Variable structure control of quantum systems

We prepare an arbitrary quantum state in the presence of noisy environment as well as systematic uncertainty using a variable structure control method involving quantum weak measurement. We first steer the quantum state to a sliding surface and then manipulate the state from the sliding surface to the target by quantum weak measurement. We demonstrate that both the two steps are robust against systematic and amplitude noises.

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

[2]  Bo Qi.  A two-step strategy for stabilizing control of quantum systems with uncertainties , 2013, Autom..

[3]  D. Alonso,et al.  Optimally robust shortcuts to population inversion in two-level quantum systems , 2012, 1206.1691.

[4]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[5]  D. D'Alessandro,et al.  Optimal control of two-level quantum systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[6]  Ren Xuemei.  Recent developments in sliding mode control and active disturbance rejection control , 2013 .

[7]  Franco Nori,et al.  Control-free control: Manipulating a quantum system using only a limited set of measurements , 2010, 1011.4463.

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

[9]  I. Petersen,et al.  Sliding mode control of quantum systems , 2009, 0911.0062.

[10]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[11]  Zairong Xi,et al.  Combating dephasing decoherence by periodically performing tracking control and projective measurement , 2007 .

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

[13]  Jean-Paul Gauthier,et al.  Equivalence between exact and approximate controllability for finite-dimensional quantum systems , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[14]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[15]  Andreea Grigoriu,et al.  Stability analysis of discontinuous quantum control systems with dipole and polarizability coupling , 2012, Autom..

[16]  A. N. Korotkov,et al.  Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback , 2012, Nature.

[17]  Ian R. Petersen,et al.  Variable Structure Control of Uncontrollable Quantum Systems , 2009 .

[18]  Herschel Rabitz,et al.  Quantum control by von Neumann measurements , 2006 .

[19]  Mazyar Mirrahimi,et al.  Stabilizing Feedback Controls for Quantum Systems , 2005, SIAM J. Control. Optim..

[20]  Jing Zhang,et al.  Quantum Coherent Nonlinear Feedback With Applications to Quantum Optics on Chip , 2011, IEEE Transactions on Automatic Control.

[21]  D. D’Alessandro.  Introduction to Quantum Control and Dynamics , 2007 .

[22]  Bo Qi,et al.  Further Results on Stabilizing Control of Quantum Systems , 2013, IEEE Transactions on Automatic Control.

[23]  Franco Nori,et al.  Feedback control of Rabi oscillations in circuit QED , 2013 .

[24]  J Eisert,et al.  Precisely timing dissipative quantum information processing. , 2012, Physical review letters.

[25]  Francesco Petruccione,et al.  The Theory of Open Quantum Systems , 2002 .

[26]  H. R. Lewis,et al.  An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field , 1969 .

[27]  Ian R. Petersen,et al.  A Popov stability condition for uncertain linear quantum systems , 2013, 2013 American Control Conference.

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

[29]  Mazyar Mirrahimi,et al.  Feedback stabilization of discrete-time quantum systems subject to non-demolition measurements with imperfections and delays , 2012, Autom..

[30]  Jean-Paul Gauthier,et al.  Approximate Controllability, Exact Controllability, and Conical Eigenvalue Intersections for Quantum Mechanical Systems , 2013, 1309.1970.

[31]  V. Belavkin.  THEORY OF THE CONTROL OF OBSERVABLE QUANTUM SYSTEMS , 2005 .

[32]  Franco Nori,et al.  Nonperturbative theory of weak pre-and post-selected measurements , 2011, 1109.6315.

[33]  F. Verstraete,et al.  Quantum computation and quantum-state engineering driven by dissipation , 2009 .

[34]  Franco Nori,et al.  Confidence and backaction in the quantum filter equation , 2012 .

[35]  V. I. Man'ko,et al.  Quantum control and the Strocchi map , 2003 .