Characteristics analysis of stochastic open quantum system models and feedback control

Shuang CONG; Jingjing XUE

doi:10.3969/j.issn.1007-5461. 2015.02.009

[3] Dong D, Petersen I R. Quantum control theory and applications: A survey ［J］. IET Control Theory and 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, et al. Experimental feedback control of quantum systems using weak measurements ［J］. Phys. Rev. Lett., 2010, 104: 080503.

[6] Nishio K, Kashima K, Imura J. Effects of time delay in feedback control of linear quantum systems ［J］. Phys. Rev. A, 2009, 79: 062105.

[7] Tsumura K. Global stabilization at arbitrary eigenstates of N-dimensional quantum spin systems via continuous feedback ［C］. American Control Conference, 2008, 4148-4153.

[8] Van Handel R, Stockton J K, Mabuchi H. Feedback control of quantum state reduction ［J］. IEEE Transactions on Automatic Control, 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 ［OL］. http://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, 4(2): 445-467.

[16] Tsumura K. Global stabilization of N-dimensional quantum spin systems via continuous feedback ［C］. 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, et al. Feedback cooling of atomic motion in cavity QED ［J］. Phys. Rev. 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, 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, et al. Transition from weak to strong measurements by nonlinear quantum feedback control ［J］. Phys. Rev. A, 2010, 82: 022101.

[22] Gleyzes S, Kuhr S, Guerlin C, et al. Quantum jumps of light recording the birth and death of a photon in a cavity ［J］. Nature, 2007, 44(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, 4(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, et al. 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 ［OL］. http://arXiv preprint math-ph/0605003, 2006.

[30] Ge S S, Vu T L, He W, et al. Non-smooth Lyapunov function-based global stabilization for 2-dimensional quantum filters ［C］. th IEEE Conference on Decision and Control, Atlanta, USA, 2010, 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 and Control Letters, 2010, 59(6): 333-339.

[34] Cong S. Control of Quantum Systems: Theory and Methods ［M］. John Wiley & Sons, Singapore Pte. Ltd, 2014.

[35] Liu J X, Cong S. Research on dynamical models of non-Markovian open quantum system ［C］. Procedings of 13th Chinese Conference on System Simulation Technology Application (CCSSTA 2011), 2011, 264-272.