Optimal control of open-quantum-system dynamics predicted by long short-term memory

Jun-Dong Zhong, Zhao-Ming Wang

The realization of high-fidelity quantum control is crucial for quantum information processing, particularly in noisy environments where control strategies must simultaneously achieve precise manipulation and effective noise suppression. Conventional optimal control designs typically require numerical calculations of the system dynamics. Recent studies have demonstrated that long short-term memory neural networks (LSTM) can accurately predict the time evolution of open quantum systems. Based on LSTM predicted dynamics, we propose an optimal control framework for rapid and efficient optimal control design in open quantum systems. As illustrative examples, we apply the proposed framework to design optimal control for adiabatic speedup in a two-level system and for quantum state transfer in a spin chain, both under non-Markovian environments. For adiabatic speedup, our optimization procedure involves two steps: driving trajectory optimization and zero-area pulse optimization. Fidelity improvements for both steps have been obtained, demonstrating the effectiveness of the scheme. Furthermore, this effectiveness is validated for quantum state transfer in a spin chain, which is a high dimensional control problem. Our optimal control design scheme utilizes predicted dynamics to generate optimized controls, offering broad application potential in quantum computing, communication, and sensing.

Victor Mukherjee, Vittorio Giovannetti, Rosario Fazio +3 more

Kunni Lin, Jiawei Peng, Feng Long Gu +1 more

The recurrent neural network with the long short-term memory cell (LSTM-NN) is employed to simulate the long-time dynamics of open quantum systems. The bootstrap method is applied in the LSTM-NN construction and prediction, which provides a Monte Carlo estimation of a 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.

Sri Hari Krishna Narayanan, Thomas Propson, Marcelo Adriano dos Santos Bongarti +2 more

Daniel Basilewitsch

Kunni Lin, Jiawei Peng, Chao Xu +2 more

The machine learning approaches are applied in the dynamical simulation of open quantum systems. The long short-term memory recurrent neural network (LSTM-RNN) models are used to simulate the long-time quantum dynamics, which are built based on the key information of the short-time evolution. We employ various hyperparameter optimization methods, including simulated annealing, Bayesian optimization with tree-structured parzen estimator, and random search, to achieve the automatic construction and adjustment of the LSTM-RNN models. The implementation details of three hyperparameter optimization methods are examined, and among them, the simulated annealing approach is strongly recommended due to its excellent performance. The uncertainties of the machine learning models are comprehensively analyzed by the combination of bootstrap sampling and Monte Carlo dropout approaches, which give the prediction confidence of the LSTM-RNN models in the simulation of the open quantum dynamics. This work builds an effective machine learning approach to simulate the dynamics evolution of open quantum systems. In addition, the current study provides an efficient protocol to build optimal neural networks and estimate the trustiness of the machine learning models.