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26
Quantum control theory and applications: A survey
 IET Control Theory & Applications
, 2010
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Controllability of quantum harmonic oscillators
 IEEE Trans Automatic Control
"... Abstract—It is proven in a previous paper that any modal approximation of the onedimensional quantum harmonic oscillator is controllable. We prove here that, contrary to such finitedimensional approximations, the original infinitedimensional system is not controllable:Its controllable part is of ..."
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Cited by 27 (5 self)
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Abstract—It is proven in a previous paper that any modal approximation of the onedimensional quantum harmonic oscillator is controllable. We prove here that, contrary to such finitedimensional approximations, the original infinitedimensional system is not controllable:Its controllable part is of dimension 2 and corresponds to the dynamics of the average position. More generally, we prove that, for the quantum harmonic oscillator of any dimension, similar lacks of controllability occur whatever the number of control is:the controllable part still corresponds to the average position dynamics. We show, with the quantum particle in a moving quadratic potential, that some physically interesting motion planning questions can be however solved. Index Terms—Nonlinear controllability, quantum systems, Schrödinger equation.
Notions of controllability for quantum mechanical systems
, 2001
"... In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as ..."
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Cited by 18 (2 self)
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In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The paper also contains results on the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove that, for the system of two interacting spin 1 2 particles, not every state transfer can be obtained in arbitrary small time. 1
Control of a quantum particle in a moving potential well
 in: IFAC Second Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
, 2003
"... Abstract: The control is the potential well absolute position. For two kinds of potential shape (periodic and box), we propose approximated solutions to the steadstate motion planing problem: steering in finite time the particle from an initial well position to a final well position, the initial an ..."
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Cited by 14 (1 self)
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Abstract: The control is the potential well absolute position. For two kinds of potential shape (periodic and box), we propose approximated solutions to the steadstate motion planing problem: steering in finite time the particle from an initial well position to a final well position, the initial and final particle energies being identical. This problem is a quantum analogue of the water tank problem, where a tank filled with liquid is moved from one position where the surface is horizontal to another position where the surface is also horizontal. Copyright © 2003 IFAC
Feedback generation of quantum Fock states by discrete QND measures
 in "IEEE Control and Decision Conference
"... Abstract — A feedback scheme for preparation of photon number states in a microwave cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity field provides information on its actual state. The control consists in injecting into the cavity mode a microwave pulse adjusted to increase ..."
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Cited by 9 (3 self)
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Abstract — A feedback scheme for preparation of photon number states in a microwave cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity field provides information on its actual state. The control consists in injecting into the cavity mode a microwave pulse adjusted to increase the population of the desired target photon number. In the ideal case (perfect cavity and measures), we present the feedback scheme and its detailed convergence proof through stochastic Lyapunov techniques based on supermartingales and other probabilistic arguments. Quantum MonteCarlo simulations performed with experimental parameters illustrate convergence and robustness of such feedback scheme. I.
Control of Quantum Systems Using ModelBased Feedback Strategies
"... New modelbased feedback control strategies are presented for the steering problem of a quantum system. Both the infinite and finite dimensional cases are discusses. This approach is illustrated by means of a simple spin system example. ..."
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Cited by 6 (0 self)
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New modelbased feedback control strategies are presented for the steering problem of a quantum system. Both the infinite and finite dimensional cases are discusses. This approach is illustrated by means of a simple spin system example.
Quantum coherent nonlinear feedback with applications to quantum optics on chip
 IEEE TRANS. AUTOM. CONTROL
, 2012
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The Lie algebra structure and nonlinear controllability of spin systems
 Linear Algebra Appl
, 2002
"... In this paper, we provide a complete analysis of the Lie algebra structure of a system of n interacting spin 1 2 particles with different gyromagnetic ratios in an electromagnetic field. We relate the structure of this Lie algebra to the properties of a graph whose nodes represent the particles and ..."
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Cited by 4 (2 self)
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In this paper, we provide a complete analysis of the Lie algebra structure of a system of n interacting spin 1 2 particles with different gyromagnetic ratios in an electromagnetic field. We relate the structure of this Lie algebra to the properties of a graph whose nodes represent the particles and an edge connects two nodes if and only if the interaction between the two corresponding particles is active. We prove that for these systems all the controllability notions, including the possibility of driving the state or the evolution operator of the system, are equivalent. We also provide a necessary and sufficient condition for controllability in terms of the properties of the above described graph. We analyze low dimensional problems (number of particles less then or equal to three) with possibly equal gyromagnetic ratios. This provides an example of quantum mechanical systems where controllability of the state is verified while controllability of the evolution operator is not.
Discretetime controllability for feedback quantum dynamics
 Automatica
, 2011
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