Machine Learning for Finding Suboptimal Final Times and Coherent and Incoherent Controls for an Open Two-Level Quantum System


This work considers an open two-level quantum system evolving under coherent and incoherent piecewise constant controls constrained in their magnitude and variations. The control goal is to steer an initial pure density matrix into a given target density matrix in a minimal time. A machine learning algorithm was developed, which combines the approach of \(k\) nearest neighbors and training a multi-layer perceptron neural network, to predict suboptimal final times and controls. For 18 sets of initial pure states with different size (between 10 and 200) training datasets were constructed. The numerical results are described, including the analysis of the dependence of the quality of the machine learning algorithm on the size of the training set.

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Derivation of the dynamical equations given in Section 2.2 was performed in [27] within the project no. 1.669.2016/1.4 of the Ministry of Science and Higher Education of the Russian Federation. Other results were obtained within the project of the Russian Science Foundation no. 17-11-01388 in Steklov Mathematical Institute of Russian Academy of Sciences.

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Correspondence to O. V. Morzhin or A. N. Pechen.

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(Submitted by S. A. Grigoryan)

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Morzhin, O.V., Pechen, A.N. Machine Learning for Finding Suboptimal Final Times and Coherent and Incoherent Controls for an Open Two-Level Quantum System. Lobachevskii J Math 41, 2353–2368 (2020).

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  • open quantum system
  • quantum control
  • machine learning