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arXiv:2504.17837 · Frontiers in Physics

Quantumness can enhance resilience to statistical noise in spin-network quantum reservoir computing

Youssef Kora, Christoph Simon

Published Apr 29, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum reservoir computing offers a promising approach to the utilization of complex quantum dynamics in machine learning. Statistical noise inevitably arises in real settings of quantum reservoir computing (QRC) due to the practical necessity of taking a small to moderate number of measurements. We investigate the effect of statistical noise in spin-network QRC on the possible performance benefits conferred by quantumness. As our measures of quantumness, we employ both quantum entanglement, which we quantify by the partial transpose of the density matrix, and coherence, which we quantify as the sum of the absolute values of the off-diagonal elements of the density matrix. We find that reservoirs which enjoy a finite degree of quantum entanglement and coherence are more stable against the adverse effects of statistical noise on performance compared to their unentangled, incoherent counterparts. Our results thus indicate that the potential benefit reservoir computers may derive from quantumness depends on the number of measurements used for training and testing, and that statistical noise, albeit detrimental on the whole, may leave quantum reservoirs in a stronger position relative to less quantum ones. These findings not only emphasize the importance of incorporating realistic noise models, but also suggest that the search for computational regimes that benefit from quantumness may be aided rather than impeded by the practical constraints of implementation within existing machines.

DOI
10.3389/fphy.2026.1817739

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Quantum reservoir computing offers a promising approach to the utilization of complex quantum dynamics in machine learning. Statistical noise inevitably arises in real settings of quantum reservoir computing (QRC) due to the practical necessity of taking a small to moderate number of measurements. We investigate the effect of statistical noise in spin-network QRC on the possible performance benefits conferred by quantumness. As our measures of quantumness, we employ both quantum entanglement, which we quantify by the partial transpose of the density matrix, and coherence, which we quantify as the sum of the absolute values of the off-diagonal elements of the density matrix. We find that reservoirs which enjoy a finite degree of quantum entanglement and coherence are more stable against the adverse effects of statistical noise on performance compared to their unentangled, incoherent counterparts. Our results thus indicate that the potential benefit reservoir computers may derive from quantumness depends on the number of measurements used for training and testing, and that statistical noise, albeit detrimental on the whole, may leave quantum reservoirs in a stronger position relative to less quantum ones. These findings not only emphasize the importance of incorporating realistic noise models, but also suggest that the search for computational regimes that benefit from quantumness may be aided rather than impeded by the practical constraints of implementation within existing machines.
We study the performance of an Ising spin network for quantum reservoir computing in linear and nonlinear memory tasks. We investigate the extent to which quantumness enhances performance by monitoring the behavior of quantum entanglement, which we quantify by the partial transpose of the density matrix. In the most general case where the effects of dissipation are incorporated, our results indicate that the strength of the entanglement advantage depends on the frequency of the input signal; the benefit of entanglement is greater with more rapidly fluctuating signals, whereas a low-frequency input is better suited to a nonentangled reservoir. This may be understood as a condition for an entanglement advantage to manifest itself: the system's quantum memory must survive long enough for the temporal structure of the input signal to reveal itself. We also find that quantum entanglement empowers a spin-network quantum reservoir to remember a greater number of temporal features.
We analyze numerically the performance of Quantum Reservoir Computing (QRC) for statistical and financial problems. We use a reservoir composed of two superconducting islands coupled via their charge degrees of freedom. The key non-linear elements that provide the reservoir with rich and complex dynamics are the Josephson junctions that connect each island to the ground. We show that QRC implemented in this circuit can accurately classify complex probability distributions, including those with heavy tails, and identify regimes in correlated time series, such as periods of high volatility generated by standard econometric models. We find QRC to outperform some of the best classical methods when the amount of information is limited. This demonstrates its potential to be a noise-resilient quantum learning approach capable of tackling real-world problems within currently available superconducting platforms. We further discuss how to improve our QRC algorithm in real superconducting hardware to benefit from a much larger Hilbert space.
Quantum Reservoir Computing (QRC) offers potential advantages over classical reservoir computing, including inherent processing of quantum inputs and a vast Hilbert space for state exploration. Yet, the relation between the performance of reservoirs based on complex and many-body quantum systems and non-classical state features is not established. Through an extensive analysis of QRC based on a transverse-field Ising model we show how different quantum effects, such as quantum coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir’s dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime. Quantum Reservoir Computing leverages the quantum properties of physical systems for solving temporal tasks. This study shows the importance of quantum effects, such as coherence and superposition, in the reservoir’s performance for different dynamical regimes, while considering the impact of finite measurements and noisy environments.
The growing demand for efficient machine learning has motivated the exploration of neuro-morphic and reservoir computing, which are rooted in brain-inspired approaches that mimic the recurrent dynamics and adaptive information processing of biological neural circuits. These methods leverage the intrinsic dynamics of physical systems to process temporal in-formation with minimal training. Extending these ideas, Quantum Reservoir Computing (QRC) seeks to exploit uniquely quantum features—such as coherence, entanglement, and nonlinearity—for enhanced performance. Yet, the precise role of quantum resources in QRC remains unclear. This thesis investigates entanglement as a computational resource in QRC, focusing on a model of two coupled Kerr nonlinear oscillators. The Kerr platform is well suited for time-series prediction tasks due to its nonlinear interactions and access to a large Hilbert space. Using logarithmic negativity to quantify entanglement and normalized root mean square error (NRMSE) to measure predictive accuracy, we evaluate the effect of input drive strength, Kerr nonlinearity, and oscillator coupling on reservoir performance. Our results show that entanglement is related to improved computational accuracy on average and in worst-case scenarios, though it does not reduce the best-case error. The advantage persists under realistic imperfections: dissipation can enhance performance in certain regimes, while moderate dephasing does not completely remove the benefit. This thesis situates QRC within the context of neuromorphic and reservoir computing. It demonstrates the computational role of entanglement in a physically motivated QRC model and evaluates how key physical parameters affect performance under realistic conditions. This work advances understanding of whether and how quantum phenomena can be har-nessed for efficient learning, paving the way for high-performance quantum machine learning and time-series forecasting.
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Quantum reservoir computing uses genuine quantum properties to process temporal information. It combines machine learning with physical computing in a novel quantum computing paradigm. Unlike gate-based quantum computing, which requires precise qubit control and decoherence suppression, quantum reservoir computing utilizes the dynamics of disordered quantum networks, with moderate noise even benefiting the reservoir's memory capacity. In this study, we explore how quantum properties affect a system's suitability as a reservoir computer. We investigate the relationship between entanglement in the reservoir and phase space dimension. Our findings show higher entanglement increases the percentage of the exponentially large phase space used for computation. Additionally, we discuss methods to quantify information spread throughout the network. Network symmetries, accidental or intentional, significantly influence dynamics and the reservoir's memory capacity. Lastly, we highlight the potential and limitations of using arrays of semiconductor-based coupled microcavities for hybrid quantum-photonic implementations of reservoir computing.