Forecasting dynamical systems is of importance to numerous real-world applications. Typically, these are obtained using first-principles-based models such as through the use of differential equations. When these equations are unknown, non-intrusive techniques must be utilized to build predictive models from data alone. Machine learning (ML) methods have recently been used for such tasks with the added advantage of significant reductions in time-to-solution for predictions during deployment. However, many state-of-the-art ML-based methods for forecasting rely on neural networks, which are expensive to train and require large amounts of memory. In this work, we propose a quantum mechanics inspired ML strategy for forecasting nonlinear dynamical systems that results in reduced training time and memory requirements. This approach, denoted the quantum reservoir computing technique (QRC), is a hybrid quantum-classical framework employing an ensemble of interconnected small quantum systems via classical linear feedback connections. By mapping the dynamical state to a suitable quantum representation amenable to unitary operations, QRC is able to predict complex nonlinear dynamical systems in a stable and accurate manner. We demonstrate the efficacy of this framework through benchmark forecasts of the NOAA Optimal Interpolation Sea Surface Temperature dataset and compare the performance of QRC to other ML methods.
Forecasting dynamical systems is of importance to numerous real-world applications. Typically, these are obtained using first-principles-based models such as through the use of differential equations. When these equations are unknown, non-intrusive techniques must be utilized to build predictive models from data alone. Machine learning (ML) methods have recently been used for such tasks with the added advantage of significant reductions in time-to-solution for predictions during deployment. However, many state-of-the-art ML-based methods for forecasting rely on neural networks, which are expensive to train and require large amounts of memory. In this work, we propose a quantum mechanics inspired ML strategy for forecasting nonlinear dynamical systems that results in reduced training time and memory requirements. This approach, denoted the quantum reservoir computing technique (QRC), is a hybrid quantum-classical framework employing an ensemble of interconnected small quantum systems via classical linear feedback connections. By mapping the dynamical state to a suitable quantum representation amenable to unitary operations, QRC is able to predict complex nonlinear dynamical systems in a stable and accurate manner. We demonstrate the efficacy of this framework through benchmark forecasts of the NOAA Optimal Interpolation Sea Surface Temperature dataset and compare the performance of QRC to other ML methods.
Quantum reservoir computing (QRC) is an emerging paradigm for harnessing the natural dynamics of quantum systems as computational resources that can be used for temporal machine learning tasks. In the current setup, QRC is difficult to deal with high-dimensional data and has a major drawback of scalability in physical implementations. We propose higher-order QRC, a hybrid quantum-classical framework consisting of multiple but small quantum systems that are mutually communicated via classical connections like linear feedback. By utilizing the advantages of both classical and quantum techniques, our framework enables an efficient implementation to boost the scalability and performance of QRC. Furthermore, higher-order settings allow us to implement a FORCE learning or an innate training scheme, which provides flexibility and high operability to harness high-dimensional quantum dynamics and significantly extends the application domain of QRC. We demonstrate the effectiveness of our framework in emulating large-scale nonlinear dynamical systems, including complex spatiotemporal chaos, which outperforms many of the existing machine learning techniques in certain situations.
This paper investigates the application of quantum reservoir computing (QRC) to time series prediction. Classical reservoir computing (RC) utilizes a complex, high-dimensional system – the 'reservoir' – as a non-linear feature extractor, followed by a linear regression model for prediction. QRC extends this concept by leveraging the inherent dynamics of a quantum system as the reservoir. We hypothesize that quantum systems, due to their superposition and entanglement properties, can provide richer and more complex dynamics than classical reservoirs, potentially leading to improved prediction accuracy. This work outlines the theoretical framework for QRC, detailing the setup of a suitable quantum reservoir (e.g., a superconducting qubit array), the measurement process, and the training strategy involving a classical machine learning model. We demonstrate a conceptual approach, focusing on the potential advantages and challenges of employing quantum systems for this task. The core claim is that QRC can achieve superior time series prediction accuracy compared to classical RC methods. Key elements explored include the input signal's influence on the quantum reservoir, the selection of appropriate measurement schemes, and the choice of classical learning algorithms. The paper concludes with a discussion of future research directions and the potential impact of QRC on various time series prediction applications.
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.
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.
Physical reservoir computing provides a powerful machine learning paradigm that exploits nonlinear physical dynamics for efficient information processing. By incorporating quantum effects, quantum reservoir computing offers superior potential for machine learning applications, as quantum dynamics are exponentially costly to simulate classically. Here, we present a novel quantum reservoir computing approach based on correlated quantum spin systems, exploiting natural quantum many-body interactions to generate reservoir dynamics, thereby circumventing the practical challenges of deep quantum circuits. Our experimental implementation supports nontrivial quantum entanglement and exhibits sufficient dynamical complexity for high-performance machine learning. We achieve state-of-the-art performance in experiments on standard time-series benchmarks, reducing prediction error by 1 to 2 orders of magnitude compared to previous quantum reservoir experiments. In long-term weather forecasting, our 9-spin quantum reservoir delivers greater prediction accuracy than classical reservoirs with thousands of nodes. This represents the first experimental demonstration of quantum machine learning outperforming large-scale classical models on real-world tasks.
We investigate quantum reservoir computing (QRC) using a hybrid qubit-boson system described by the Jaynes-Cummings (JC) Hamiltonian and its dispersive limit (DJC). These models provide high-dimensional Hilbert spaces and intrinsic nonlinear dynamics, making them powerful substrates for temporal information processing. We systematically benchmark both reservoirs through linear and nonlinear memory tasks, demonstrating that they exhibit an unusual superior nonlinear over linear memory capacity. We further test their predictive performance on the Mackey-Glass time series, a widely used benchmark for chaotic dynamics, and show comparable forecasting ability. We also investigate how memory and prediction accuracy vary with reservoir parameters and show the role of higher-order bosonic observables and time multiplexing in enhancing expressivity, even in minimal spin-boson configurations. Our results establish JC- and DJC-based reservoirs as versatile platforms for time-series processing and as elementary units that overcome the setting of equivalent qubit pairs and offer pathways toward tunable, high-performance quantum machine learning architectures.