Mathematical computation of quantum optical control systems

Document Type : Original Article


Electrical and Computer Engineering Department, Qom University of Technology, Qom, Iran


Some models of linear control system schemas are developed here for quantum linear systems. The most important linear devices in quantum optics are introduced with their differential equations. These linear quantum systems are zero-order and first-order transfer functions with one pole and one zero. We mathematical compute transfer function of different interconnections by using zero-order and first-order systems. for instance, by designing series and feedback interconnection, we will obtain higher-order quantum linear systems. Also, we will analyze a closed-loop feedback of a first-order linear quantum system containing a gain in feedback path


[1] C. Altafini, F. Ticozzi, Almost global stochastic feedback stabilization of conditional quantum dynamics, arxiv: quantph/
0510222v1, 2005.
[2] H.A. Bachor, T.C Ralph, A Guide to Experiment in Quantum Optics, Second Edition, Wiley-VCH, 2004.
[3] L. Bouten, R.V Handel, On the separation principle in quantum control, Quantum Stochastics and Information: Statistics,
Filtering and Control, World Scientific, 2008, 206-238.
[4] H.J. Carmichael, An Open Systems Approach to Quantum Optics, Springer Science and Business Media, 2009.
[5] P. Christiane Koch, et. al, Quantum control of molecular rotation, Reviews of Modern Physics ,91(3) 2019, 035005.
[6] A. De Vries, Global stability criterion for a quantum feedback control process on a single qubit and exponential stability
in case of perfect detection efficiency, Physical Review A 75(3) 2007, 032101.
[7] D. Dong, J. Lam, R. Petersen, Robust incoherent control of qubit systems via switching and optimization, International
Journal of Control, 83(1) 2009, 206-217.
[8] A. Fert, Nobel Lecture: Origin, development, and future of spintronics, Review of Modern Physics, 80(4) 2008, 1517-
[9] C.W. Gardiner, P. Zoller, Quantum Noise, second edition, Springer, 2000.
[10] S. Grivopoulos, B. Bamieh, Optimal Population Transfers in a Quantum System for Large Transfer Time, IEEE
Transactions on Automatic Control, 53(4) 2008, 980-992.
[11] J. Gough, M.R. James, The Series Product and Its Application to Quantum Feedforward and Feedback Networks, IEEE
Transaction on Automatic Control, 54(11) 2009, 2530-2544.
[12] M. Mirrahimi, R. van Handel, Stabilizing feedback controls for quantum systems, SIAM Journal of Control and Optimization, 46(2) 2007, 445-467.
[13] B.C. Roy, P.K. Das, Modelling of quantum networks of feedback QED systems in interacting Fock space, International Journal of Control, 82(12) 2009, 2267-2276.
[14] J. Sharifi, H.R. Momeni, Optimal Control Equation for Quantum Stochastic Differential Equations, Proceeding of 49th IEEE conference on decision and control, 2010, 15-17.
[15] J. Sharifi, H.R. Momeni, Lyapunov Control of Squeezed Noise Quantum Trajectory, Physics Letters A, 375(3) 2011, 522-528.
[16] R. Somaraj, I.R. Petersen, Lyapunov Stability of Quantum Markov Process, American Control Conference, 2009, 715-724.
[17] A. Spörl, T. Schulte-Herbrüggen, S.J. Glaser, V. Bergholm, M.J. Storcz, J. Ferber and F. K. Wilhelm, Optimal control of coupled Josephson Qubits, Physical Review A, 75(1) 2007, 012302.
[18] R. Van Handel, J. K. Stockton and H. Mabuchi, Feedback Control of Quantum State Reduction, IEEE Transaction on automatic control, 50(6) 2005, 768-780.
[19] R. Van Handel, J.K. Stockton and H. Mabuchi, Modeling and feedback control design for quantum state preparation, Journal of Optics B: Quantum Semiclass Optics, 7(10) 2005, 179-197.
[20] G.O.M. Yanagisawa and H. Kimura, Transfer function approach to quantum control part I: Dynamics of Quantum Feedback Systems, IEEE Trans. Automatic Control, 48(12) 2003, 2107–2120.
[21] G.O.M. Yanagisawa and H. Kimura, Transfer function approach to quantum control part I: Control Concepts and Applications, IEEE Trans. Automatic Control, 48(12) 2003, 2121–2132.
Volume 1, Issue 1
October 2020
Pages 25-31
  • Receive Date: 26 July 2020
  • Revise Date: 01 September 2020
  • Accept Date: 04 September 2020
  • First Publish Date: 01 October 2020