Reservoir computing is a temporal machine-learning architecture particularly suitable for learning and predicting complex nonlinear dynamical systems. A classicalreservoir computer is typically trained to act as a self-evolving dynamical system and its performance can often be maximized at the “edge of chaos.” Extending thisparadigm to quantum systems reveals a broader landscape of physical phenomena. Bridging machine-learning theory and quantum condensed matter physics, thisPerspective synthesizes a unifying framework where the computational power of both classical and quantum reservoirs is fundamentally governed by their dynamical phases. In particular, how quantum phases, such as many-body localized versus ergodic, dictate memory-nonlinearity trade-offs is analyzed. A roadmap for parameter-adaptable quantum AI, transforming encoding, readout, and noise bottlenecks into scalable computational resources is outlined.
Reservoir computing is a temporal machine-learning architecture particularly suitable for learning and predicting complex nonlinear dynamical systems. A classicalreservoir computer is typically trained to act as a self-evolving dynamical system and its performance can often be maximized at the “edge of chaos.” Extending thisparadigm to quantum systems reveals a broader landscape of physical phenomena. Bridging machine-learning theory and quantum condensed matter physics, thisPerspective synthesizes a unifying framework where the computational power of both classical and quantum reservoirs is fundamentally governed by their dynamical phases. In particular, how quantum phases, such as many-body localized versus ergodic, dictate memory-nonlinearity trade-offs is analyzed. A roadmap for parameter-adaptable quantum AI, transforming encoding, readout, and noise bottlenecks into scalable computational resources is outlined.
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.
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing and develop state-of-the-art variants capable of addressing diverse applications in machine learning. The research demonstrates the algorithm's robustness and adaptability across very different domains, including agricultural time series forecasting and the time propagation of quantum systems. The first contribution of this thesis consists in developing a reservoir computing-based methodology to predict future agricultural product prices, which is crucial for ensuring the sustainability of the food market. The next contribution of the thesis is devoted to solving the Schrödinger equation for complex quantum systems. A novel reservoir computing framework is proposed to efficiently propagate quantum wavefunctions in time, enabling the computation of all eigenstates of a quantum system within a specific energy range. This approach is used to study prominent systems in the field of quantum chemistry and quantum chaos. The last contribution of this thesis focuses on optimizing algorithm designs for quantum reservoir computing. The results demonstrate that families of quantum circuits with higher complexity, according to the majorization criterion, yield superior performance in quantum machine learning. Moreover, the impact of quantum noise on the algorithm performance is evaluated, revealing that the amplitude damping noise can actually be beneficial for the performance of quantum reservoir computing, while the depolarizing and phase damping noise should be prioritized for correction. Furthermore, the optimal design of quantum reservoirs is employed to construct a hybrid quantum-classical neural network that tackles a fundamental problem in drug design.
Quantum reservoir computing (QRC) uses the dynamics of a fixed or weakly tuned quantum system to transform temporal and sequential inputs into measured features, while training is typically confined to a classical readout. This separation reduces reliance on repeated quantum parameter updates and avoids the barren plateaus associated with variational circuit training. Its computational power is often attributed to the exponentially large Hilbert space of the quantum system. However, the memory, nonlinearity, and expressivity that determine what a reservoir can actually compute depend jointly on the input encoding, quantum evolution, observables, measurement, and readout, not on Hilbert space dimension alone. On hardware, these capabilities are further constrained by finite sampling, hardware noise, measurement backaction, and the cost of estimating observables, so a large state space alone does not guarantee useful computation. In this survey, we develop a common system model that connects these components and use it to organize QRC foundations, computational properties, reservoir architectures, operating protocols, and physical implementations. We examine spin, photonic, superconducting, bosonic, neutral atom, and other analog platforms, together with applications, software and high performance computing support, benchmarking, and reproducibility. The analysis distinguishes hardware demonstrations from simulations and identifies the assumptions and resources that govern comparisons across implementations. Current results do not establish a broad quantum advantage over well matched classical reservoirs. We therefore specify the resource accounting, benchmark standards, and theoretical criteria needed to evaluate claims of quantum advantage.
[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.
Numerical studies suggest that quantum reservoir computing performs optimally near the edge of chaos, a behavior commonly attributed to a balance between memory retention and nonlinear information processing. Here we develop an explicit quantum reservoir model and rigorously analyze its chaotic regime and integrable point. In the chaotic regime, we show that Gaussian-unitary-ensemble statistics lead to rapid memory loss: learning performance decays exponentially with the storage time required by a temporal task. This decay limits the ability of chaotic reservoirs to learn long-range temporal dependencies. At the integrable point, described by a free-fermion model, we prove that amplitude encoding and a linear readout of fermionic two-point correlations cannot learn a representative class of nonlinear tasks coupling present and past inputs. Introducing interactions alleviates this obstruction. By identifying distinct limitations on memory retention in the chaotic regime and nonlinear processing at the integrable point, our analysis provides a theoretical basis for the observed edge-of-chaos advantage and guides the design of quantum reservoirs for temporal learning.
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.