Time series prediction (TSP) has been widely used in various fields, such as life sciences and finance, to forecast future trends based on historical data. However, to date, there has been relatively little research conducted on the TSP for quantum physics. In this paper, we explore the potential application of TSP in forecasting the dynamical evolution of open quantum systems. We employ deep learning techniques to train a TSP model and evaluate its performance by comparison with exact solution. We use the ratio of the prediction step length and the sequence length to define short and long-term forecasting. Our results show that the trained model has the ability to effectively capture the inherent characteristics of time series for both short-term and long-term forecasting. Accurate predictions for different coupling intensities and initial states are obtained. Furthermore, we use our method to train another model and find that it can successfully predict the steady state of the system. These findings suggests that TSP is a valuable tool for the prediction of the dynamics in open quantum systems.
Time series prediction (TSP) has been widely used in various fields, such as life sciences and finance, to forecast future trends based on historical data. However, to date, there has been relatively little research conducted on the TSP for quantum physics. In this paper, we explore the potential application of TSP in forecasting the dynamical evolution of open quantum systems. We employ deep learning techniques to train a TSP model and evaluate its performance by comparison with exact solution. We use the ratio of the prediction step length and the sequence length to define short and long-term forecasting. Our results show that the trained model has the ability to effectively capture the inherent characteristics of time series for both short-term and long-term forecasting. Accurate predictions for different coupling intensities and initial states are obtained. Furthermore, we use our method to train another model and find that it can successfully predict the steady state of the system. These findings suggests that TSP is a valuable tool for the prediction of the dynamics in open quantum systems.
The dynamics of open quantum systems play a crucial role in quantum information science. However, obtaining numerically exact solutions for the Lindblad master equation is often computationally expensive. Recently, machine learning techniques have gained considerable attention for simulating open quantum system dynamics. In this paper, we propose a deep learning model based on time series prediction (TSP) to forecast the dynamical evolution of open quantum systems. We employ the positive operator-valued measure (POVM) approach to convert the density matrix of the system into a probability distribution and construct a TSP model based on Transformer neural networks. This model effectively captures the historical evolution patterns of the system and accurately predicts its future behavior. Our results show that the model achieves high-fidelity predictions of the system's evolution trajectory in both short- and long-term scenarios, and exhibits robust generalization under varying initial states and coupling strengths. Moreover, we successfully predicted the steady-state behavior of the system, further proving the practicality and scalability of the method.
Time series forecasting is a critical problem with applications in various fields, such as finance, energy, and environmental science. While classical machine learning methods have shown significant progress in this domain, the advent of quantum machine learning introduces a new perspective to address the complexities of time series prediction. In this research, we propose a novel Quantum Neural Network (QNN) approach for time series forecasting, leveraging the unique capabilities of quantum computing to capture intricate temporal dependencies and exploit quantum parallelism. By encoding time series data into quantum states and designing quantum circuits for processing, the QNN aims to achieve improved predictive accuracy compared to classical neural networks. Through extensive experiments on diverse time series datasets, we demonstrate the potential of our QNN framework and discuss the future prospects of quantum-powered time series prediction in real-world applications.
Time series forecasting involves analyzing historical data to predict future trends and is useful for reducing uncertainty in various phenomena. Recurrent Neural Network-based Long Short-Term Memory (LSTM) has been shown to be used for time series forecasting. However, the introduction of a hybrid quantum-classical model of LSTM, i.e., Quantum LSTM (QLSTM), opens up avenues for faster and more efficient computing and, therefore, is of significant potential. These potentials underscore the necessity for a comparative analysis of both models to assess their effectiveness and efficiency. This study evaluates the performance of QLSTM and classical LSTM models in time series forecasting. Through controlled parametric numerical experiments, the study examines the performance of both models using CPUs and GPUs in cloud environments. Our findings reveal significant improvements in the QLSTM model, with enhanced training accuracy and reduced test loss compared to the classical LSTM under similar epochs and batch sizes. The results demonstrate the superior efficiency of the QLSTM model in handling large, complex data sets compared to the classical LSTM model.
Time series forecasting is a valuable tool for many applications, such as stock price predictions, demand forecasting or logistical optimization. There are many well-established statistical and machine learning models that are used for this purpose. Recently in the field of quantum machine learning many candidate models for forecasting have been proposed, however in the absence of theoretical grounds for advantage thorough benchmarking is essential for scientific evaluation. To this end, we performed a benchmarking study using real data of various quantum models, both gate-based and annealing-based, comparing them to the state-of-the-art classical approaches, including extensive hyperparameter optimization. Overall we found that the best classical models outperformed the best quantum models. Most of the quantum models were able to achieve comparable results and for one data set two quantum models outperformed the classical ARIMA model. These results serve as a useful point of comparison for the field of forecasting with quantum machine learning.
This paper explores the application of quantum reservoir computing (QRC) to time-series forecasting. Traditional reservoir computing methods, while effective for certain time-series, often face limitations when dealing with complex, high-dimensional data. This research proposes a novel approach utilizing a quantum system, such as a driven oscillator, as the reservoir, capitalizing on the inherent quantum properties for enhanced temporal processing. The core idea involves mapping the input time series onto the quantum reservoir, allowing the reservoir's quantum state to evolve dynamically. A linear readout layer is then trained to predict future values based on the evolved state. We investigate the potential advantages of QRC, specifically its ability to capture non-linear relationships and high-dimensional correlations within the time series data. The theoretical framework is presented, outlining the key components and the training methodology. Simulation results (described in detail below) demonstrate the feasibility and potential performance gains of QRC compared to classical reservoir computing. This research contributes to the growing field of quantum computing applied to time-series analysis.
We explore the efficacy of the novel use of parametrised quantum circuits (PQCs) as quantum neural networks (QNNs) for forecasting time series signals with simulated quantum forward propagation. The temporal signals consist of several sinusoidal components (deterministic signal), blended together with trends and additive noise. The performance of the PQCs is compared against that of classical bidirectional long short-term memory (BiLSTM) neural networks. Our results show that for time series signals consisting of small amplitude noise variations (up to 40 per cent of the amplitude of the deterministic signal) PQCs, with only a few parameters, perform similar to classical BiLSTM networks, with thousands of parameters, and outperform them for signals with higher amplitude noise variations. Thus, QNNs can be used effectively to model time series having, at the same time, the significant advantage of being trained significantly faster than a classical machine learning model in a quantum computer.