Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

Zhang, Qi; Chen, Xi; Guéry-Odelin, David

doi:10.3390/e23010084

Cited by 19 publications

(15 citation statements)

References 82 publications

(93 reference statements)

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“…The mathematical property which allows for such an inverse use of the dynamical (including nonlinear) equations is known as the flatness property, and can be considered as an extension of the Kalman's controllability criterion [61]. This strategy has been successfully used to transport a particle in a moving harmonic potential, both in classical and quantum physics [62][63][64], or to shuttle the particle, i.e. to set a given velocity to the particle-see [65] and references therein.…”

Section: A Inverse Engineeringmentioning

confidence: 99%

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Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Guéry-Odelin¹,

Jarzynski²,

Plata³

et al. 2022

Preprint

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Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes-which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finitetime state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems. Contents 1. Langevin and Fokker-Planck descriptions 2. Stochastic thermodynamics C. Conditions for the existence of Boltzmann's breathers under static confinement D. Derivation of the expression for the minimum irreversible work E. Comparison of speed limit inequalities for the harmonic case

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Section: A Inverse Engineeringmentioning

confidence: 99%

“…(See for instance Refs. [64,83] for specific examples, ranging from ultracold atoms to granular systems. )…”

Section: Optimal Control Theorymentioning

confidence: 99%

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Guéry-Odelin¹,

Jarzynski²,

Plata³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…It has been applied for deriving and implementing experimentally a one-qubit quantum gate [572], to generate specific states in a chain of coupled spins [44,535] and in a three-level quantum system [421], for the control of entanglement in bosonic Josephson junctions [534], but also in many-body physics [109]. The connection between STA and QOCT has been discussed in [649] for standard quantum control examples. By using the optimal trajectory as a guide, the authors show that very precise STA protocols can be achieved.…”

Section: Quantum Optimal Control Vs Shortcuts To Adiabaticitymentioning

confidence: 99%

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Koch,

Boscain,

Calarco

et al. 2022

Preprint

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Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.

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“…Shortcuts to adiabaticity based on invariants or inverse engineering approaches, and Optimal Control Theory (OCT) blend quite well [7,25,40,[55][56][57][58][59], usually via Pontryagin's maximal principle. While STA techniques provide families of ideal trap trajectories, OCT helps to select the best among them to minimize some cost function, restricting the selection space if necessary to domains imposed by physically motivated constraints.…”

Section: Shortcuts To Adiabaticity and Optimal Control Theorymentioning

confidence: 99%

Fast and robust particle shuttling for quantum science and technology

Qi,

Chiaverini,

Espinós

et al. 2021

Preprint

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We review methods to shuttle quantum particles fast and robustly. Ideal robustness amounts to the invariance of the desired transport results with respect to deviations, noisy or otherwise, from the nominal driving protocol for the control parameters; this can include environmental perturbations. "Fast" is defined with respect to adiabatic transport times. Special attention is paid to shortcut-toadiabaticity protocols that achieve, in faster-than-adiabatic times, the same results of slow adiabatic driving.

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Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

Cited by 19 publications

References 82 publications

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Fast and robust particle shuttling for quantum science and technology

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