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

Wang, L.C.; Hou, S. C.; Dong, Daoyi; Petersen, Ian R.

doi:10.1016/j.physleta.2014.02.027

Cited by 29 publications

(13 citation statements)

References 23 publications

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“…Next, a feedforward neural network with 2(n−1) input nodes, M + 1 output neurons, plus some hidden layers is set up with the activation function Eq. (9). For an input vector X, the output of the neural network is a linear combination of all the basis vectors, i.e.,…”

Section: A Classification: Selecting Control Schemesmentioning

confidence: 99%

“…The method has the merits of simplicity in generating control fields and flexibility in designing the control field shapes. In recent years, numerous efforts have been devoted to investigate or improve the convergence of Lyapunov control for different quantum control models [5][6][7][8][9][10][11][12]. Meanwhile, Lyapunov control method is successfully employed for diverse quantum information processing tasks [12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Lyapunov control with machine learning

Hou

2019

Quantum Inf Process

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Quantum state engineering is a central task in Lyapunov-based quantum control. Given different initial states, better performance may be achieved if the control parameters, such as the Lyapunov function, are individually optimized for each initial state, however, at the expense of computing resources. To tackle this issue, we propose an initial-state-adaptive Lyapunov control strategy with machine learning, specifically, artificial neural networks trained through supervised learning. Two designs are presented and illustrated where the feedforward neural network and the general regression neural network are used to select control schemes and design Lyapunov functions, respectively. Since the sample generation and the training of neural networks are carried out in advance, the initial-state-adaptive Lyapunov control can be implemented without much increase of computational resources.

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Section: A Classification: Selecting Control Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Lyapunov control with machine learning

Hou

2019

Quantum Inf Process

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“…Usually, the states of two-level quantum systems are considered as arrows from the origin to points on the Bloch sphere [24].…”

Section: Problem Formulationmentioning

confidence: 99%

Quantum Genetic Learning Control of Quantum Ensembles with Hamiltonian Uncertainties

Arjmandzadeh

Yarahmadi

2017

Entropy

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Abstract:In this paper, a new method for controlling a quantum ensemble that its members have uncertainties in Hamiltonian parameters is designed. Based on combining the sampling-based learning control (SLC) and a new quantum genetic algorithm (QGA) method, the control of an ensemble of a two-level quantum system with Hamiltonian uncertainties is achieved. To simultaneously transfer the ensemble members to a desired state, an SLC algorithm is designed. For reducing the transfer error significantly, an optimization problem is defined. Considering the advantages of QGA and the nature of the problem, the optimization problem by using the QGA method is solved. For this purpose, N samples through sampling of the uncertainty parameters via uniform distribution are generated and an augmented system is also created. By using QGA in the training step, the best control signal is obtained. To test the performance and validation of the method, the obtained control is implemented for some random selected samples. A couple of examples are simulated for investigating the proposed model. The results of the simulations indicate the effectiveness and the advantages of the proposed method.

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“…Transfer control between quantum states is one of the basic tasks in quantum control. Different control strategies such as optimal control [7,8,9,10], adiabatic control [11,12], Lyapunov control methods [13,14,15,16,17,18,19,20,21,22,23], H ∞ and LQG control [24,25,26], and sliding mode control [27,28] have been presented for controller design in quantum systems. Among these control strategies, Lyapunov control methods have been extensively studied for quantum systems due to their simplicity and intuitive nature in the design of control fields [29,30,31,32,33].…”

Section: Introductionmentioning

confidence: 99%

“…Among these control strategies, Lyapunov control methods have been extensively studied for quantum systems due to their simplicity and intuitive nature in the design of control fields [29,30,31,32,33]. In Lyapunov control, a Lyapunov function is constructed using information on states or operators related to the quantum system [13,14,15,16,17,18,19,20,21,22,23,29,30,31,32,33] and the associated control law is designed based on the Lyapunov function (feedback design). Then the control law can be implemented in an open-loop way.…”

Section: Introductionmentioning

confidence: 99%

Rapid Lyapunov control of finite-dimensional quantum systems

2017

Self Cite

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Rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang-bang Lyapunov control can speed up the control process, but cannot guarantee convergence to a target state. This paper proposes two classes of new Lyapunov control methods that can achieve rapidly convergent control for quantum states. One class is switching Lyapunov control where the control law is designed by switching between bang-bang Lyapunov control and standard Lyapunov control. The other class is approximate bang-bang Lyapunov control where we propose two special control functions which are continuously differentiable and yet have a bang-bang type property. Related stability results are given and a construction method for the degrees of freedom in the Lyapunov function is presented to guarantee rapid convergence to a target eigenstate being isolated in the invariant set. Several numerical examples demonstrate that the proposed methods can achieve improved performance for rapid state control of quantum systems.

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

Cited by 29 publications

References 23 publications

Quantum Lyapunov control with machine learning

Quantum Lyapunov control with machine learning

Quantum Genetic Learning Control of Quantum Ensembles with Hamiltonian Uncertainties

Rapid Lyapunov control of finite-dimensional quantum systems

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