Quantum reservoir computing offers a promising route toward energy-efficient machine learning by processing temporal information with minimal training overhead. Yet, the physical principles linking its energetic cost to computational performance remain largely unexplored. Here we show that, in an interacting spin reservoir, information encoding and information processing are governed by distinct physical mechanisms. In the weak interacting regime, we derive an analytical expression for the average (switching) work, showing that the energetic cost of encoding new inputs is determined by the local response of the reservoir units. In contrast, interactions primarily redistribute the encoded information, generating memory and nonlinear features while only weakly affecting the work. This separation produces opposite correlations between energetic cost and performance for representative linear and nonlinear benchmark tasks. Our results identify the switching work as the energetic signature of information encoding and clarify when energetic efficiency and computational performance are compatible.
Quantum reservoir computing offers a promising route toward energy-efficient machine learning by processing temporal information with minimal training overhead. Yet, the physical principles linking its energetic cost to computational performance remain largely unexplored. Here we show that, in an interacting spin reservoir, information encoding and information processing are governed by distinct physical mechanisms. In the weak interacting regime, we derive an analytical expression for the average (switching) work, showing that the energetic cost of encoding new inputs is determined by the local response of the reservoir units. In contrast, interactions primarily redistribute the encoded information, generating memory and nonlinear features while only weakly affecting the work. This separation produces opposite correlations between energetic cost and performance for representative linear and nonlinear benchmark tasks. Our results identify the switching work as the energetic signature of information encoding and clarify when energetic efficiency and computational performance are compatible.
The intersection of quantum information processing and machine learning has recently at-tracted considerable interest within the physics and artificial intelligence communities. From a physical perspective, quantum computing offers fundamentally new modes of information processing, enabled by superposition, interference, and entanglement, which can lead to ad-vantages in computational speed and resource efficiency over classical approaches. These developments have motivated the exploration of machine learning paradigms that lever-age quantum dynamics as a computational resource. In parallel, reservoir computing—a non–von Neumann and neuromorphic computing framework—has gained attention due to its reliance on high-dimensional dynamical systems, in-memory computation, and low en-ergy consumption. Quantum reservoir computing extends this paradigm by exploiting the intrinsic dynamics of quantum many-body systems, such as spin networks, to process tem-poral information. Despite growing interest in quantum reservoir architectures, the role of genuinely quantum resources, in particular entanglement, in determining their information-processing capabilities remains incompletely understood. In this thesis, we study a distributed spin-network reservoir in which two independent time series are injected into separate qubits. Using short-term memory capacity as an opera-tional measure, we analyze how information introduced at distinct sites propagates through the network and how different entanglement structures contribute to storing and combining past inputs. Focusing on bilinear memory tasks, which require reconstructing the product of the two inputs at various delays, we probe temporal memory. Due to the computational cost associated with simulating open quantum many-body dynamics, the present study focuses on a minimal spin-network architecture consisting of four qubits, with two qubits serving as input nodes that receive independent time series. Even for such moderate system sizes, the numerical integration of the open-system dynamics are computationally demanding. Nevertheless, this minimal setting already captures the essential mechanisms of distributed information processing in quantum reservoirs. By computing the logarithmic negativity across different bipartitions of the reservoir, we investigate how memory performance relates to the underlying entanglement structure. We find that the short-term memory capacity is maximized at relatively weak coupling strengths, where entanglement is present but remains moderate. Among the various bipar-titions, the entanglement between the two input qubits consistently plays the most promi-nent role in learning performance. In this optimal regime, the reservoir exhibits long-lived memory, while a characteristic reduction in performance at zero delay, observed across all frequencies, reflects the finite time required for information to propagate through the sys-tem. Taken together, these results indicate that effective learning in distributed quantum reservoir computing is enabled by moderate, well-structured entanglement, rather than by maximal correlations.
Open quantum systems offer a physical substrate for temporal information processing in quantum reservoir computing, yet the microscopic mechanisms linking their dynamics to computational performance remain unclear. Here we establish a microscopic response-to-performance framework that connects Liouvillian dynamics directly to task performance. We decompose observable Volterra weights as W(q)=BH(q), separating internal input-history pathways from their readout visibility, and show that a dynamical response contributes to a task only if it is input-generated, readout-visible, target-correlated, and resolvable above the regularization scale. This framework reveals how Liouvillian modes govern the retention and propagation of task-relevant information, while symmetries determine which components remain visible to the readout. It further establishes how distinct covariance modes encode different temporal information structures and how system parameters and processing protocols can reshape their contributions to improve QRC performance. Thermalization drives the reservoir from processing that retains input history to a response dominated by the most recent input before regularization suppresses the residual information. We finally show that weak measurement can activate task-relevant covariance modes by lifting symmetry-imposed channel equivalence, whereas delayed feedback creates controlled return pathways for historical information. These results establish a microscopic connection between open-system dynamics and computational performance, providing principles for engineering task-relevant information flow in quantum reservoirs.
Quantum reservoir computing provides a framework for processing complex temporal data, yet its fundamental computational and energetic limits remain unresolved. Here, we establish a non-equilibrium thermodynamic framework that links the macroscopic predictive performance of driven open quantum systems to their microscopic energetic costs. By mapping Holevo capacities onto the Bogoliubov-Kubo-Mori geometric manifold, we analytically prove that the computational peak within the quantum critical region originates from a spectral resonance: the closing of the intrinsic energy gap forces the reservoir's internal transition frequencies to align with the chaotic drive. To evaluate the associated thermodynamic costs, we introduce quantum informational dissipation to quantify the non-predictive historical data retained by the reservoir. This allows us to derive a generalized Landauer bound for continuous temporal processing, which reveals a fundamental thermodynamic trade-off: the critical resonance that maximizes predictive capacity simultaneously maximizes informational dissipation and the irreversible work required for environmental erasure. Furthermore, coherence decomposition demonstrates that quantum coherences amplify predictive capacity without demanding additional mechanical work. These findings establish the fundamental energetic limits of quantum learning devices, providing theoretical principles for designing energy-efficient quantum neuromorphic hardware.
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.
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.