Control of quantum particle dynamics by impulses of magnetic field

Архинчеев, В. Е.

doi:10.1007/s11071-016-3159-5

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…Control problems for two-level closed and open quantum systems were considered, e.g. in [16][17][18][19][20][21][22]. Various master, kinetic and transport equations are used for modelling dynamics of open classical and quantum systems.…”

Section: Introductionmentioning

confidence: 99%

On optimization of coherent and incoherent controls for two-level quantum systems

Моржин¹,

Pechen²

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

On optimization of coherent and incoherent controls for two-level quantum systems

Моржин¹,

Pechen²

2022

Preprint

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“…IV in [3] and the survey [14]), methods of the geometric control theory [15], iterative optimization methods, including gradient-based methods (for quantum control, see, for example, [16]), the Krotov method (see the survey [17] for references) are widely used. Control problems for two-level closed and open quantum systems were considered, for example in [18]- [24]. Various master, kinetic and transport equations are used for modelling dynamics of open classical and quantum systems.…”

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confidence: 99%

On optimization of coherent and incoherent controls for two-level quantum systems

Morzhin,

Pechen

2023

Izv. Math.

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This paper considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schrödinger equation with coherent control. The open system dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation whose Hamiltonian depends on coherent control and superoperator of dissipation depends on incoherent control. For the closed system, we consider the problem of generation of the phase shift gate for some values of phases and final times for which we numerically show that zero coherent control, which is a stationary point of the objective functional, is not optimal; it gives an example of subtle point for practical solving quantum control problems. The two-stage method, which was developed in [48] for generic $N$-level open quantum systems for approximate generation of a given target density matrix, is modified here for the case of two-level systems. We modify the first ("incoherent") stage by numerically optimizing piecewise constant incoherent control instead of using constant incoherent control analytically computed using eigenvalues of the target density matrix. Exact analytical formulas are derived for the system state evolution, the objective functions and their gradients for the modified first stage. These formulas are then applied in the two-step gradient projection method. The numerical simulations show that the modified first stage duration can be significantly less than the unmodified first stage duration, but at the cost of performing optimization in the class of piecewise constant controls.

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On optimization of coherent and incoherent controls for two-level quantum systems

Morzhin,

Pechen

2023

Известия Российской академии наук. Серия математическая

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This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schrödinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation whose Hamiltonian depends on coherent control and superoperator of dissipation depends on incoherent control. For the closed system, we consider the problem for generation of the phase shift gate for some values of phases and final times for which we numerically show that zero coherent control, which is a stationary point of the objective functional, is not optimal; it gives an example of subtle point for practical solving quantum control problems. The two-stage method, which was developed in [A. Pechen, Phys. Rev. A., 84, 042106 (2011)] for generic $N$-level open quantum systems for approximate generation of a given target density matrix, is modified here for the case of two-level systems. We modify the first ("incoherent") stage by numerically optimizing piecewise constant incoherent control instead of using constant incoherent control analytically computed using eigenvalues of the target density matrix. Exact analytical formulas are derived for the system's state evolution, the objective functions and their gradients for the modified first stage. These formulas are then applied in the two-step gradient projection method. The numerical simulations show that the modified first stage's duration can be significantly less than the unmodified first stage's duration, but at the cost of performing optimization in the class of piecewise constant controls. Bibliography: 72 titles.

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Control of quantum particle dynamics by impulses of magnetic field

Cited by 3 publications

References 16 publications

On optimization of coherent and incoherent controls for two-level quantum systems

On optimization of coherent and incoherent controls for two-level quantum systems

On optimization of coherent and incoherent controls for two-level quantum systems

On optimization of coherent and incoherent controls for two-level quantum systems

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