Machine learning (ML) architectures such as convolutional neural networks (CNNs) have garnered considerable recent attention in the study of quantum many-body systems. However, advanced ML approaches such as gated recurrent neural networks (RNNs) have seldom been applied to such contexts. Here we demonstrate that a special class of RNNs known as long short-term memory (LSTM) networks is capable of learning and accurately predicting the time evolution of one-dimensional (1D) Ising model with simultaneous transverse and parallel magnetic fields, as quantitatively corroborated by relative entropy measurements and magnetization between the predicted and exact state distributions. In this unsupervised learning task, the many-body state evolution was predicted in an autoregressive way from an initial state, without any guidance or knowledge of any Hamiltonian. Our work paves the way for future applications of advanced ML methods in quantum many-body dynamics without relying on the explicit form of the Hamiltonian.
Machine learning (ML) architectures such as convolutional neural networks (CNNs) have garnered considerable recent attention in the study of quantum many-body systems. However, advanced ML approaches such as gated recurrent neural networks (RNNs) have seldom been applied to such contexts. Here we demonstrate that a special class of RNNs known as long short-term memory (LSTM) networks is capable of learning and accurately predicting the time evolution of one-dimensional (1D) Ising model with simultaneous transverse and parallel magnetic fields, as quantitatively corroborated by relative entropy measurements and magnetization between the predicted and exact state distributions. In this unsupervised learning task, the many-body state evolution was predicted in an autoregressive way from an initial state, without any guidance or knowledge of any Hamiltonian. Our work paves the way for future applications of advanced ML methods in quantum many-body dynamics without relying on the explicit form of the Hamiltonian.
Advanced machine learning (ML) approaches such as transfer learning have seldom been applied to approximate quantum many-body systems. Here we demonstrate that a simple recurrent unit (SRU) based efficient and transferable sequence learning framework is capable of learning and accurately predicting the time evolution of the one-dimensional (1D) Ising model with simultaneous transverse and parallel magnetic fields, as quantitatively corroborated by relative entropy measurements between the predicted and exact state distributions. At a cost of constant computational complexity, a larger many-body state evolution is predicted in an autoregressive way from just one initial state, without any guidance or knowledge of any Hamiltonian. Our work paves the way for future applications of advanced ML methods in quantum many-body dynamics with knowledge only from a smaller system.
Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling on noisy intermediate-scale quantum (NISQ) devices.
Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling such as natural language processing, speech recognition on noisy intermediate-scale quantum (NISQ) devices.
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.
The non-Markovian stochastic Schrödinger equation (NMSSE) offers a promising approach for open quantum simulations owing to its low scaling complexity and suitability for parallel computing. However, its application at low temperatures faces significant convergence challenges. While short-time evolution converges quickly, long-time evolution requires a much larger number of stochastic trajectories, leading to high computational costs. To this end, we propose a scheme that utilizes neural networks to extract effective information from long-time simulations of the non-Markovian stochastic Schrödinger equation, fine-tunes the networks using converged short-time data, and predicts long-term system evolution, eliminating the influence of stochastic oscillations. By integrating convolutional neural networks (CNNs) and long short-term memory recurrent neural networks (LSTMs), along with the iterative attentional feature fusion (iAFF) technique, this approach significantly reduces the number of trajectories required for long-time simulations, particularly at low temperatures, thus substantially lowering computational costs and improving convergence. To demonstrate our approach, we investigated the dynamics of the spin-boson model and the Fenna-Matthews-Olson (FMO) complex across a range of parameter variations.
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.