开放量子系统状态最优跟踪控制的研究

计算机科学 ›› 2013, Vol. 40 ›› Issue (12): 251-253.

开放量子系统状态最优跟踪控制的研究

黄泽霞,黄德才,俞攸红

浙江工业大学信息学院杭州310023;浙江工业大学计算机科学与技术学院、软件学院杭州310023;浙江工业大学理学院杭州310023

出版日期:2018-11-16 发布日期:2018-11-16
基金资助:
本文受国家自然科学基金项目(10774131)资助

Optimal Tracking Control of Population Transfer in Open Quantum Systems

HUANG Ze-xia,HUANG De-cai and YU You-hong

Online:2018-11-16 Published:2018-11-16

摘要/Abstract

摘要： 利用Liouville超算符变换方法,对伴随着耗散的开放量子系统状态演化的方程进行精简,并在最优控制的基础上,利用随时间变化的密度函数来设计性能指标,提出了一种高效的单调收敛的最优跟踪控制方法。此方法可以使系统在实数空间中沿给定时间变化的轨迹运动,并控制其随时间变化的布居数。同时,在MATLAB环境下以两能级开放量子系统为例,对这种方法进行了实验仿真,分析了不同惩罚因子α的变化与选取对系统性能的影响。

关键词: Liouville超算符,开放量子系统,最优跟踪控制

Abstract: In order to controll the open quantum systems with dissipation,we simplified the process of treating with the dynamics of open quantum systems using Liouville superoperator form．For this system,we proposed an efficient,monotonical convergent optimal tracking control method according to a special performance indicator which was designed based on the optimal control theory and the time-dependent density．This method can drive the time-dependent density along a given time-dependent trajectory in real space and control the time-dependent occupation numbers．We simulated the control process in MATLAB,and analyzed the influence of different penalty factors on system performance．

Key words: Liouville superoperator,Open quantum system,Optimal tracking control

黄泽霞,黄德才,俞攸红. 开放量子系统状态最优跟踪控制的研究[J]. 计算机科学, 2013, 40(12): 251-253. https://doi.org/

HUANG Ze-xia,HUANG De-cai and YU You-hong. Optimal Tracking Control of Population Transfer in Open Quantum Systems[J]. Computer Science, 2013, 40(12): 251-253. https://doi.org/

参考文献

[1] Kuang Sen,Cong Shuang．Lyapunov control methods of closed quantum systems [J]．Automatica,2008,4(1):98-108
[2] Hwang B,Goan H-S．Optimal control for non-Markovian open quantum systems [J]．Physical Review A,2012,5:032321
[3] Palao J P,Kosloff R,Koch C P．Protecting coherence in Optimal Control Theory:state dependent constraint approach [J]．Physical Review A,2008,77(6):063412(11)
[4] Lapert M,Zhang Y,Braun M,et al．Singular extremals for the time-optimal control of dissipative spin 1/2particles [J]．Physical Review Letters,2010,4(8):083001-083004
[5] Castro A,Gross E K U．Acceleration of quantum optimal control theory algorithms with mixing strategies [J]．Physical Review E,2009,9(5):056704-056710
[6] Ohtsuki Y,Turinici G,Rabitz H．Generalized monotonically convergent algorithms for solving quantum optimal control problems [J]．The Journal of Chemical Physics,2004,0:5509
[7] Ho T-S,Rabitz H．Accelerated monotonic convergence of optimal control over quantum dynamics [J]．Physical Review E,2010,2:026703
[8] Paulo E M F Mendona,Gilchrist A,et al．Optimal tracking for pairs of qubit states [J]．Physical Review A,2008,78:012319
[9] Peirce A P,Dahleh M,Rabitz H．Optimal control of quantum mechanical systems:Existence,numerical approximation,and applications [J]．Physical Review A,1988,37(12):495024964
[10] Grigorenko I,Garcia M E,Bennemann K H．Theory for the optimal control of time-averaged quantities in quantum systems [J].Physical Review Letters,2002,89:233003
[11] Zhu W,Rabitz H．Quantum control design via adaptive tracking [J]．The Journal of Chemical Physics,2003,119:3619
[12] Sugawara M．General formulation of locally designed coherent control theory for quantum system [J]．The Journal of Chemical Physics,2003,118:6784
[13] Serban I,Werschnik J,Gross E K U．Optimal control of time-dependent targets [J]．Physical Review A,2005,71:053810
[14] Schirmer S G,Solomon A I．Constraints on relaxation rates for N-level quantum systems [J]．Physical Review A,2004,70(2):2107-2119
[15] Maximov I I,Toner Z,Nielsen N C．Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms [J]．The Journal of Chemical Physics,2008,128:184505

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed