Reservoir computing promises a fast method for handling large amounts of temporal data. This hinges on constructing a good reservoir--a dynamical system capable of transforming inputs into a high-dimensional representation while remembering properties of earlier data. In this work, we introduce a reservoir based on recurrent quantum feature maps where a fixed quantum circuit is reused to encode both current inputs and a classical feedback signal derived from previous outputs. We evaluate the model on the Mackey-Glass time-series prediction task using our recently introduced CP feature map, and find that it achieves lower mean squared error than standard classical baselines, including echo state networks and multilayer perceptrons, while maintaining compact circuit depth and qubit requirements. We further analyze memory capacity and show that the model effectively retains temporal information, consistent with its forecasting accuracy. Finally, we study the impact of realistic noise and find that performance is robust to several noise channels but remains sensitive to two-qubit gate errors, identifying a key limitation for near-term implementations.
Reservoir computing promises a fast method for handling large amounts of temporal data. This hinges on constructing a good reservoir--a dynamical system capable of transforming inputs into a high-dimensional representation while remembering properties of earlier data. In this work, we introduce a reservoir based on recurrent quantum feature maps where a fixed quantum circuit is reused to encode both current inputs and a classical feedback signal derived from previous outputs. We evaluate the model on the Mackey-Glass time-series prediction task using our recently introduced CP feature map, and find that it achieves lower mean squared error than standard classical baselines, including echo state networks and multilayer perceptrons, while maintaining compact circuit depth and qubit requirements. We further analyze memory capacity and show that the model effectively retains temporal information, consistent with its forecasting accuracy. Finally, we study the impact of realistic noise and find that performance is robust to several noise channels but remains sensitive to two-qubit gate errors, identifying a key limitation for near-term implementations.
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.
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.
Forecasting neural activity from short recordings remains a fundamental challenge. Reservoir computing may offer an efficient paradigm for temporal prediction, however classical reservoirs typically underperform in small-data regimes. Here we investigate whether quantum reservoir computing (QRC) can help overcome this limitation. Building on recent advances, we introduce a quantum reservoir based on a transverse-field Ising model, combined with heterogeneous quantum measurements and polynomial ridge regression. On a standard benchmark task, results show that the quantum reservoir outperforms a classical counterpart overall, with prediction accuracy strongly dependent on reservoir parameters. We further demonstrate feasibility by running the same task on quantum hardware. To assess performance on biological signals, we evaluate QRC on simulated human electroencephalography (EEG) data with a parallel reservoir architecture. On this challenging task, the tested quantum reservoir did not match the performance of the classical one, but it produced stable, convergent predictions. This is a meaningful first step toward forecasting of biologically realistic neural data using a quantum reservoir. Overall, our findings indicate that although current quantum hardware and parallel reservoir architectures do not yet surpass classical methods on complex neural signals, QRC can be executed on near-term devices and does converge with realistic EEG-like data. This work establishes a practical baseline for future algorithmic and hardware developments aimed at clinical time-series forecasting with quantum systems.
Reservoir computing is a framework which is primarily used for temporal information processing, using the intrinsic dynamics of an underlying physical system. The framework, in a quantum setup, is implemented using ergodic dynamics associated with Hamiltonian models. The computational power of the reservoir is closely tied to this underlying dynamical nature, and to probe this further, we study the effectiveness of a reservoir that is made using structured brickwall circuits built from two-qubit gates. Here, the global ergodic nature of the circuit model results from the said arrangement, which has an important role in extracting useful performance with a minimal setup that is independent of an associated Hamiltonian. We focus on the nature of the gates used in this setup and evaluate the resulting reservoir performance, correlating the same with known results on the dynamical nature of the circuit in question. As a baseline, we analyse brickwall circuits composed of Haar-random two-qubit gates, before moving on to dual-unitaries, where tunable ergodic properties allow us to systematically investigate its relationship with reservoir performance. We further consider a class of non-random two-qubit gates obeying a specific solvability condition, wherein the associated dynamics surpasses the equivalent circuit made up of two qubit Haar random unitaries in terms of randomness. Finally, we consider examples of Krylov space analytics, which allow for a reliable prediction of effective circuit reservoirs for sufficient task performance. Using the introduced metrics we validate the reservoir for time-series prediction using standard synthetic data sets to evaluate the fading memory capacity and accuracy for prediction tasks. Our results indicate that structured quantum circuits would serve as effective models that yield better and efficient task performance in reservoir computing applications.
Reservoir computing (RC) has demonstrated significant promise in time series forecasting, particularly for chaotic systems. However, a critical limitation of traditional RC approaches is their vulnerability to non-Gaussian noise, a common characteristic of real-world time series data. This paper proposes a novel framework, Quantum Reservoir Computing (QRC), designed to address this challenge. QRC utilizes a quantum reservoir – a randomly initialized quantum circuit – to leverage the inherent noise robustness of quantum mechanics, specifically quantum entanglement and superposition. The quantum reservoir is coupled with a variational quantum circuit for output mapping. We demonstrate that this approach significantly improves forecasting accuracy when dealing with non-Gaussian noise, offering a pathway to more reliable RC implementations. The core claim of this work is that reservoir computing struggles with non-Gaussian noise, which is prevalent in many time series datasets. The core mechanism involves extending reservoir computing using a quantum reservoir – a randomly initialized quantum circuit – that is inherently robust to non-Gaussian noise due to quantum entanglement and superposition, combined with a variational quantum circuit for output mapping. The methodology incorporates a mapping function to translate quantum states into time series predictions, and the variational quantum circuit is trained to minimize the error between predicted and actual time series values. We explore the theoretical underpinnings of this method and discuss its potential for various time series forecasting applications.
Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to generate expressive, nonlinear signals that are efficiently learned with a single linear output layer. We address the need for quantum reservoir tuning with a novel and generally applicable approach to quantum circuit parameterization, in which tunable noise models are programmed to the quantum reservoir circuit to be fully controlled for effective optimization. Our systematic approach also involves reductions in quantum reservoir circuits in the number of qubits and entanglement scheme complexity. We show that with only a single noise model and small memory capacities, excellent simulation results were obtained on nonlinear benchmarks that include the Mackey-Glass system for 100 steps ahead in the challenging chaotic regime.