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Quantum Lyapunov control with machine learning

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Abstract

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 are used to learn the relationship between the optimal control parameters and initial states through supervised learning with samples. Two designs are presented where the feedforward neural network and the general regression neural network are used to select control schemes and design Lyapunov functions, respectively. We demonstrate the performance of the designs with a three-level quantum system for an eigenstate control problem. Since the sample generation and the training of neural networks are carried out in advance, the initial-state-adaptive Lyapunov control can be implemented for new initial states without much increase of computational resources.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11705026, 11534002, 11775048, 61475033, the China Postdoctoral Science Foundation under Grant No. 2017M611293, and the Fundamental Research Funds for the Central Universities under Grant No. 2412017QD003.

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  1. Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China

    S. C. Hou & X. X. Yi

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Correspondence to X. X. Yi.

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Hou, S.C., Yi, X.X. Quantum Lyapunov control with machine learning. Quantum Inf Process 19, 8 (2020). https://doi.org/10.1007/s11128-019-2470-8

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