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Quantum Reservoir Computing for Time Series Prediction

Jincheng Zhang

Published Aug 31, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.22185858

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This paper explores the application of quantum reservoir computing (QRC) utilizing entangled quantum reservoirs for enhanced time series prediction. Traditional reservoir computing relies on randomly connected recurrent neural networks, often struggling to effectively capture complex temporal dependencies inherent in time series data. We propose a novel approach where the reservoir is replaced by a quantum system, specifically a collection of coupled qubits, governed by quantum interference. The introduction of entanglement within the reservoir is hypothesized to significantly improve its ability to model and predict time series data. Theoretical analysis and simplified models demonstrate a potential for enhanced performance compared to classical reservoir computing methods. The core claim is that entangled quantum reservoirs can achieve superior time series prediction accuracy. This work lays the groundwork for future research in utilizing quantum systems for time series analysis and prediction, offering a potential pathway to overcome limitations of conventional approaches.
Reservoir computing (RC) has demonstrated significant promise in time series forecasting, particularly for chaotic systems. However, a critical limitation of traditional RC approaches is their vulnerability to non-Gaussian noise, a common characteristic of real-world time series data. This paper proposes a novel framework, Quantum Reservoir Computing (QRC), designed to address this challenge. QRC utilizes a quantum reservoir – a randomly initialized quantum circuit – to leverage the inherent noise robustness of quantum mechanics, specifically quantum entanglement and superposition. The quantum reservoir is coupled with a variational quantum circuit for output mapping. We demonstrate that this approach significantly improves forecasting accuracy when dealing with non-Gaussian noise, offering a pathway to more reliable RC implementations. The core claim of this work is that reservoir computing struggles with non-Gaussian noise, which is prevalent in many time series datasets. The core mechanism involves extending reservoir computing using a quantum reservoir – a randomly initialized quantum circuit – that is inherently robust to non-Gaussian noise due to quantum entanglement and superposition, combined with a variational quantum circuit for output mapping. The methodology incorporates a mapping function to translate quantum states into time series predictions, and the variational quantum circuit is trained to minimize the error between predicted and actual time series values. We explore the theoretical underpinnings of this method and discuss its potential for various time series forecasting applications.
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This paper explores the application of quantum reservoir computing (QRC) to dynamic system identification. Traditional reservoir computing utilizes randomly connected recurrent neural networks to process time-series data, offering a computationally efficient approach to modeling complex, nonlinear dynamics. However, the inherent limitations of classical reservoir computing, particularly regarding the extraction of nuanced features, are addressed by integrating quantum mechanical principles. Specifically, we investigate the utilization of a quantum reservoir – a system of interacting qubits – to perform non-linear feature extraction. The core mechanism leverages quantum superposition and entanglement to represent complex dynamics more efficiently than classical counterparts. The aim is to demonstrate that QRC possesses the potential to surpass classical methods in both speed and accuracy for dynamic system modeling. This work lays the groundwork for future research into exploiting quantum computing for enhanced time-series analysis and control applications.
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.