Abstract Quantum reservoir computing (QRC) offers a powerful approach to exploit the rich dynamics of quantum systems for information processing. However, the computational performance of conventional Hermitian reservoirs is inherently constrained by their nonlinearity and information-spreading ability. In this work, we propose a non-Hermitian QRC in which non-Hermitian dynamics are employed as a tunable resource to significantly enhance the QRC performance. By incorporating an imaginary interaction term into the one-dimensional X Y spin model, the reservoir’s information propagation extends beyond the Lieb–Robinson bound, resulting in accelerated information scrambling. Through spectral analysis and memory evaluation, we demonstrate that the non-Hermitian reservoir can be tuned toward the edge of chaos by varying a single parameter that controls the non-Hermitian strength. This tuning optimizes both memory and computational capacities, which are crucial for processing temporal sequences. For applications, we evaluate the predictive performance of both classical and quantum chaotic time series. Our results demonstrate superior performance compared with the Hermitian counterpart, with particularly notable advantages in predicting signals generated by the Sachdev–Ye–Kitaev model.
Abstract Quantum reservoir computing (QRC) offers a powerful approach to exploit the rich dynamics of quantum systems for information processing. However, the computational performance of conventional Hermitian reservoirs is inherently constrained by their nonlinearity and information-spreading ability. In this work, we propose a non-Hermitian QRC in which non-Hermitian dynamics are employed as a tunable resource to significantly enhance the QRC performance. By incorporating an imaginary interaction term into the one-dimensional X Y spin model, the reservoir’s information propagation extends beyond the Lieb–Robinson bound, resulting in accelerated information scrambling. Through spectral analysis and memory evaluation, we demonstrate that the non-Hermitian reservoir can be tuned toward the edge of chaos by varying a single parameter that controls the non-Hermitian strength. This tuning optimizes both memory and computational capacities, which are crucial for processing temporal sequences. For applications, we evaluate the predictive performance of both classical and quantum chaotic time series. Our results demonstrate superior performance compared with the Hermitian counterpart, with particularly notable advantages in predicting signals generated by the Sachdev–Ye–Kitaev model.
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.
Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated approaches-including memory restriction, weak measurements, operation near the edge of quantum chaos, and dissipative dynamics-are in fact governed by the same underlying principle, namely a tunable balance between memory retention and nonlinear response. Using the information processing capacity, a dynamical measure from nonlinear systems theory, we place these behaviors in a unified framework and identify the regimes in which quantum reservoirs surpass the standard protocol. Our results reveal a fundamental connection between memory and nonlinear response. This provides a general design principle for enhanced information processing and enables systematic analysis and optimization inspired by classical dynamical quantifiers.
Reservoir computing (RC) is a machine learning paradigm that harnesses dynamical systems as computational resources. In its quantum extension-quantum reservoir computing (QRC)-these principles are applied to quantum systems, whose rich dynamics broadens the landscape of information processing. In classical RC, optimal performance is typically achieved at the "edge of chaos," the boundary between order and chaos. Here, we identify its quantum many-body counterpart using the QRC implemented on the celebrated Sachdev-Ye-Kitaev model. Our analysis reveals substantial performance enhancements near two distinct characteristic "edges": a temporal boundary defined by the Thouless time, beyond which system dynamics is described by random matrix theory, and a parametric boundary governing the transition from integrable to chaotic regimes. These findings establish the "edge of many-body quantum chaos" as a design guideline for QRC.
[eng] Quantum technologies are rapidly evolving toward regimes where controllable quantum dynamics can be exploited for information processing, simulation, and machine learning. Within this landscape, quantum reservoir computing (QRC) has emerged as an appealing paradigm: it harnesses the high-dimensional dynamics of quantum systems to perform temporal tasks with minimal training overhead, making it particularly well suited for current noisy intermediate-scale quantum devices. In parallel, modern perspectives on quantum many-body systems reveal that tools such as complex-network theory and spectral methods can uncover structures in quantum states and dynamics that remain hidden to conventional approaches. This thesis brings these threads together. It explores how quantum statistics, many-body correlations, chaoticity, and metastability shape information processing in QRC. Furthermore, we have also demonstrated how network-theoretic methods can reveal new features of strongly correlated phases. This thesis contributes to the emerging field of quantum reservoir computing by examining how different physical models shape the learning capabilities of quantum reservoirs. Each article investigates a distinct class of systems: simple hopping networks governed by particle statistics, interacting atomic lattices described by the Bose–Hubbard model, driven-dissipative oscillators exhibiting metastability. Through these diverse settings, a central goal is to identify which physical ingredients enhance the performance of QRC. To address these questions, we combine analytical insights with a broad range of numerical techniques, including exact diagonalization, tensor-network simulations, and open-system dynamics. Together, these approaches provide a unified framework for understanding how quantum dynamics can be exploited for computation. The main findings of the thesis on QRC and complex networks can be summarized as follows. (i) Particle statistics fundamentally shape computational power: fermions exhibit superior information spreading due to their algebra, while bosons can outperform all other substrates when input encoding is optimized. (ii) Metastability constitutes a computational resource: long-lived metastable states enhance memory capacity and allow a fast-injection protocol. (iii) In atomic lattices described by the Bose–Hubbard model, QRC performance is governed by the interplay between interactions and tunneling, with optimal regimes appearing both in the weakly interacting limit and near the onset of quantum chaos; importantly, disorder is not required to achieve high performance. (iv) Complex-network analysis reveals hidden features of the Kitaev chain: network observables sharply detect the topological transition in the Kitaev chain and uncover a previously unnoticed fully connected, perfectly clustered regime linked to ground-state factorization observed in the Ising spin chain.
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.
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.