Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling

Coron, Jean‐Michel; Grigoriu, Andreea; Lefter, Cătălin; Turinici, Gabriel

doi:10.1088/1367-2630/11/10/105034

Cited by 44 publications

(42 citation statements)

References 28 publications

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“…For the important case when some of the coupling are realized by µ 2 instead of µ 1 formulas (8) are ineffective. Discontinuous and time varying feedback have been proposed to stabilize the system (see [6]). …”

Section: Discontinuous Feedbackmentioning

confidence: 99%

“…This can be studied via the general accessibility criteria [3,23] based on Lie brackets; more specific results can be found in [26]. A detailed presentation has been made in [6].…”

Section: Introductionmentioning

confidence: 99%

“…When the same property holds for Hamiltonian H(t) = H 0 + ǫ(t)µ 1 +ǫ 2 (t)µ 2 the same type of feedback formulas hold. When some of the (direct) coupling is realized through µ 2 instead of µ 1 , the previous feedback formulas do not hold any more and two alternatives have been proposed (see [6] for more details): discontinuous feedback and time varying feedback.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of discontinuous quantum control systems with dipole and polarizability coupling

Grigoriu

2012

Automatica

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Closed quantum systems under the influence of a laser field, whose interaction is modeled by a Schrödinger equation with a coupling control operator containing both a linear (dipole) and a quadratic (polarizability) term are analyzed. Discontinuous feedbacks, obtained by a Lyapunov trajectory tracking procedure, have been recently proposed to control these type of systems. The purpose of this paper is to study the asymptotic stability by considering the solutions in the Filippov sense. The analysis is developed by applying a variant of LaSalle invariance principle for differential inclusions. Numerical simulations are included to illustrate the efficiency of the discontinuous control.

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Section: Discontinuous Feedbackmentioning

confidence: 99%

“…This can be studied via the general accessibility criteria [3,23] based on Lie brackets; more specific results can be found in [26]. A detailed presentation has been made in [6].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability analysis of discontinuous quantum control systems with dipole and polarizability coupling

Grigoriu

2012

Automatica

Self Cite

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“…It uses feedback design to construct control fields but applies the fields to a quantum system in an open-loop way. It provides us with a simple way to design control fields for the manipulation of quantum state transfer [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Optimal Lyapunov quantum control of two-level systems: Convergence and extended techniques

et al. 2014

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Taking a two-level system as an example, we show that a strong control field may enhance the efficiency of optimal Lyapunov quantum control in [Hou et al., Phys. Rev. A 86, 022321 (2012)] but could decrease its control fidelity. A relationship between the strength of the control field and the control fidelity is established. An extended technique, which combines free evolution and external control, is proposed to improve the control fidelity. We analytically demonstrate that the extended technique can be used to design a control law for steering a two-level system exactly to the target state. In such a way, the convergence of the extended optimal Lyapunov quantum control can be guaranteed.

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“…Lyapunov control is a form of local optimal control with numerous variants [22][23][24][25], which has the advantage of being sufficiently simple to be amenable to rigorous analysis and has been used to manipulate open quantum systems [25][26][27]. For example, Yi et al proposed a scheme in 2009 to drive a finite-dimensional quantum system into the decoherence-free subspaces by Lyapunov control [25].…”

mentioning

confidence: 99%

Coherent control in quantum open systems: An approach for accelerating dissipation-based quantum state generation

Chen¹,

Shi²,

Song³

et al. 2017

Phys. Rev. A

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In this paper, we propose an approach to accelerate the dissipation dynamics for quantum state generation with Lyapunov control. The strategy is to add target-state-related coherent control fields into the dissipation process to intuitively improve the evolution speed. By applying the current approach, without losing the advantages of dissipation dynamics, the target stationary states can be generated in a much shorter time as compared to that via traditional dissipation dynamics. As a result, the current approach containing the advantages of coherent unitary dynamics and dissipation dynamics allows for significant improvement in quantum state generation. where the overdot stands for a time derivative and L k are the so-called Lindblad operators. By using dissipation, one can generate high-fidelity quantum states without accurately controlling the initial state or the operation time (usually, the longer the operation time is, the higher is the fidelity). Besides, dissipation dynamics is shown to be robust against parameter (instantaneous) fluctuations [1]. Due to these advantages, many schemes [9-21] have been proposed for dissipation-based quantum state generation in recent years based on different physical systems. Generally speaking, to generate quantum states by quantum dissipation, the key point is to find (or design) a unique stationary state (marked as |S ) which can not be transferred to other states while other states can be transferred to it. That is, the reduced system should satisfywhere |M (M = S) are the orthogonal partners of the state |S in a reduced system satisfying M |S = 0 and M |M M | + |S S| = 1, andL k are the effective Lindblad operators. Hence, if the system is in |M , it will always be transferred to other states because H 0 |M = 0 andL † k |S = 0, while if the system is in |S , it remains invariant. Therefore, the process of pumping and decaying continues until the system is finally stabilized into the stationary state |S . * E-mail: xia-208@163.comTo show such a dissipation process in more detail, we introduce a functionV to describe the system evolution speed, where V = Tr(ρρ s ) is known as the Lyapunov function [22] and ρ s is the density matrix of the target state |S . Lyapunov control is a form of local optimal control with numerous variants [22][23][24][25], which has the advantage of being sufficiently simple to be amenable to rigorous analysis and has been used to manipulate open quantum systems [25][26][27]. For example, Yi et al. proposed a scheme in 2009 to drive a finite-dimensional quantum system into the decoherence-free subspaces by Lyapunov control [25].When the system evolves into a target state at a final time t f , i.e., ρ| t=t f → ρ s , V approaches a maximum value V = 1. Based on Eqs. (1) and (2), we finḋin which we have assumedL k = √ Γ k |S E k |, with Γ k being the effective dissipation rates and |E k being the effective excited states. Obviously, the evolution speed strongly dependents on the effective dissipation rates and the total population of effective ex...

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Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling

Cited by 44 publications

References 28 publications

Stability analysis of discontinuous quantum control systems with dipole and polarizability coupling

Stability analysis of discontinuous quantum control systems with dipole and polarizability coupling

Optimal Lyapunov quantum control of two-level systems: Convergence and extended techniques

Coherent control in quantum open systems: An approach for accelerating dissipation-based quantum state generation

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