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.
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.
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 has emerged as a promising paradigm for harnessing quantum systems to process temporal data efficiently by bypassing the costly training of gradient-based learning methods. Here, we demonstrate the capability of this approach to predict and characterize chaotic dynamics in discrete nonlinear maps, exemplified through the logistic and Hénon maps. While achieving excellent predictive accuracy, we also demonstrate the optimization of training hyperparameters of the quantum reservoir based on the properties of the underlying map, thus paving the way for efficient forecasting with other discrete and continuous time-series data. Using closed-loop prediction of distant future steps, our protocol discriminates between chaotic and nonchaotic phases without prior knowledge of the underlying map or the nature of the time series. Furthermore, the framework exhibits robustness against decoherence when trained and shows insensitivity to reservoir Hamiltonian variations as well as robustness to finite-sampling error. These results highlight quantum reservoir computing as a scalable and noise-resilient tool for modeling complex dynamical systems, with immediate applicability in near-term quantum hardware.
We propose a scheme that can enhance the performance and reduce the computational cost of quantum reservoir computing. Quantum reservoir computing is a computing approach which aims at utilizing the complexity and high dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The suitability of quantum reservoir computing for solving temporal tasks is hindered by the collapse of the quantum system when measurements are made. This leads to the erasure of the memory of the reservoir. Hence, for every output, the entire input signal is needed to reinitialize the reservoir, leading to quadratic time complexity. Another critical issue for the hardware implementation of quantum reservoir computing is the need for an experimentally accessible means of tuning the nonlinearity of the quantum reservoir. We present an approach which addresses both of these issues. We propose artificially restricting the memory of the quantum reservoir by only using a small number inputs to reinitialize the reservoir after measurements are performed. This strongly influences the nonlinearity of the reservoir response due to the influence of the initial reservoir state, while also substantially reducing the number of quantum operations needed to perform time-series prediction tasks due to the linear rather than quadratic time complexity. The reinitialization length therefore provides an experimental accessible means of tuning the nonlinearity of the response of the reservoir, which can lead to significant task-specific performance improvement. We numerically study the linear and quadratic algorithms for a fully connected transverse Ising model and a quantum processor model. Published by the American Physical Society 2024
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.
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.
This paper investigates the application of quantum reservoir computing (QRC) to time series prediction. Classical reservoir computing (RC) utilizes a complex, high-dimensional system – the 'reservoir' – as a non-linear feature extractor, followed by a linear regression model for prediction. QRC extends this concept by leveraging the inherent dynamics of a quantum system as the reservoir. We hypothesize that quantum systems, due to their superposition and entanglement properties, can provide richer and more complex dynamics than classical reservoirs, potentially leading to improved prediction accuracy. This work outlines the theoretical framework for QRC, detailing the setup of a suitable quantum reservoir (e.g., a superconducting qubit array), the measurement process, and the training strategy involving a classical machine learning model. We demonstrate a conceptual approach, focusing on the potential advantages and challenges of employing quantum systems for this task. The core claim is that QRC can achieve superior time series prediction accuracy compared to classical RC methods. Key elements explored include the input signal's influence on the quantum reservoir, the selection of appropriate measurement schemes, and the choice of classical learning algorithms. The paper concludes with a discussion of future research directions and the potential impact of QRC on various time series prediction applications.