随机开放量子系统模型及其反馈控制的特性分析

J4 ›› 2015, Vol. 32 ›› Issue (2): 186-197.

随机开放量子系统模型及其反馈控制的特性分析

丛爽, 薛静静

中国科学技术大学自动化系，安徽合肥，230026)

收稿日期:2014-05-29 修回日期:2014-07-18 出版日期:2015-03-28 发布日期:2015-03-17
通讯作者: 丛爽（1961- ），女，山东文登人，博士，教授，博士生导师，现主要从事人工神经网络、模糊神经系统、运动控制、智能控制、量子系统控制等方向的研究。 E-mail:scong@ustc.edu.cn
作者简介:薛静静（1989-）江苏南通人，研究生，主要从事随机量子建模及其控制方面的研究。 E-mail: xuejj@mail.ustc.edu.cn
基金资助:
国家重点基础研究发展计划（973）（2011CBA00200）

Characteristics analysis of stochastic open quantum system models and feedback control

CONG Shuang, Xue Jingjing

Department of Automation, University of Science and Technology of China, Hefei 230027, China

Received:2014-05-29 Revised:2014-07-18 Published:2015-03-28 Online:2015-03-17

摘要/Abstract

摘要：

研究了不同情况下基于连续测量的随机开放量子系统模型。对于受到测量影响的不同开放量子系统模型，分析了模型建立的条件、模型的组成及其影响；对于所简化的模型，分析了其简化的过程；同时对不同模型之间的关系进行对比分析。基于估计状态的随机开放量子系统的反馈控制，分别对目前已有的开关控制和连续性控制在本征态之间状态转移的控制思想、所具有的特性、控制效果、适用条件、改进过程等进行了对比研究。同时还探讨了环境退相干和时间延迟影响下反馈控制器的设计。

关键词: 量子控制, 随机开放量子系统模型, 量子连续测量, 量子滤波器, 量子反馈控制

Abstract:

The stochastic open quantum system models undergoing continuous measurement in different cases are investigated. For different stochastic open quantum system models affected by the measurement, the model establishment conditions, the composition of model component and its effect are analyzed. For the simplified models, the processes of simplification are also analyzed. At the same time, the relationships between different models are compared. Based on the stochastic open quantum systems with the state estimation, , the existed switch and continuous control laws which are used to transfer the quantum states between the eigenstates are comparative analyzed from their control ideas, the characteristics, the control effect, the condition of using, to the improving process. The feedback controller design is also discussed under the influences of environment decoherence and time-delay.

Key words: quantum control, stochastic open quantum system models, quantum continuous measurement, quantum filter, quantum feedback control

中图分类号:

O411，TP13

丛爽薛静静. 随机开放量子系统模型及其反馈控制的特性分析[J]. J4, 2015, 32(2): 186-197.

CONG Shuang, Xue Jingjing. Characteristics analysis of stochastic open quantum system models and feedback control[J]. J4, 2015, 32(2): 186-197.

参考文献

[1] Yang J, Cong S. Research on models of open quantum system interacted with bath[J]. Chinese Journal of Quantum Electronics, 2012, 28(6): 660-673 (in Chinese)
[2] Cong S. State manipulation in Lyapunov-based quantum system control methods[J]. Control Theory & Applications, 2012, 29(3): 273-281 (in Chinese)
[3] Dong D, Petersen I R. Quantum control theory and applications: a survey[J]. IET Control Theory & Applications, 2010, 4(12): 2651-2671.
[4] Cong S, Kuang S. Review of state estimation methods in quantum systems[J]. Control and Decision, 2008, 23(2): 121-126.
[5] Gillett G G, Dalton R B, Lanyon B P, Almeida M P, Barbieri M, Pryde G J, O'Brien J L, Resch K J, Bartlett S D, White A G. Experimental Feedback Control of Quantum Systems Using Weak Measurements[J]. Physical Review Letters, 2010, 104, 080503
[6] Nishio K, Kashima K, Imura J. Effects of time delay in feedback control of linear quantum systems[J]. Physical Review A, 2009, 79, 062105
[7] Tsumura K. Global stabilization at arbitrary eigenstates of N-dimensional quantum spin systems via continuous feedback[C], 2008 American Control Conference, 2008: 4148 - 4153
[8] Van Handel R, Stockton J K, Mabuchi H. Feedback control of quantum state reduction[J]. Automatic Control, IEEE Transactions on, 2005, 50(6): 768-780.
[9] Belavkin V. Theory of the control of observable quantum systems[J]. Automatica and Remote Control, 1983, 44(2): 178-188.
[10] Bouten L, van Handel R, James M R. A Discrete Invitation to Quantum Filtering and Feedback Control[J]. Siam Review, 2009, 51(2): 239-316.
[11] Stockton J, Armen M, Mabuchi H. Programmable logic devices in experimental quantum optics[J]. Journal of the Optical Society of America B-Optical Physics, 2002, 19(12): 3019-3027.
[12] James M R, Nurdin H I, Petersen I R. Control of Linear Quantum Stochastic Systems[J]. IEEE Transactions on Automatic Control, 2008, 53(8): 1787-1803.
[13] Bouten L, Edwards S, Belavkin V P. Bellman equations for optimal feedback control of qubit states[J]. Journal of Physics B-Atomic Molecular and Optical Physics, 2005, 38(3): 151-160.
[14] Edwards S C, Belavkin V P. Optimal quantum filtering and quantum feedback control[J]. arXiv preprint quant-ph/0506018, 2005.
[15] Mirrahimi M, Van Handel R. Stabilizing feedback controls for quantum systems[J]. Siam Journal on Control and Optimization, 2007, 46(2): 445-467.
[16] Tsumura K. Global stabilization of N-dimensional quantum spin systems via continuous feedback[C]. in 2007 American Control Conference. 2007, 2129 - 2134
[17] Ge S S, Vu T L, Hang C C. Non-smooth Lyapunov function-based global stabilization for quantum filters[J]. Automatica, 2012, 48(6): 1031-1044.
[18] Steck D A, Jacobs K, Mabuchi H, Habib S, Bhattacharya T. Feedback cooling of atomic motion in cavity QED[J]. Physical Review A, 2006, 74(1): 012322
[19] Kashima K, Nishio K. Global stabilization of two-dimensional quantum spin systems despite estimation delay[C], the 46th IEEE Conference on Decision and Control. New Orleans, LA, USA, Dec. 12-14 , 2007: 6352-6357-
[20] Ge S S, Vu T L, Lee T H. Quantum Measurement-Based Feedback Control: A Nonsmooth Time Delay Control Approach[J]. Siam Journal on Control and Optimization, 2012, 50(2): 845-863.
[21] Zhang J, Liu Y X, Wu R B, Li C W, Tarn T J. Transition from weak to strong measurements by nonlinear quantum feedback control[J]. Physical Review A, 2010, 82, 022101
[22] Gleyzes S, Kuhr S, Guerlin C, Bernu J, Deleglise S, Hoff U B, Brune M, Raimond J-M, Haroche S. Quantum jumps of light recording the birth and death of a photon in a cavity[J]. Nature, 2007, 446(7133): 297-300.
[23] Bouten L, Van Handel R, James M R. An introduction to quantum filtering[J]. SIAM Journal on Control and Optimization, 2007, 46(6): 2199-2241.
[24] Altafini C, Ticozzi F. Modeling and Control of Quantum Systems: An Introduction[J]. IEEE Transactions on Automatic Control, 2012, 57(8): 1898-1917.
[25] Thomsen L, Mancini S, Wiseman H M. Continuous quantum nondemolition feedback and unconditional atomic spin squeezing[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2002, 35(23): 4937.
[26] Kashima K, Yamamoto N. Control of quantum systems despite feedback delay[J]. IEEE Transactions on Automatic Control, 2009, 54(4): 876-881.
[27] Gough J, Belavkin V P, Smolyanov O G. Hamilton–Jacobi–Bellman equations for quantum optimal feedback control[J]. Journal of Optics B: Quantum and Semiclassical Optics, 2005, 7(10): S237-S244.
[28] Jacobs K, Steck D A. A straightforward introduction to continuous quantum measurement[J]. Contemporary Physics, 2006, 47(5): 279-303.
[29] Matsumoto K, Tsumura K, Hara S. Synthesis of stabilizing switched controllers for N-dimensional quantum angular momentum systems[J]. arXiv preprint math-ph/0605003, 2006.
[30] Ge S S, Vu T L, He W, Hang C C. Non-smooth Lyapunov Function-Based Global Stabilization for 2-Dimensional Quantum Filters[C]. in 49th IEEE Conference on Decision and Control. Dec. 2010, Atlanta, USA, 3772-3777
[31] Liberzon D, Morse A S. Basic problems in stability and design of switched systems[J]. Control Systems, IEEE, 1999, 19(5): 59-70.
[32] Han T-T, Ge S S, Lee T H. Persistent dwell-time switched nonlinear systems: variation paradigm and gauge design[J]. IEEE Transactions on Automatic Control, 2010, 55(2): 321-337.
[33] Qi B, Guo L. Is measurement-based feedback still better for quantum control systems?[J]. Systems & Control Letters, 2010, 59(6): 333-339.
[34] Cong S, Control of Quantum Systems: Theory and Methods, John Wiley & Sons, Singapore Pte. Ltd, 2014