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Asian Control Conference (ASCC)

Ensemble control of open quantum systems using differential evolution

Yingying Sun, Hailan Ma, Chengzhi Wu, Chunlin Chen, Daoyi Dong

Published May 1, 2015• 7 citations
Publisher

Abstract

Ensemble control of open quantum systems from one state to another is much more difficult than closed quantum systems due to their interactions with the environment. In this paper, a sampling-based learning control (SLC) method is applied to the optimal control design for inhomogeneous open quantum ensembles regarding the state-to-state transition task. A differential evolution (DE) algorithm is adopted for the training step of the SLC design to find the optimal control for the generalized system constructed by sampling members of the inhomogeneous quantum ensembles. Numerical results, including two-level, three-level and four-level open quantum ensembles, demonstrate the effectiveness of the proposed control approach for open quantum ensembles.

DOI
10.1109/ascc.2015.7244533

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Ensemble control of open quantum systems from one state to another is much more difficult than closed quantum systems due to their interactions with the environment. In this paper, a sampling-based learning control (SLC) method is applied to the optimal control design for inhomogeneous open quantum ensembles regarding the state-to-state transition task. A differential evolution (DE) algorithm is adopted for the training step of the SLC design to find the optimal control for the generalized system constructed by sampling members of the inhomogeneous quantum ensembles. Numerical results, including two-level, three-level and four-level open quantum ensembles, demonstrate the effectiveness of the proposed control approach for open quantum ensembles.
This paper investigates the application of an evolutionary algorithm, evolution strategy (ES)(μ+λ\mu+\lambdaμ+λ) to the control design in several inhomogeneous open quantum ensembles. We apply the ES (μ+λ\mu+\lambdaμ+λ) to assist the sampling-based learning control (SLC) technique, by which a set of control signals is designed to drive the inhomogeneous open quantum ensemble to a given target state. We illustrate our algorithm in two-level and four-level inhomogeneous open quantum ensembles. Numerical results show the effectiveness of the proposed control algorithm. The comparison with other evolutionary algorithms such as differential evolution (DE) and genetic algorithm (GA) shows the superiority of our ES (μ+λ\mu+\lambdaμ+λ) both in average fidelity and stability. In a four-level open quantum ensemble, for example, the fitness error after optimization using the ES (μ+λ\mu+\lambdaμ+λ) is decreased by around 59% compared to DE, and the standard deviation is lowered by about 47%.
Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present the systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\ensuremath{\Lambda}$-type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find an optimal control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented, showing the effectiveness of the SLC method.
Robust control of open quantum systems from one state to another is much more difficult than closed quantum systems as a result of system-environment interactions. In this paper, we adopt the sampling-based learning control approach with the motivation of utilizing some artificial samples instead of unknown uncertainties to design an optimal control field against parameter fluctuations. To enhance the learning performance, we introduce an improved differential evolution (DE) algorithm with equally-mixed strategies in the training step of the control design for open quantum systems. Numerical results verify the effectiveness of the proposed equally-mixed strategies DE (EMSDE) algorithm regarding the control design for open quantum systems with uncertainties.
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.
Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.
Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with Hamiltonian uncertainties. The SLC method includes two steps of “training” and “testing and evaluation”. In the training step, an augmented system is constructed by sampling uncertainties according to possible distributions of uncertainty parameters. A gradient flow based learning and optimization algorithm is adopted to find the control for the augmented system. In the process of testing and evaluation, a number of samples obtained through sampling the uncertainties are tested to evaluate the control performance. Numerical results demonstrate the success of the SLC approach. The SLC method has potential applications for robust control design of quantum systems.