A Deep‐Learning Approach to the Dynamics of Landau–Zenner Transitions

Abstract

Traditional approaches to the dynamics of the open quantum systems with high precision are often resource intensive. How to improve computation accuracy and efficiency for target systems is an extremely difficult challenge. In this work, combining unsupervised and supervised learning algorithms, a deep-learning approach is introduced to simulate and predict Landau-Zenner dynamics. Data obtained from multiple Davydov D 2 Ansatz with a low multiplicity of four are used for training, while the data from the trial state with a high multiplicity of ten are adopted as target data to assess the accuracy of prediction. After proper training, our method can successfully predict and simulate Landau-Zenner dynamics using only random noise and two adjustable model parameters. Compared to the high-precision dynamics data from multiple Davydov D 2 Ansatz with a multiplicity of ten, the error rate falls below 0.6%.

Automatic Evolution of Machine-Learning-Based Quantum Dynamics with Uncertainty Analysis

“…With the rapid development of computer artificial intelligence, machine learning (ML) plays more and more important roles in theoretical chemistry, including the construction of the molecular Hamiltonian, − the analysis of trajectory-based molecular dynamics evolution, − the prediction of molecular properties and chemical reactions, − and the design of novel functional materials. , In addition to these, considerable efforts were made to employ the ML approach to simulate dynamics evolutions recently. − …”

Modeling molecular J and H aggregates using multiple-Davydov D2 ansatz

“…The mD 2 Ansatz and, its more complex variant, mD 1 Ansatz 14 have been applied to study polaron dynamics in Holstein molecular crystals, 13 the spin-boson models 15 and for nonadiabatic dynamics of single molecules, 6,16 as well as to simulate nonlinear response function of molecular aggregates 7,13 and others. [17][18][19][20] A more in-depth overview of the various types of Davydov Ansatze and their applications can be found in a recent review article by Zhao et al 21 However, a well-defined strategy to determine the required number of multiples in mD 2 Ansatz (or the depth) needed to obtain the converged result is lacking. The absorption spectrum and excitation relaxation dynamics of a linear molecular aggregate are key quantities that may serve for establishing the relationship between model parameters and the parameters of the Ansatz.…”

“…The mD 2 Ansatz and, its more complex variant, mD 1 Ansatz 14 have been applied to study polaron dynamics in Holstein molecular crystals, 13 the spin-boson models 15 and for nonadiabatic dynamics of single molecules, 6,16 as well as to simulate nonlinear response function of molecular aggregates 7,13 and others. 17–20 A more in-depth overview of the various types of Davydov Ansatze and their applications can be found in a recent review article by Zhao et al 21…”

Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network

“…As powerful techniques that can extract the essential features of input raw data and make the prediction of unknown outputs, machine learning algorithms , were widely applied in many scientific fields, − such as physics, chemistry, computational science, bioinformatics, and so on. Especially, the recurrent neural network (RNN) displays the excellent ability to interpret the complex temporal behavior for time-series problems.…”

“…Because of the excellent performance of LSTM-NNs, they have been widely used in various types of time-series analysis and forecasting problems, − such as speech recognition and natural language processing. The applications of RNN and LSTM-NN in the simulation of the evolution of open quantum systems were conducted by Yang Zhao and co-workers. − This indicates that the LSTM-NN method may be an excellent approach to propagate the long-time dissipative dynamics of open quantum systems. In fact, the LSTM-NN approach can be viewed as a nonlinear model, while the transfer tensor formulism is a linear map model.…”