.1998. Quantum entangled states and quasiclassical dynamics in macroscopic spin systems [OL]. arXiv:quant-ph/9802015.
Bloch AM, Brockett RW, Rangan C.2009. Finite controllability of infinite-dimensional quantum systems [OL]. arXiv:quant-ph/0608075v2,1-34.
Boscaina U, Mason P.2006. Time minimal trajectories for a spin 1/2 particle in a magnetic field [J]. J. Math. Phys.,47(6):062101.
Braginsky VB, Vorontsov YI, Thorne KS.1980. Quantum nondemolition Measurements [J]. Science,209:547-557.
Braginsky VB, Khalili FY.1996. Quantum nondemolition measurements:the route from toys to tools [J]. Reviews of Modern Physics,68:1-11.
Brumer PW, Shapiro M.2003.Principles of the quantum control of molecular processes[M]. Wiley.
Byrd MS, Lidar DA.2003. Empirical determination of dynamical decoupling operations [J]. Phys. Rev. A,67:012324.
Cao J, Bardeen CJ, Wilson KR.1998. Molecular "pulse" for total inversion of electronic state population [J]. Phys. Rev. Lett.,80(7):1406-1409.
Chelkowski S, Bandrauk AD.1997. Raman chirped adiabatic passage:a new method for selective excitation of high vibrational states [J]. J. Raman Spectroscopy,28:459-466.
Chelkowski S, Gibson G.1995. Adiabatic climbing of vibrational ladders using Raman transitions with a chirped pump laser [J]. Phys. Rev. A,52(5):R3417-R3420.
Chu S.2002. Cold atoms and quantum control [J]. Nature,416:206-210.
Clark JW, Ong CK, Tarn TJ et al.1985. Quantum nondemolition filters [J]. Mathematical Systems Theory,18:33-35.
Clemente-Gallardo J, Leite FS.2003. Spin systems and minimal switching decompositions [C]. IEEE Int. Conf. Physics and Control,855-860.
Cong S, Kuang S.2007. Quantum control strategy based on state distance [J]. Acta Automatica Sinica,33(1):28-31.
Cong S, Lou YS.2008. Design of control sequence of pulses for the population transfer of high dimensional spin 1/2 quantum systems [J]. Journal of Systems Engineering and Electronics, 19(6):1226-1234.
Cook RL, Martin PJ, Geremia JM.2007. Optical coherent state discrimination using a closed loop quantum measurement [J]. Nature,446:774-777.
D'Alessandro D, Dahleh MA.2001. Optimal control of Two-level Quantum Systems [J]. IEEE Trans. Automat. Contr.,46:866-876.
Doherty AC, Jacobs K.1999a. Feedback-control of quantum systems using continuous state estimation [J]. Phys. Rev. A,60(4):2700-2711.
Doherty AC, Tan SM, Parkins AS et al.1999b. State determination in continuous measurement [J]. Phys. Rev. A,60(3):2380-2392.
Doherty AC, Doyle J, Mabuchi H et al.2000a. Robust control in the quantum domain [C]. Proc. 39th IEEE Conf. Decision and Control,949-954.
Doherty AC, Habib S, Jacobs K. et al.2000b. Quantum feedback control and classical control theory [J]. Phys. Rev. A,62:012105-012118.
Doherty AC, Habib S, Jungman G. 2001. Information, disturbance and Hamiltonian quantum feedback control [J]. Phys. Rev. A,63:062306-062318.
Duan LM, Guo G C.1997. Preserving coherence in quantum computation by pairing quantum bits [J]. Phys. Rev. Lett.,79:1953.
Duan LM, Guo G C.1998. Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment [J]. Phys. Rev. A,57:737
Facchi P, Pascazio S.2002. Quantum Zeno subspaces [J]. Phys. Rev. Lett.,89:080401.
Facchi P, Lidar D A, Pascazio S.2004. Unification of dynamical decoupling and the quantum Zeno effect [J]. Phys. Rev. A,69:032314.
Facchi P, Tasaki S, Pascazio S et al.2005. Control of decoherence:analysis and comparison of three different strategies [J]. Phys. Rev. A,71:022302.
Ferrante A, Pavon M, Raccanelli G.2002. Driving the propagator of a spin system:a feedback approach [C]. Proc.41st IEEE Conf. Decision and Control.
Fischer T, Maunz P, Pinkse PWH et al.2002. Feedback on the motion of a single atom in an optical cavity [J]. Phys. Rev. Lett.,88(16):163002.
Ganesan N, Tarn TJ.2007. Decoherence control in open quantum systems via classical feedback [J]. Phys. Rev. A,75:032323-032341.
Grivopoulos S, Bamieh B,2003, Lyapunov-based control of quantum systems [C]. Proc.42th IEEE Conf. Decision and Control,434-438.
Gross P, Neudauser D, Rabitz H.1993. Teaching Lasers to control molecules in the presence of laboratory field uncertainty and measurement imprecision [J]. J. Chem. Phys.,98:4557-4566
Herek JL. Wohlleben W. Cogdell R J et al.2002. Quantum control of energy flow in light harvesting [J]. Nature,417:533-535.
Huang GM, Tarn TJ.1983. On the controllability of quantum-mechanical systems [J]. J. Math. Phys.,24(11):2608-2618.
Imoto N.1996. Controlling two-level atoms with a quantized pi or pi/2 pulse [J]. Prog. Crystal Growth and Charact,33:295-301.
Itano WM, Heinzen DJ, Bollinger JJ et al.1990. Quantum zeno effect [J]. Phys. Rev. A,41(6): 2295-2301.
Johansen LM.2004. Weak measurement with arbitary probe states [J]. Phys. Rev. Lett.,93: 120402-120405.
Johansen LM, Luis A.2004. Nonclassicality in weak measurements [J]. Phys. Rev. A,70(5): 052115-052126.
Judson RS, Rabitz H.1992. Teaching Lasers to control molecules [J]. Phys. Rev. Lett.,68(10): 1500-1503.
Kaluza M, Muckerman JT.1995. Short-pulse population inversion and transmittance [J]. Phys. Rev. A,51(2):1694-1697.
Khaneja N, Brockett R, Glaser SJ.2001. Time optimal control in spin systems [J]. Phys. Rev. A, 63(3):032308.
Kodama R.2002. Nuclear fusion:fast heating scalable to laser fusion ignition [J]. Nature,418: 933-934.
Kosloff R, Rice SA, Gaspard P et al.1989. Wavepacket dancing:achieving chemical selectivity by shaping light pulses [J]. Chemical Physics,139:201-220.
Kuang S, Cong S.2008. Lyapunov control methods of closed quantum systems [J]. Automatica, 44(1):98-108.
Kuang S, Cong S, Lou YS.2009. Population control of quantum states based on invariant subsets under a diagonal Lyapunov function [C]. Joint 48th IEEE Conf. Decision and Control and 28th Chinese Conference,2486-2491.
Kuklinski JR, Gaubatz U, Hioe FT et al.1989. Adiabatic population transfer in a three-level system driven by delayed laser pulses [J]. Phys. Rev. A,40(11):6741-6744.
Lan CH.2003. Controllability of time-dependent quantum control systems [D]. [Ph.D.]. Saint Louis:Washington University.
LaSalle J, Lefschetz S.1961. Stability by Lyapunov's direct method with applications [M]. New York:Academic Press.
Last I, Jortner J,2002. Nuclear fusion driven by coulomb explosion of methane clusters [J]. J. Phys. Chem. A,106:10877-10885.
Levis RJ, Menkir GM, Rabitz H.2001. Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses [J]. Science,292:709-713.
Lidar DA, Chuang IL, Whaley KB.1998. Decoherence free subspaces for quantum computation [J]. Phys. Rev. Lett.,81:2594.
Lidar DA, Bacon D, Whaley KB.1999. Concatenating decoherence free subspaces with quantum error correcting codes [J]. Phys. Rev. Lett.,82:4556.
Lidar DA, Whaley KB.2003. in Irreversible quantum dynamics [M]. edited by F. Benatti and R. Floreanini, Lecture Notes in Physics, Berlin:Springer,622:83-120.
Lidar DA, Schneider S.2005. Stabilizing qubit coherence via tracking-control [J]. Quantum Information and Computation,5:350-363.
Lin EB.1989. Quantum control theory [J]. Contemporary Mathematics,97:269-278.
Lloyd S, Slotine JJE.2000. Quantum feedback with weak measurements [J]. Phys. Rev. A,62: 012307-012311.
Lou YS, Cong S.2008. Purity and coherence compensation by using interactions betwween particles in quantum system [J]. Journal of the Graduate of the Chinese of Science,25(5): 687-697.
Lou YS, Cong S, Xu RX.2009. Purity preservation of quantum systems by resonant field [C]. Proc.7th Asian Control Conference,959-963.
Lou YS, Cong S.2010. Weak Measurement-based Decoherence Control of Quantum Systems. Journal of the Graduate of the Chinese of Science, to be published
Mabuchi H, Khaneja N.2005. Principles and applications of control in quantum systems[J]. International Journal of Robust and Nonlinear Control,15:647-667.
Magnus W.1954. On the exponential solution of differential equations for linear operator [J]. Comm. Pure Appl. Math.,7:649-673.
Malinovsky VS.2004a. Quantum control of entanglement by phase manipulation of time-delayed pulse sequences [J]. Phys. Rev. A,70:042305.
Malinovsky VS, Sola IR.2004b. Quantum phase control of entanglement [J]. Phys. Rev. Lett.,93: 190502.
Mancini S. Bonifacio R.2001. Quantum Zeno-like effect due to competing decoherence mechanisms [J]. Phys. Rev. A,64:042111.
Mandilara A, Clark JW, Byrd MS.2005. Elliptical orbits in the Bloch sphere [J]. J. Optics B: Quantum and Semiclassical Optics,7:S277-S282.
Melinger JS, Gandhi SR, Hariharan A et al.1994. Adiabatic population transfer with frequency swept laser pulses [J]. J. Chem. Phys.,101(8):6439-6454.
Mensky M.1996. A note on reversibility of quantum jumps [J]. Phys. Lett. A,222:137-140.
Mirowski E, Stauffer HU, Ballard JB et al.2002. Effect of nonresonnant frequencies on the enhancement of quantum beat amplitudes in rovibrational states of Li2:the role of state spacing [J]. J. Chem. Phys.,117(24):11228-11238.
Mirrahimi M, Rouchon P.2004a. Trajectory generation for quantum systems based on Lyapunov techniques [C]. Proc. IFAC symposium NOLCOS.
Mirrahimi M, Rouchon P.2004b. Trajectory tracking for quantum systems:a Lyapunov approach [C]. Proc. Internationa] symposium MTNS.
Mirrahimi M, Rouchon P, Turinici G.2005. Lyapunov control of bilinear Schrodinger equations [J]. Automatica,41:1987-1994.
Mishima K, Hayashi M, Lina SH.2003. Coherence control between two quantum systems using spatial phase [J]. Physics Letters A,315:16-22.
Misra B, Sudarshan ECG.1977. The zeno's paradox in quantum theory [J]. Phys. Rev. A,18(4): 756-763.
Morrow NV, Dutta SK, Raithel G.2002. Feedback control of atomic motion in an optical lattice [J]. Phys. Rev. Lett.,88(9):093003.
Negrevergne C, Somma R, Ortiz G et al.2005. Liquid-state NMR simulation of quantum many body problems [J]. Phys. Rev. A,71:032344-032354.
Nielsen MA, Chuang 1L.2000. Quantum computation and quantum information [M]. Cambridge University Press.
Nugent-Glandorf L, Scheer M, Samuels DA et al.2001. Ultrafast time-resolved soft X-ray photoelectron spectroscopy of dissociating Br2 [J]. Phys. Rev. Lett.,87(19):193002-193005.
Ong CK, Huang GM, Tarn T J et al.1984. Invertibility of quantum-mechanical control systems [J]. Mathematical Systems Theory,17:335-350.
Oreshkov O, Brun TA.2005. Weak measurement are universal [J]. Phys. Rev. Lett.,95: 110409-110412.
Palma GM, Suominen K A, Ekert A K.1996. Quantum computers and dissipation [C]. Proc. Roc. London Ser. A,452:567-584.
Paul B, Moshe S.1992. Laser control of molecular processes [J]. Annu. Rev. Phys. Chem,43: 257-282.
Pearson BJ, White JL, Weinacht TC et al.2001. Coherent control using adaptive learning algorithms [J]. Phys. Rev. A,63:063412.
Peirce AP, Dahleh MA, Rabitz H.1988. Optimal control of quantum-mechanical systems: existence, numerical approximation and applications [J]. Phys. Rev. A,37(12):4950-4956.
Peirce AP.2003. Fifteen years of quantum control:from concept to experiment [J]. Multidiciplinary Research in control, LNCIS,289:65-72.
Petta JR, Johnson AC, Taylor JM et al.2005. Coherent manipulation of coupled electron spin in semiconductor quantum dots [J]. Science,309(5744):2180-2184.
Phan MQ, Rabitz H.1999. A self-guided algorithm for learning control of quantum-mechanical systems [J]. J. Chem. Phys.,110(1):34-41.
Prakelt A, Wollenhaupt M, Sarpe-Tudoran C et al.2004. Phase control of a two-photon transition
with shaped femtosecond laser-pulse sequences [J]. Phys. Rev. A,70(6):063407-063416.
Presilla C, Onofrio R, Tambini U.1996. Measurement quantum mechanics and experiments on quantum zeno effect [J]. Annals of Physics,248:95-121.
Rabitz H.2000. Algorithms for closed loop control of quantum dynamics [C]. IEEE int. Conf. Decision and Control,937-941.
Rabitz H, de Vivie-Riedle R, Motzkus M et al.2000. Whither the future of controlling quantum phenomena [J]. Science,288:824-828.
Ramakrishna V, Salapaka MV, Dahleh M et al.1995. Controllability of molecular systems [J]. Phys. Rev. A,51:960-966.
Rangelov AA, Vitanov NV, Yatsenko LP et al.2005. Stark-shift-chirped rapid-adiabatic-passage technique among three states [J]. Phys. Rev. A,72:053403.
Ruskov R, Korothov AN, Mize A.2006. Signatures of quantum behavior in single-qubit weak measurements [J]. Phys. Rev. Lett.,96:200404-200407.
Schirmer SG, Fu H, Solomon AI.2001. Complete controllability of quntum systems [J]. Phys. Rev. A,63:063410.
Schirmer SG, Leahy JV, Solomon AI.2002. Degrees of controllability for quantum systems and application to atomic systems [J]. J. Physics A,35:4125-4141.
Schirmer SG. 2001. Quantum control using lie group decompositions [C]. Proc.40th IEEE Conf. Decision and Control,289-303.
Schirmer SG, Pullen ICH, Solomon AI.2003. Controllability of quantum systems [OL]. arXiv: quant-ph/0302121,1-6.
Shapiro EA, Pe'er A, Ye J et al.2008. Piecewise adiabatic population transfer in a molecule vie a wave packet [J]. Phys. Rev. Lett.,101:023601.
Shi S, Rabitz H,1989. Selective excitation in harmonic molecular systems by optimally designed fields [J]. Chemical Physics,139:185-199.
Shor P.1995. Scheme for reducing decoherence in quantum computer memory [J]. Phys. Rev. A, 52:2493.
Smirnov AY.2003. Theory of weak continuous measurements in a strongly driven quantum bit [J]. Phys. Rev. B,68(13):134514-134530.
Smith GA, Silberfarb A, Deutsch IH et al.2006.Efficient quantum-state estimation by continuous weak measurement and dynamical control [J]. Phys. Rev. Lett.,97(18):180403-180406.
Steane AM.1995. Error correcting codes in quantum theory [J]. Phys. Rev. Lett.,77:793-797.
Steane AM.1999. in Introduction to quantum computation and information [M]. edited by H. K.Lo, S. Popescu, and T. P. Spiller, Singapore:World Scientific.
Sugawara M.2002. Local control theory for coherent manipulation of population dynamics [J]. Chem. Phys. Lett.,358:290-297.
Sugawara M.2003. General formulation of locally designed coherent control theory for quantum system [J]. J. Chem. Phys.,118(15):6784-6800
Suhail PS, David JT, Stuart AR.2002. Controllability of population transfer to degenerate states: Analytical and numerical results for a four-level system [J]. Phys. Rev. A,66:033405.
Tarn TJ, Huang GM, Clark J W.1980. Modelling of quantum mechanical control systems [J]. Jernal of Mathematical Modelling,1:109-121.
Tarn TJ, Clark JW, Lucarelli DG.2000. Contollability of quantum mechanical systems with continuous spectra [C]. Proc.39th IEEE Conference on Decision and Control,1:943-948.
Uhrig GS.2007. Keeping a physical quantum bit alive by optimized pi-pulse sequence[J]. Phys. Rev. Lett.,98:100504.
Vandersypen LMK, Chuang I L.2004. NMR techniques for quantum control and computation [J]. Rev. Mod. Phys.,76:1037-1069.
Vettori P.2002. On the convergence of a feedback control strategy for multilevel quantum systems [C]. Proc. MTNS Conf.
Viola L, Lloyd S.1998. Dynamical suppression of decoherence in two-state quantum systems [J]. Phys. Rev. A,58:2733.
Viola L, Knill E, Lloyd S.1999a. Dynamical decoupling of open quantum systems [J]. Phys. Rev. Lett.,82:2417-2421.
Viola L, Knill E, Lloyd S.1999b. Universal control of decoupled quantum systems [J]. Phys. Rev. Lett.,83:4888-4891.
Viola L, Knill E, Lloyd S.2000. Dynamical generation of Noiseless quantum subsystems [J]. Phys. Rev. Lett.,85:3520-3523.
Vitali D, Tombesi P.1999.Using parity kicks for decoherence control[J].Phys.Rev.A,59:4178-4186.
Vitali D, Tombesi P.2001. Heating and decoherence suppression using decoupling techniques [J]. Phys. Rev. A,65:012305.
Vitanov NV, Fleischhauer M, Shore BW et al.2001. in Advances in atomic molecular and optical physics [M]. edited by B. Bederson and H. Walther, New York:Academic,46:55-190.
Walls DF, Milburn G J.1994. Quantum Optics [M]. Berlin:Springer.
Wang SK, Jin JS, Li XQ.2004. Continuous weak measurement and feedback control of a solid state charge qubit:a physical unravelling of non-indblad master equation [J]. Phys. Rev. B, 76(4):1037-1069.
Wang X, Schirmer S.2008. Analysis of Lyapunov method for control of quantum states [OL]. arXiv:quant-ph/0801.0702v2.
Warren WS, Rabitz H, Dahleh M.1993. Coherent control of quantum dynamics [J]. Science, 259(12):1581-1585.
Wei J, Norman E.1964. On global representations of the solutions of linear differential equations as a product of exponentials [C]. Proc. Amer. Math. Soc.,15:327-334.
Weiner AM.2000. Femtosecond pulse shaping using spatial light modulators [J]. Rev.Sci.Instrum, 71:1929.
Wiseman HM, Milburn G J.1993. Quantum theory of optical feedback via homodyne detection [J]. Phys. Rev. Lett.,70(5):548-551.
Wisemen HM, Milburn GJ.1994. All-optical versus electro-optical quantum limited feedback [J]. Phys. Rev. A,49:4110-4125.
Wiseman H, Mancini S, Wang J.2002. Bayesian feedback versus Markovian feedback in a two level atom [J]. Phys. Rev. A,66:013807.
Wu RB, Li CW, Wang YZ.2002. Explicitly solvable extremals of time optimal control for 2-level quantum systems [J]. Phys. Lett. A,295:20-24.
Wu RB, Tarn TJ, Li CW.2006. Smooth controllability of infinite-dimensional quantum Markovian master equations [J]. Phys. Rev. A,73:012719.
Wu RB, Pechen A, Brif C et al.2007. Controllability of open quantum systems with Kraus-map dynamics [J]. J. Phys. A:Math. Theor.,40:5681-5693.
Wu RB, Pechen A, Rabitz H et al.2008. Control landscapes for observable preparation with open quantum systems [J]. J. Math. Phys.,49:022108.
Yanagisawa M, Kimra H.2003. Transfer function approch to quantum control--part I:Dyanamics of quantum feedback systems [J]. IEEE Trans. Automat. Contr.,48(12):2107-2120.
Zanardi P, Rasetti M.1997a. Noiseless quantum codes [J]. Phys. Rev. Lett..79:3306.
Zanardi P, Rasetti M.1997b. Error avoiding quantum codes [J]. Mod. Phys. Lett. B,11:1085.
Zanardi P.1998. Dissipation and decoherence in a quantum register [J]. Phys. Rev. A,57:3276.
Zanardi P.1999. Symmetrizing evolutions [J]. Phys. Rev. A,258:77-82.
Zhang CB, Dong DY, Chen ZH.2005. Control of non-controllable quantum systems:A quantum control algorithm based on Grover iteration [J]. J. Optics B:Quantum and Semiclassical Optics,7(10):S313-S317.
陈宗海,董道毅,张陈斌.2005.量子控制导论[M].合肥：中国科学技术大学出版社.
丛爽,郑毅松,姬北辰等.2003a.量子系统控制发展综述[J].量子电子学报,20(1)：1-9.
从爽,郑毅松.2003b.量子力学系统控制的基础及现状[J].自动化博览,20(1)：41-44.
从爽.2006.量子力学系统控制导论[M].北京：科学出版社.
丛爽,东宁.2006.量子力学系统与双线性系统可控性关系的对比研究[J].量子电子学报,23：83-92.
从爽,杨洁,楼越升.2007.基于马尔科夫决策的量子系统状态布居数转移最短路径的决策[C].中国控制与决策学术年会论文集,东北大学出版社,367-370.
从爽,楼越升.2008a.开放量子系统中消相干及其控制策略[J].量子电子学报,25(6)：665-669.
丛爽,楼越升.2008b.利用相位的自旋1／2量子系统的相干控制[J].控制理论与应用,25(2)：187-192.
东宁,从爽.2005.量子系统中幺正演化矩阵分解办法的对比[C].第二十四届中国控制会议论文集.
董道毅,陈宗海,陈春林.2004a.量子控制系统模型的比较研究[C].系统仿真技术及应用,6：29-34.
董道毅,陈宗海.2004b.量子控制系统的建模与仿真研究[C].Proc. WCICA 2004, IEEEPress,276-279.
匡森.2007.基于Lyapunov和最优控制理论的量子系统控制方法的研究[D].[博士].合肥：中国科学技术大学.
楼越升,从爽.2007.基于Bloch球的量子系统状态演化的轨迹控制[C].第26届中国控制会议论文集,6：576-580.
叶怀安.1991.时变与泛函[M].合肥：中国科学技术大学出版社.
张永德.2006.量子信息物理原理[M].北京：科学出版社.
曾谨言.2000.量子力学[M].第三版.北京：科学出版社.
Albertini F, D'Alessandro D.2003. Notions of controllability for bilinear multilevel quantum systems [J]. IEEE Trans. Automat. Contr.,48:1399-1403.
Aliki R.2005. A unified picture of decoherence control [OL]. arXiv:quant-ph/0501109v2,1-14.
Altafini C.2003. Controllability properties for finite dimensional quantum Markovian master equations [J]. J. Math. Phys.,44(6):2357-2372.
Altafini C.2005. Feedback stabilization of quantum ensembles:a global convergence analysis on complex flag manifold [OL]. arXiv:quant-ph/0506268vl.
Altafini C.2007a.Feedback control of spin systems[J].Quantum Information Processing,6(1):9-36.
Altafini C.2007b.Feedback stabilization of isospectrol control systems on complex flag manifolds: Application to quantum ensembles [J]. IEEE Trans. Automat. Contr.,52(11):2019-2028.
Ardeen CJB, Yakovlev VV, Wilson KR et al.1997. Feedback quantum control of molecular electronic population transfer [J]. Chem. Phys. Lett.,280:151.
Armen MA, Au JK, Stockton JK et al.2002. Adaptive homodyne measurement of optical phase [J]. Phys. Rev. Lett.,89(13):133602.
Armstrong JA, Courtens E.1968. Solution of a pi-pulse problem [J]. J. Quantum Electronics,4(6): 411-419.
Assion A, Baumert T, Bergt M et al.1998. Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses [J]. Science,282:919-922.
Audretsch J, Diosi L, Konrad T.2002. Evolution of qubit under the influence of a succession of weak measurements with unitary feedback [J]. Phys. Rev. A,66:022310-022320.
Bardeen CJ, Yakovlev VV, Squier JA et al.1998. Quantum control of population transfer in green fluorescent protein by using chirped femtosecond pulses [J]. J. Am. Chem. Soc., 120(50):13023-13027.
Bartels RA, Backus S, Zeek E et al.2000. Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays [J]. Nature,406:164-166.
Bartels RA.2002. Coherent control of atoms and molecules [D]. [Ph. D.]. The University of Michigan.
Beauchard K, Coron JM, Mirrahimi M et al.2007. Implicit Lyapunov control of finite dimensional Schrodinger equations [J]. Systems & Control Letters,56:388-395.
Bennett CH, Divincenzo DP, Fuchs C A et al.1999. Quantum nonlocality without entanglement [J]. Phys. Rev. A,59(2):1070-1090.
Bennett CH, Divincenzo DP.2000. Quantum information and computation [J]. Nature,404: 247-252.
Bergmann K, Theuer H, Shore B.1998. Coherent population transfer among quantum states [J]. Rev. Mod. Phys.,70:1003.
Bergt M, Brixner T, Kiefer B et al.1999. Controlling the femtochemistry of Fe(Co)5 [J]. J. Phys. Chem. A,103(49):10381-10389.
Berman GP, Doolen GD, Lopez GV et al.1998. Quantum entangled states and quasiclassical dynamics in macroscopic spin systems [OL]. arXiv:quant-ph/9802015.
Bloch AM, Brockett RW, Rangan C.2009. Finite controllability of infinite-dimensional quantum systems [OL]. arXiv:quant-ph/0608075v2,1-34.
Boscaina U, Mason P.2006. Time minimal trajectories for a spin 1/2 particle in a magnetic field [J]. J. Math. Phys.,47(6):062101.
Braginsky VB, Vorontsov YI, Thorne KS.1980. Quantum nondemolition Measurements [J]. Science,209:547-557.
Braginsky VB, Khalili FY.1996. Quantum nondemolition measurements:the route from toys to tools [J]. Reviews of Modern Physics,68:1-11.
Brumer PW, Shapiro M.2003.Principles of the quantum control of molecular processes[M]. Wiley.
Byrd MS, Lidar DA.2003. Empirical determination of dynamical decoupling operations [J]. Phys. Rev. A,67:012324.
Cao J, Bardeen CJ, Wilson KR.1998. Molecular "pulse" for total inversion of electronic state population [J]. Phys. Rev. Lett.,80(7):1406-1409.
Chelkowski S, Bandrauk AD.1997. Raman chirped adiabatic passage:a new method for selective excitation of high vibrational states [J]. J. Raman Spectroscopy,28:459-466.
Chelkowski S, Gibson G.1995. Adiabatic climbing of vibrational ladders using Raman transitions with a chirped pump laser [J]. Phys. Rev. A,52(5):R3417-R3420.
Chu S.2002. Cold atoms and quantum control [J]. Nature,416:206-210.
Clark JW, Ong CK, Tarn TJ et al.1985. Quantum nondemolition filters [J]. Mathematical Systems Theory,18:33-35.
Clemente-Gallardo J, Leite FS.2003. Spin systems and minimal switching decompositions [C]. IEEE Int. Conf. Physics and Control,855-860.
Cong S, Kuang S.2007. Quantum control strategy based on state distance [J]. Acta Automatica Sinica,33(1):28-31.
Cong S, Lou YS.2008. Design of control sequence of pulses for the population transfer of high dimensional spin 1/2 quantum systems [J]. Journal of Systems Engineering and Electronics, 19(6):1226-1234.
Cook RL, Martin PJ, Geremia JM.2007. Optical coherent state discrimination using a closed loop quantum measurement [J]. Nature,446:774-777.
D'Alessandro D, Dahleh MA.2001. Optimal control of Two-level Quantum Systems [J]. IEEE Trans. Automat. Contr.,46:866-876.
Doherty AC, Jacobs K.1999a. Feedback-control of quantum systems using continuous state estimation [J]. Phys. Rev. A,60(4):2700-2711.
Doherty AC, Tan SM, Parkins AS et al.1999b. State determination in continuous measurement [J]. Phys. Rev. A,60(3):2380-2392.
Doherty AC, Doyle J, Mabuchi H et al.2000a. Robust control in the quantum domain [C]. Proc. 39th IEEE Conf. Decision and Control,949-954.
Doherty AC, Habib S, Jacobs K. et al.2000b. Quantum feedback control and classical control theory [J]. Phys. Rev. A,62:012105-012118.
Doherty AC, Habib S, Jungman G. 2001. Information, disturbance and Hamiltonian quantum feedback control [J]. Phys. Rev. A,63:062306-062318.
Duan LM, Guo G C.1997. Preserving coherence in quantum computation by pairing quantum bits [J]. Phys. Rev. Lett.,79:1953.
Duan LM, Guo G C.1998. Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment [J]. Phys. Rev. A,57:737
Facchi P, Pascazio S.2002. Quantum Zeno subspaces [J]. Phys. Rev. Lett.,89:080401.
Facchi P, Lidar D A, Pascazio S.2004. Unification of dynamical decoupling and the quantum Zeno effect [J]. Phys. Rev. A,69:032314.
Facchi P, Tasaki S, Pascazio S et al.2005. Control of decoherence:analysis and comparison of three different strategies [J]. Phys. Rev. A,71:022302.
Ferrante A, Pavon M, Raccanelli G.2002. Driving the propagator of a spin system:a feedback approach [C]. Proc.41st IEEE Conf. Decision and Control.
Fischer T, Maunz P, Pinkse PWH et al.2002. Feedback on the motion of a single atom in an optical cavity [J]. Phys. Rev. Lett.,88(16):163002.
Ganesan N, Tarn TJ.2007. Decoherence control in open quantum systems via classical feedback [J]. Phys. Rev. A,75:032323-032341.
Grivopoulos S, Bamieh B,2003, Lyapunov-based control of quantum systems [C]. Proc.42th IEEE Conf. Decision and Control,434-438.
Gross P, Neudauser D, Rabitz H.1993. Teaching Lasers to control molecules in the presence of laboratory field uncertainty and measurement imprecision [J]. J. Chem. Phys.,98:4557-4566
Herek JL. Wohlleben W. Cogdell R J et al.2002. Quantum control of energy flow in light harvesting [J]. Nature,417:533-535.
Huang GM, Tarn TJ.1983. On the controllability of quantum-mechanical systems [J]. J. Math. Phys.,24(11):2608-2618.
Imoto N.1996. Controlling two-level atoms with a quantized pi or pi/2 pulse [J]. Prog. Crystal Growth and Charact,33:295-301.
Itano WM, Heinzen DJ, Bollinger JJ et al.1990. Quantum zeno effect [J]. Phys. Rev. A,41(6): 2295-2301.
Johansen LM.2004. Weak measurement with arbitary probe states [J]. Phys. Rev. Lett.,93: 120402-120405.
Johansen LM, Luis A.2004. Nonclassicality in weak measurements [J]. Phys. Rev. A,70(5): 052115-052126.
Judson RS, Rabitz H.1992. Teaching Lasers to control molecules [J]. Phys. Rev. Lett.,68(10): 1500-1503.
Kaluza M, Muckerman JT.1995. Short-pulse population inversion and transmittance [J]. Phys. Rev. A,51(2):1694-1697.
Khaneja N, Brockett R, Glaser SJ.2001. Time optimal control in spin systems [J]. Phys. Rev. A, 63(3):032308.
Kodama R.2002. Nuclear fusion:fast heating scalable to laser fusion ignition [J]. Nature,418: 933-934.
Kosloff R, Rice SA, Gaspard P et al.1989. Wavepacket dancing:achieving chemical selectivity by shaping light pulses [J]. Chemical Physics,139:201-220.
Kuang S, Cong S.2008. Lyapunov control methods of closed quantum systems [J]. Automatica, 44(1):98-108.
Kuang S, Cong S, Lou YS.2009. Population control of quantum states based on invariant subsets under a diagonal Lyapunov function [C]. Joint 48th IEEE Conf. Decision and Control and 28th Chinese Conference,2486-2491.
Kuklinski JR, Gaubatz U, Hioe FT et al.1989. Adiabatic population transfer in a three-level system driven by delayed laser pulses [J]. Phys. Rev. A,40(11):6741-6744.
Lan CH.2003. Controllability of time-dependent quantum control systems [D]. [Ph.D.]. Saint Louis:Washington University.
LaSalle J, Lefschetz S.1961. Stability by Lyapunov's direct method with applications [M]. New York:Academic Press.
Last I, Jortner J,2002. Nuclear fusion driven by coulomb explosion of methane clusters [J]. J. Phys. Chem. A,106:10877-10885.
Levis RJ, Menkir GM, Rabitz H.2001. Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses [J]. Science,292:709-713.
Lidar DA, Chuang IL, Whaley KB.1998. Decoherence free subspaces for quantum computation [J]. Phys. Rev. Lett.,81:2594.
Lidar DA, Bacon D, Whaley KB.1999. Concatenating decoherence free subspaces with quantum error correcting codes [J]. Phys. Rev. Lett.,82:4556.
Lidar DA, Whaley KB.2003. in Irreversible quantum dynamics [M]. edited by F. Benatti and R. Floreanini, Lecture Notes in Physics, Berlin:Springer,622:83-120.
Lidar DA, Schneider S.2005. Stabilizing qubit coherence via tracking-control [J]. Quantum Information and Computation,5:350-363.
Lin EB.1989. Quantum control theory [J]. Contemporary Mathematics,97:269-278.
Lloyd S, Slotine JJE.2000. Quantum feedback with weak measurements [J]. Phys. Rev. A,62: 012307-012311.
Lou YS, Cong S.2008. Purity and coherence compensation by using interactions betwween particles in quantum system [J]. Journal of the Graduate of the Chinese of Science,25(5): 687-697.
Lou YS, Cong S, Xu RX.2009. Purity preservation of quantum systems by resonant field [C]. Proc.7th Asian Control Conference,959-963.
Lou YS, Cong S.2010. Weak Measurement-based Decoherence Control of Quantum Systems. Journal of the Graduate of the Chinese of Science, to be published
Mabuchi H, Khaneja N.2005. Principles and applications of control in quantum systems[J]. International Journal of Robust and Nonlinear Control,15:647-667.
Magnus W.1954. On the exponential solution of differential equations for linear operator [J]. Comm. Pure Appl. Math.,7:649-673.
Malinovsky VS.2004a. Quantum control of entanglement by phase manipulation of time-delayed pulse sequences [J]. Phys. Rev. A,70:042305.
Malinovsky VS, Sola IR.2004b. Quantum phase control of entanglement [J]. Phys. Rev. Lett.,93: 190502.
Mancini S. Bonifacio R.2001. Quantum Zeno-like effect due to competing decoherence mechanisms [J]. Phys. Rev. A,64:042111.
Mandilara A, Clark JW, Byrd MS.2005. Elliptical orbits in the Bloch sphere [J]. J. Optics B: Quantum and Semiclassical Optics,7:S277-S282.
Melinger JS, Gandhi SR, Hariharan A et al.1994. Adiabatic population transfer with frequency swept laser pulses [J]. J. Chem. Phys.,101(8):6439-6454.
Mensky M.1996. A note on reversibility of quantum jumps [J]. Phys. Lett. A,222:137-140.
Mirowski E, Stauffer HU, Ballard JB et al.2002. Effect of nonresonnant frequencies on the enhancement of quantum beat amplitudes in rovibrational states of Li2:the role of state spacing [J]. J. Chem. Phys.,117(24):11228-11238.
Mirrahimi M, Rouchon P.2004a. Trajectory generation for quantum systems based on Lyapunov techniques [C]. Proc. IFAC symposium NOLCOS.
Mirrahimi M, Rouchon P.2004b. Trajectory tracking for quantum systems:a Lyapunov approach [C]. Proc. Internationa] symposium MTNS.
Mirrahimi M, Rouchon P, Turinici G.2005. Lyapunov control of bilinear Schrodinger equations [J]. Automatica,41:1987-1994.
Mishima K, Hayashi M, Lina SH.2003. Coherence control between two quantum systems using spatial phase [J]. Physics Letters A,315:16-22.
Misra B, Sudarshan ECG.1977. The zeno's paradox in quantum theory [J]. Phys. Rev. A,18(4): 756-763.
Morrow NV, Dutta SK, Raithel G.2002. Feedback control of atomic motion in an optical lattice [J]. Phys. Rev. Lett.,88(9):093003.
Negrevergne C, Somma R, Ortiz G et al.2005. Liquid-state NMR simulation of quantum many body problems [J]. Phys. Rev. A,71:032344-032354.
Nielsen MA, Chuang 1L.2000. Quantum computation and quantum information [M]. Cambridge University Press.
Nugent-Glandorf L, Scheer M, Samuels DA et al.2001. Ultrafast time-resolved soft X-ray photoelectron spectroscopy of dissociating Br2 [J]. Phys. Rev. Lett.,87(19):193002-193005.
Ong CK, Huang GM, Tarn T J et al.1984. Invertibility of quantum-mechanical control systems [J]. Mathematical Systems Theory,17:335-350.
Oreshkov O, Brun TA.2005. Weak measurement are universal [J]. Phys. Rev. Lett.,95: 110409-110412.
Palma GM, Suominen K A, Ekert A K.1996. Quantum computers and dissipation [C]. Proc. Roc. London Ser. A,452:567-584.
Paul B, Moshe S.1992. Laser control of molecular processes [J]. Annu. Rev. Phys. Chem,43: 257-282.
Pearson BJ, White JL, Weinacht TC et al.2001. Coherent control using adaptive learning algorithms [J]. Phys. Rev. A,63:063412.
Peirce AP, Dahleh MA, Rabitz H.1988. Optimal control of quantum-mechanical systems: existence, numerical approximation and applications [J]. Phys. Rev. A,37(12):4950-4956.
Peirce AP.2003. Fifteen years of quantum control:from concept to experiment [J]. Multidiciplinary Research in control, LNCIS,289:65-72.
Petta JR, Johnson AC, Taylor JM et al.2005. Coherent manipulation of coupled electron spin in semiconductor quantum dots [J]. Science,309(5744):2180-2184.
Phan MQ, Rabitz H.1999. A self-guided algorithm for learning control of quantum-mechanical systems [J]. J. Chem. Phys.,110(1):34-41.
Prakelt A, Wollenhaupt M, Sarpe-Tudoran C et al.2004. Phase control of a two-photon transition
with shaped femtosecond laser-pulse sequences [J]. Phys. Rev. A,70(6):063407-063416.
Presilla C, Onofrio R, Tambini U.1996. Measurement quantum mechanics and experiments on quantum zeno effect [J]. Annals of Physics,248:95-121.
Rabitz H.2000. Algorithms for closed loop control of quantum dynamics [C]. IEEE int. Conf. Decision and Control,937-941.
Rabitz H, de Vivie-Riedle R, Motzkus M et al.2000. Whither the future of controlling quantum phenomena [J]. Science,288:824-828.
Ramakrishna V, Salapaka MV, Dahleh M et al.1995. Controllability of molecular systems [J]. Phys. Rev. A,51:960-966.
Rangelov AA, Vitanov NV, Yatsenko LP et al.2005. Stark-shift-chirped rapid-adiabatic-passage technique among three states [J]. Phys. Rev. A,72:053403.
Ruskov R, Korothov AN, Mize A.2006. Signatures of quantum behavior in single-qubit weak measurements [J]. Phys. Rev. Lett.,96:200404-200407.
Schirmer SG, Fu H, Solomon AI.2001. Complete controllability of quntum systems [J]. Phys. Rev. A,63:063410.
Schirmer SG, Leahy JV, Solomon AI.2002. Degrees of controllability for quantum systems and application to atomic systems [J]. J. Physics A,35:4125-4141.
Schirmer SG. 2001. Quantum control using lie group decompositions [C]. Proc.40th IEEE Conf. Decision and Control,289-303.
Schirmer SG, Pullen ICH, Solomon AI.2003. Controllability of quantum systems [OL]. arXiv: quant-ph/0302121,1-6.
Shapiro EA, Pe'er A, Ye J et al.2008. Piecewise adiabatic population transfer in a molecule vie a wave packet [J]. Phys. Rev. Lett.,101:023601.
Shi S, Rabitz H,1989. Selective excitation in harmonic molecular systems by optimally designed fields [J]. Chemical Physics,139:185-199.
Shor P.1995. Scheme for reducing decoherence in quantum computer memory [J]. Phys. Rev. A, 52:2493.
Smirnov AY.2003. Theory of weak continuous measurements in a strongly driven quantum bit [J]. Phys. Rev. B,68(13):134514-134530.
Smith GA, Silberfarb A, Deutsch IH et al.2006.Efficient quantum-state estimation by continuous weak measurement and dynamical control [J]. Phys. Rev. Lett.,97(18):180403-180406.
Steane AM.1995. Error correcting codes in quantum theory [J]. Phys. Rev. Lett.,77:793-797.
Steane AM.1999. in Introduction to quantum computation and information [M]. edited by H. K.Lo, S. Popescu, and T. P. Spiller, Singapore:World Scientific.
Sugawara M.2002. Local control theory for coherent manipulation of population dynamics [J]. Chem. Phys. Lett.,358:290-297.
Sugawara M.2003. General formulation of locally designed coherent control theory for quantum system [J]. J. Chem. Phys.,118(15):6784-6800
Suhail PS, David JT, Stuart AR.2002. Controllability of population transfer to degenerate states: Analytical and numerical results for a four-level system [J]. Phys. Rev. A,66:033405.
Tarn TJ, Huang GM, Clark J W.1980. Modelling of quantum mechanical control systems [J]. Jernal of Mathematical Modelling,1:109-121.
Tarn TJ, Clark JW, Lucarelli DG.2000. Contollability of quantum mechanical systems with continuous spectra [C]. Proc.39th IEEE Conference on Decision and Control,1:943-948.
Uhrig GS.2007. Keeping a physical quantum bit alive by optimized pi-pulse sequence[J]. Phys. Rev. Lett.,98:100504.
Vandersypen LMK, Chuang I L.2004. NMR techniques for quantum control and computation [J]. Rev. Mod. Phys.,76:1037-1069.
Vettori P.2002. On the convergence of a feedback control strategy for multilevel quantum systems [C]. Proc. MTNS Conf.
Viola L, Lloyd S.1998. Dynamical suppression of decoherence in two-state quantum systems [J]. Phys. Rev. A,58:2733.
Viola L, Knill E, Lloyd S.1999a. Dynamical decoupling of open quantum systems [J]. Phys. Rev. Lett.,82:2417-2421.
Viola L, Knill E, Lloyd S.1999b. Universal control of decoupled quantum systems [J]. Phys. Rev. Lett.,83:4888-4891.
Viola L, Knill E, Lloyd S.2000. Dynamical generation of Noiseless quantum subsystems [J]. Phys. Rev. Lett.,85:3520-3523.
Vitali D, Tombesi P.1999.Using parity kicks for decoherence control[J].Phys.Rev.A,59:4178-4186.
Vitali D, Tombesi P.2001. Heating and decoherence suppression using decoupling techniques [J]. Phys. Rev. A,65:012305.
Vitanov NV, Fleischhauer M, Shore BW et al.2001. in Advances in atomic molecular and optical physics [M]. edited by B. Bederson and H. Walther, New York:Academic,46:55-190.
Walls DF, Milburn G J.1994. Quantum Optics [M]. Berlin:Springer.
Wang SK, Jin JS, Li XQ.2004. Continuous weak measurement and feedback control of a solid state charge qubit:a physical unravelling of non-indblad master equation [J]. Phys. Rev. B, 76(4):1037-1069.
Wang X, Schirmer S.2008. Analysis of Lyapunov method for control of quantum states [OL]. arXiv:quant-ph/0801.0702v2.
Warren WS, Rabitz H, Dahleh M.1993. Coherent control of quantum dynamics [J]. Science, 259(12):1581-1585.
Wei J, Norman E.1964. On global representations of the solutions of linear differential equations as a product of exponentials [C]. Proc. Amer. Math. Soc.,15:327-334.
Weiner AM.2000. Femtosecond pulse shaping using spatial light modulators [J]. Rev.Sci.Instrum, 71:1929.
Wiseman HM, Milburn G J.1993. Quantum theory of optical feedback via homodyne detection [J]. Phys. Rev. Lett.,70(5):548-551.
Wisemen HM, Milburn GJ.1994. All-optical versus electro-optical quantum limited feedback [J]. Phys. Rev. A,49:4110-4125.
Wiseman H, Mancini S, Wang J.2002. Bayesian feedback versus Markovian feedback in a two level atom [J]. Phys. Rev. A,66:013807.
Wu RB, Li CW, Wang YZ.2002. Explicitly solvable extremals of time optimal control for 2-level quantum systems [J]. Phys. Lett. A,295:20-24.
Wu RB, Tarn TJ, Li CW.2006. Smooth controllability of infinite-dimensional quantum Markovian master equations [J]. Phys. Rev. A,73:012719.
Wu RB, Pechen A, Brif C et al.2007. Controllability of open quantum systems with Kraus-map dynamics [J]. J. Phys. A:Math. Theor.,40:5681-5693.
Wu RB, Pechen A, Rabitz H et al.2008. Control landscapes for observable preparation with open quantum systems [J]. J. Math. Phys.,49:022108.
Yanagisawa M, Kimra H.2003. Transfer function approch to quantum control--part I:Dyanamics of quantum feedback systems [J]. IEEE Trans. Automat. Contr.,48(12):2107-2120.
Zanardi P, Rasetti M.1997a. Noiseless quantum codes [J]. Phys. Rev. Lett..79:3306.
Zanardi P, Rasetti M.1997b. Error avoiding quantum codes [J]. Mod. Phys. Lett. B,11:1085.
Zanardi P.1998. Dissipation and decoherence in a quantum register [J]. Phys. Rev. A,57:3276.
Zanardi P.1999. Symmetrizing evolutions [J]. Phys. Rev. A,258:77-82.
Zhang CB, Dong DY, Chen ZH.2005. Control of non-controllable quantum systems:A quantum control algorithm based on Grover iteration [J]. J. Optics B:Quantum and Semiclassical Optics,7(10):S313-S317.
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