Given the challenge of modeling multidimensional dynamical systems, which stems from the complexity of their intrinsic interactions and nonlinear dynamics, reservoir computing (RC) offers a robust framework for time series processing and analyzing. To further enhance the scalability and expressive power of this approach, this work introduces a higher-order quantum reservoir computing (HoQRC) framework. This architecture utilizes a quantum Ising reservoir to harness inherent quantum properties—superposition and entanglement—thereby enhancing computational information processing. Notably, the framework is designed to simultaneously encode both temporal sequences and higher-order structural features at the input layer. In addition, to address NISQ-era hardware limitations, the integrated high-dimensional input is decomposed into subsystems, each processed in parallel by dedicated compact quantum Ising reservoir modules. This strategy reduces peak qubit requirements from scaling with full system dimensionality to scaling with subsystem complexity, thereby mitigating decoherence and noise in practical implementations. Extensive experiments across diverse complex systems validate HoQRC's efficacy, while hyperparameter analyses confirm the critical role of the edge of chaos and global ergodic phase in dynamical modeling. This work establishes algorithmic foundations for the feasible deployment of the HoQRC framework, demonstrating significant potential for application in the study of large-scale complex systems.
Given the challenge of modeling multidimensional dynamical systems, which stems from the complexity of their intrinsic interactions and nonlinear dynamics, reservoir computing (RC) offers a robust framework for time series processing and analyzing. To further enhance the scalability and expressive power of this approach, this work introduces a higher-order quantum reservoir computing (HoQRC) framework. This architecture utilizes a quantum Ising reservoir to harness inherent quantum properties—superposition and entanglement—thereby enhancing computational information processing. Notably, the framework is designed to simultaneously encode both temporal sequences and higher-order structural features at the input layer. In addition, to address NISQ-era hardware limitations, the integrated high-dimensional input is decomposed into subsystems, each processed in parallel by dedicated compact quantum Ising reservoir modules. This strategy reduces peak qubit requirements from scaling with full system dimensionality to scaling with subsystem complexity, thereby mitigating decoherence and noise in practical implementations. Extensive experiments across diverse complex systems validate HoQRC's efficacy, while hyperparameter analyses confirm the critical role of the edge of chaos and global ergodic phase in dynamical modeling. This work establishes algorithmic foundations for the feasible deployment of the HoQRC framework, demonstrating significant potential for application in the study of large-scale complex systems.
Motivated by the perspective of advanced time-series prediction and exploitation of Quantum Reservoir Computing (QRC), we explored the design and implementation of a Hybrid Photonic-Quantum Reservoir Computing (HPQRC) paradigm. It brings together the high-speed parallelism of photonic systems with the quantum reservoir's capacity of modeling complex, nonlinear dynamics, and hence acts as a powerful tool for performing real-time prediction in resource resource-constrained environment with low latency. We have engineered a solution using this architecture to address issues like computational bottlenecks, energy inefficiency, and sensitivity to noise that are common in existing reservoir computing models. Our simulation results show that HPQRC attains much higher accuracy with lower computational time than both classical and quantum-only models. This model is robust when environments are noisy and scales well across large datasets, and therefore is suitable for application on diverse problems such as financial forecasting, industrial automation, and smart sensor networks. Our results substantiate that HPQRC performs significantly faster than traditional architectures and could be a viable and highly scalable platform for actual edge computing systems. Overall, HPQRC demonstrates significant advancements in time series modeling capabilities. In combination with enhanced predictive accuracy with reduced computational requirements, HPQRC establishes itself as an effective analytical tool for complex dynamic systems that require both precision and processing efficiency.
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.
Quantum Reservoir Computing (QRC) utilizes the intrinsic dynamics of quantum systems to process temporal data efficiently, offering potential advantages in computational power and energy efficiency. Unlike classical reservoirs, quantum reservoirs leverage properties such as superposition and entanglement, which may enhance information processing capabilities. In this work, we investigate a QRC framework based on two coupled Kerr nonlinear oscillators, a system well-suited for time-series prediction tasks due to its complex nonlinear interactions and potentially high-dimensional state space. We explore how its performance in time-series prediction depends on key physical parameters: input drive strength, Kerr nonlinearity, and oscillator coupling, and analyze the role of entanglement in improving the reservoir’s computational performance, focusing on its effect on predicting non-trivial time series. Using logarithmic negativity to quantify entanglement and normalized root mean square error (NRMSE) to evaluate predictive accuracy, our results suggest that entanglement provides a computational advantage on average up to a threshold in the input frequency, which persists under some levels of dissipation and dephasing. These findings contribute to the broader understanding of quantum reservoirs and highlight their potential for high performance, efficient quantum machine learning and time-series forecasting.
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.
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.