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

Abstract

The recurrent neural network with the long short-term memory cell (LSTM-NN) is employed to simulate the long-time dynamics of open quantum system. The bootstrap method is applied in the LSTM-NN construction and prediction, which provides a Monte-Carlo estimation of forecasting confidence interval. Within this approach, a large number of LSTM-NNs are constructed by resampling time-series sequences that were obtained from the early-stage quantum evolution given by numerically-exact multilayer multiconfigurational time-dependent Hartree method. The built LSTM-NN ensemble is used for the reliable propagation of the long-time quantum dynamics and the simulated result is highly consistent with the exact evolution. The forecasting uncertainty that partially reflects the reliability of the LSTM-NN prediction is also given. This demonstrates the bootstrap-based LSTM-NN approach is a practical and powerful tool to propagate the long-time quantum dynamics of open systems with high accuracy and low computational cost.

References in corpus (16)

• Deep learning for universal linear embeddings of nonlinear dynamics
• Time-evolution methods for matrix-product states
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine
• Deep and Confident Prediction for Time Series at Uber
• Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature
• A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems
• A Deep Network Model for Paraphrase Detection in Short Text Messages
• An exact equilibrium reduced density matrix formulation I: The influence of noise, disorder, and temperature on localization in excitonic systems
• Machine learning based energy-free structure predictions of molecules (closed and open-shell), transition states, and solids
• Prediction and real-time compensation of qubit decoherence via machine-learning
• Efficient simulation of non-Markovian system-environment interaction
• Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks
• Initial System-Environment Correlations via the Transfer Tensor Method