Static and dynamic coherent robust control for a class of uncertain quantum systems

Abstract This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. In order to obtain improved control performance, we propose two methods to design coherent robust controllers for the system. One is to formulate a static quantum controller by adding a controller Hamiltonian to the given system, and the other is to build a dynamic quantum controller which is directly coupled to the given system.

[1]  Daoyi Dong,et al.  Attosecond all-optical control and visualization of quantum interference between degenerate magnetic states by circularly polarized pulses. , 2020, Optics letters.

[2]  Ian R. Petersen,et al.  Sampled-data LQG control for a class of linear quantum systems , 2012, 2012 American Control Conference (ACC).

[3]  Claudio Altafini,et al.  Modeling and Control of Quantum Systems: An Introduction , 2012, IEEE Transactions on Automatic Control.

[4]  Dennis S. Bernstein,et al.  Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory , 2005 .

[5]  Claudio Altafini,et al.  Stabilization of Stochastic Quantum Dynamics via Open- and Closed-Loop Control , 2011, IEEE Transactions on Automatic Control.

[6]  Ian R. Petersen,et al.  Coherent quantum LQG control , 2007, Autom..

[7]  Ian R. Petersen,et al.  Sliding mode control of two-level quantum systems , 2010, Autom..

[8]  Milburn,et al.  All-optical versus electro-optical quantum-limited feedback. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[9]  Ian R. Petersen,et al.  Dark Modes of Quantum Linear Systems , 2016, IEEE Transactions on Automatic Control.

[10]  Ian R. Petersen,et al.  Performance Analysis and Coherent Guaranteed Cost Control for Uncertain Quantum Systems Using Small Gain and Popov Methods , 2017, IEEE Transactions on Automatic Control.

[11]  Naoki Yamamoto,et al.  Coherent versus measurement feedback: Linear systems theory for quantum information , 2014, 1406.6466.

[12]  M. James,et al.  Stability, gain, and robustness in quantum feedback networks (13 pages) , 2005, quant-ph/0511140.

[13]  Ian R. Petersen,et al.  Avoiding entanglement sudden death via measurement feedback control in a quantum network , 2008, 0806.4754.

[14]  Matthew R. James,et al.  Quantum Dissipative Systems and Feedback Control Design by Interconnection , 2007, IEEE Transactions on Automatic Control.

[15]  G. Milburn,et al.  Quantum Measurement and Control , 2009 .

[16]  Ian R. Petersen,et al.  Coherent robust H∞ control of linear quantum systems with uncertainties in the Hamiltonian and coupling operators , 2017, Autom..

[17]  Shan Ma,et al.  Cascade and locally dissipative realizations of linear quantum systems for pure Gaussian state covariance assignment , 2016, Autom..

[18]  M.R. James,et al.  $H^{\infty}$ Control of Linear Quantum Stochastic Systems , 2008, IEEE Transactions on Automatic Control.

[19]  Bo Qi,et al.  Is measurement-based feedback still better for quantum control systems? , 2010, Syst. Control. Lett..

[20]  Ian R. Petersen,et al.  Control of Linear Quantum Stochastic Systems , 2007 .

[21]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[22]  Hidenori Kimura,et al.  Transfer function approach to quantum Control-Part II: Control concepts and applications , 2003, IEEE Trans. Autom. Control..

[23]  Timothy C. Ralph,et al.  A Guide to Experiments in Quantum Optics , 1998 .

[24]  Franco Nori,et al.  Vanishing and Revival of Resonance Raman Scattering. , 2019, Physical review letters.

[25]  Matthew R. James,et al.  Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems , 2010, IEEE Transactions on Automatic Control.