Abstract—Reservoir computing exploits high-dimensional nonlinear dynamics to solve temporal prediction tasks with minimal training cost. We investigate Topological Quantum Reservoir Computing (TQRC), which proposes to harness the braiding dynamics of Fibonacci anyons as quantum reservoirs. Our comprehensive analysis reveals a fundamental tension: the very properties that make topological systems attractive for quantum computation (unitary evolution and information preservation) fundamentally oppose the Echo State Property (ESP) required for reservoir computing. We demonstrate rigorously that pure unitary TQRC violates the ESP: unitary evolution preserves distances in Hilbert space, preventing the fading memory necessary for reservoir computing. On Mackey-Glass time series benchmarks, pure unitary TQRC achieves NRMSE ≈1.0 (equivalent to random guessing). Introducing controlled dissipation recovers functional reservoir dynamics (best NRMSE = 0.44), but at the cost of sacrificing topological protection. Critically, we show that classical Echo State Networks outperform dissipative TQRC by 20×at equivalent state-space dimension (ESN NRMSE = 0.02 vs. TQRC NRMSE = 0.44 for d= 13). We identify four root causes: (1) probability readout constrains states to the simplex, (2) measurement destroys phase information, (3) |·|2 provides weaker nonlinearity than tanh, and (4) structured braid matrices limit state-space utilization. These results constitute a no-go theorem for topological quantum reservoir computing: topological protection and reservoir computing functionality represent fundamentally competing requirements. This finding provides essential guidance for the quantum machine learning community, establishing that topological protection should not be pursued as a route to quantum reservoir computing advantage. Index Terms—Topological quantum computing, Fibonacci anyons, reservoir computing, echo state property, quantum machine learning, negative results
Abstract—Reservoir computing exploits high-dimensional nonlinear dynamics to solve temporal prediction tasks with minimal training cost. We investigate Topological Quantum Reservoir Computing (TQRC), which proposes to harness the braiding dynamics of Fibonacci anyons as quantum reservoirs. Our comprehensive analysis reveals a fundamental tension: the very properties that make topological systems attractive for quantum computation (unitary evolution and information preservation) fundamentally oppose the Echo State Property (ESP) required for reservoir computing. We demonstrate rigorously that pure unitary TQRC violates the ESP: unitary evolution preserves distances in Hilbert space, preventing the fading memory necessary for reservoir computing. On Mackey-Glass time series benchmarks, pure unitary TQRC achieves NRMSE ≈1.0 (equivalent to random guessing). Introducing controlled dissipation recovers functional reservoir dynamics (best NRMSE = 0.44), but at the cost of sacrificing topological protection. Critically, we show that classical Echo State Networks outperform dissipative TQRC by 20×at equivalent state-space dimension (ESN NRMSE = 0.02 vs. TQRC NRMSE = 0.44 for d= 13). We identify four root causes: (1) probability readout constrains states to the simplex, (2) measurement destroys phase information, (3) |·|2 provides weaker nonlinearity than tanh, and (4) structured braid matrices limit state-space utilization. These results constitute a no-go theorem for topological quantum reservoir computing: topological protection and reservoir computing functionality represent fundamentally competing requirements. This finding provides essential guidance for the quantum machine learning community, establishing that topological protection should not be pursued as a route to quantum reservoir computing advantage. Index Terms—Topological quantum computing, Fibonacci anyons, reservoir computing, echo state property, quantum machine learning, negative results
Reservoir computing exploits high-dimensional nonlinear dynamics to solve temporal prediction tasks with minimal training cost. We investigate Topological Quantum Reservoir Computing (TQRC), which proposes to harness the braiding dynamics of Fibonacci anyons as quantum reservoirs. Our comprehensive analysis reveals a fundamental tension: the very properties that make topological systems attractive for quantum computation (unitary evolution and information preservation) fundamentally oppose the Echo State Property (ESP) required for reservoir computing. We demonstrate rigorously that pure unitary TQRC violates the ESP: unitary evolution preserves distances in Hilbert space, preventing the fading memory necessary for reservoir computing. On Mackey-Glass time series benchmarks, pure unitary TQRC achieves NRMSE ≈ 1.0 (equivalent to random guessing). Introducing controlled dissipation recovers functional reservoir dynamics (best NRMSE = 0.44), but at the cost of sacrificing topological protection. Critically, we show that classical Echo State Networks outperform dissipative TQRC by 20× at equivalent state-space dimension (ESN NRMSE = 0.02 vs. TQRC NRMSE = 0.44 for d = 13). We identify four root causes: (1) probability readout constrains states to the simplex, (2) measurement destroys phase information, (3) | • | 2 provides weaker nonlinearity than tanh, and (4) structured braid matrices limit state-space utilization. These results constitute a no-go theorem for topological quantum reservoir computing: topological protection and reservoir computing functionality represent fundamentally competing requirements. This finding provides essential guidance for the quantum machine learning community, establishing that topological protection should not be pursued as a route to quantum reservoir computing advantage.
Quantum reservoir computing (QRC) provides a hardware-efficient paradigm for temporal information processing on near-term quantum devices. Despite rapid experimental progress, a rigorous understanding of the structural conditions required for its scalable quantum-enhanced performance remains lacking. Here, we develop a theoretical framework in Pauli-Liouville space that provides a unified analytical treatment of the echo state property (ESP), nonlinear expressive power, and quantum resources. We first analyze the widely used qubit-resetting scheme and establish that quantum magic generated by reservoir dynamics is a necessary condition for effective computation, a requirement more fundamental than ESP. However, we prove that this architecture faces inherent expressivity limitations: all nonlinear processing originates exclusively from the classical encoding map, imposing an unavoidable trade-off between nonlinearity and memory capacity. To circumvent this structural bottleneck, we rigorously analyze Hamiltonian encoding, in which temporal inputs are embedded directly into the continuous dynamics generator. We show that the ESP is natively guaranteed by the Liouvillian spectral gap, decoupling it from quantum magic. Crucially, for any non-trivial drive Hamiltonian, the discrete-time update map exhibits a transcendental, infinite-order nonlinear dependence on the instantaneous input. Moreover, the intrinsic non-commutativity of the open-system generators governs the temporal coupling of these nonlinearities, producing highly non-separable processing of the input history. Our results establish a rigorous theoretical hierarchy of QRC architectures and provide prescriptive design principles for experiments targeting genuine quantum advantages in temporal processing.
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.
Quantum Reservoir Computing (QRC) exploits the rich dynamics of quantum many-body systems to process time-dependent information with high-dimensional state spaces. While neutral atom arrays offer a scalable platform for this paradigm, realizing intrinsic temporal memory without relying on external classical buffering requires precise control over the relaxation dynamics of the system. We address the necessity of specific non-unitary dynamics for enforcing fading memory while overcoming the lack of separability. This study simulates and empirically identifies the specific dynamical regimes required to maximize the computational capacity of the reservoir, addressing the amount of dissipation, the effectiveness of lying at the edge of quantum chaos, and that of time-multiplexing compared to the scaling of the physical size of the system. Here we show that controlled dissipation is strictly necessary to induce echo state property, fading memory, and separability, in neutral atom arrays. Computational performance increases at the edge of quantum chaos. The counter-intuitive residual memory provided by the unital phase damping channel is justified by introducing a model based on pure outputs. The consequent implementation enables the solution of complex non-linear tasks, such as the Mackey-Glass time series, with as few as N=5 atoms. We establish a rigorous framework for engineering dissipative quantum reservoirs required for intrinsic temporal processing on near-term quantum devices.
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.