Singular Extremals for the Time-Optimal Control of Dissipative Spin<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math>Particles

Lapert, M.; Zhang, Y.; Braun, Michael H.; Glaser, Steffen J.; Sugny, Dominique

doi:10.1103/physrevlett.104.083001

Cited by 172 publications

(189 citation statements)

References 17 publications

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“…In this framework, different numerical optimal control algorithms [7][8][9] have been developed and applied to a large variety of quantum systems. Optimal control was used in physical chemistry in order to steer chemical reactions [3], but also for spin systems [10,11] with applications in Nuclear Magnetic Resonance [7,[12][13][14][15][16] and Magnetic Resonance Imaging [17][18][19]. Recently, optimal control has attracted attention in view of applications to quantum information processing, for example as a tool to implement high-fidelity quantum gates in minimum time [4,20,21].…”

Section: Introductionmentioning

confidence: 99%

Fully efficient time-parallelized quantum optimal control algorithm

et al. 2016

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We present a time-parallelization method that enables to accelerate the computation of quantum optimal control algorithms. We show that this approach is approximately fully efficient when based on a gradient method as optimization solver: the computational time is approximately divided by the number of available processors. The control of spin systems, molecular orientation and BoseEinstein condensates are used as illustrative examples to highlight the wide range of application of this numerical scheme.

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Section: Introductionmentioning

confidence: 99%

Fully efficient time-parallelized quantum optimal control algorithm

et al. 2016

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“…Spin baths can be studied by NMR experiments and can be viewed as assemblies of qubits (a qubit is an unit of quantum information in quantum computing). These applications need to study the control of spin baths [14][15][16], but the decoherence processes can drastically decrease the efficiency of the control. Previous studies concerning decoherence of spin baths focused on decoherence induced by spin-spin interactions inner the bath (the spin bath being itself considered as an environment for one of its spins).…”

Section: Introductionmentioning

confidence: 99%

Decoherence, relaxation, and chaos in a kicked-spin ensemble

Viennot¹,

Aubourg²

2013

Phys. Rev. E

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We study the dynamics of a quantum spin ensemble controlled by trains of ultrashort pulses. To model disturbances of the kicks, we consider that the spins are submitted to different kick trains which follow regular, random, stochastic or chaotic dynamical processes. These are described by dynamical systems on a torus. We study the quantum decoherence and the population relaxation of the spin ensemble induced by these classical dynamical processes disturbing the kick trains. For chaotic kick trains we show that the decoherence and the relaxation processes exhibit a signature of chaos directly related to the Lyapunov exponents of the dynamical system. This signature is a horizon of coherence, i.e. a preliminary duration without decoherence followed by a rapid decoherence process.

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“…In the case γ = 0, this leads to a classical flip of ∆ψ = π(1 − 0.0528). Another option could be to consider the dynamics of a linear chain of three coupled spins subjected to radio-frequency magnetic fields [20,21,22]. Previous studies have shown that the optimal controlled trajectories of this system are given by solutions of Euler equations [23,24].…”

Section: Discussionmentioning

confidence: 99%

The tennis racket effect in a three-dimensional rigid body

Damme¹,

Mardešić²,

Sugny³

2017

Physica D: Nonlinear Phenomena

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We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip (π-rotation) of the head of the racket when a full (2π) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Different examples are discussed.

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Singular Extremals for the Time-Optimal Control of Dissipative Spin12Particles

Cited by 172 publications

References 17 publications

Fully efficient time-parallelized quantum optimal control algorithm

Fully efficient time-parallelized quantum optimal control algorithm

Decoherence, relaxation, and chaos in a kicked-spin ensemble

The tennis racket effect in a three-dimensional rigid body

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