Applications of neural networks to dynamics simulation of Landau-Zener transitions

We simulate the dynamics of a qubit-oscillator system obeying the Landau-Zener (LZ) model, by employing the nonlinear autoregressive neural network and the long short-term memory neural network. Initially, time-dependent transition probability of the LZ model is obtained by the Dirac-Frenkel time dependent variation with the multiple Davydov D2 Ansatz. With the first stage of a two-dimensional (2D) dataset (time versus transition probability), two different kinds of neural networks are trained and validated successfully with sufficient information to predict the future values of transition probability (the second stage) with considerable accuracy. Furthermore, we also develop a framework under which an entire time series of a LZ model with fixed tunneling strength Δ and a given qubit-bath coupling strength γ can be predicted, using neural networks that are trained on a set of pre-generated time series corresponding to various values of γ (3D data: time, γ and transition probability). Considerable accuracy is also achieved in 3D data prediction.