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.
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.
Quantum reservoir computing and its special case, quantum extreme learning, are powerful tools for predicting classical discrete time-series with quantum devices. Forecasting continuous signals, however, requires careful discretization as oversampling artificially boosts short-term accuracy but fails over realistic intervals, while undersampling captures too few features and yields poor predictions. Here, we experimentally generate four continuous time-series signals from a chaotic electronic circuit for forecasting with quantum extreme learning. Since simplified circuit models do not fully capture real behaviour, it is unclear whether algorithms that predict simulated time-series also work for experimental signals. We address discretization via two approaches: (i) sampling local peaks/troughs; and (ii) uniform sampling at the autocorrelation timescale. The former captures resonant behaviour, while the latter fully captures chaotic features as well as allowing the reconstruction of chaotic attractors. Our algorithm achieves high forecasting accuracy for both simulated and experimental signals, demonstrating its power for continuous signal processing on near-term quantum simulators, and remains robust against moderate decoherence.
Abstract In the current Noisy Intermediate Scale Quantum (NISQ) era, the presence of noise deteriorates the performance of quantum computing algorithms. Quantum reservoir computing (QRC) is a type of quantum machine learning algorithm, which, however, can benefit from different types of tuned noise. In this paper, we analyze how finite sampling noise affects the chaotic time series prediction of the gate-based QRC and recurrence-free quantum reservoir computing (RF-QRC) models. First, we examine RF-QRC and show that, even without a recurrent loop, it contains temporal information about previous reservoir states using leaky integrated neurons. This makes RF-QRC different from quantum extreme learning machines (QELM). Second, we show that finite sampling noise degrades the prediction capabilities of both QRC and RF-QRC while affecting QRC more due to the propagation of noise. Third, we optimize the training of the finite-sampled quantum reservoir computing framework using two methods: (a) singular value decomposition (SVD) applied to the data matrix containing noisy reservoir activation states and (b) data-filtering techniques to remove the high frequencies from the noisy reservoir activation states. We show that denoising reservoir activation states improves the signal-to-noise ratios with smaller training loss. Finally, we demonstrate that the training and denoising of the noisy reservoir activation signals in RF-QRC are highly parallelizable on multiple quantum processing units (QPUs) as compared to the QRC architecture with recurrent connections. The analyses are numerically showcased on prototypical chaotic dynamical systems with relevance to turbulence. This work opens opportunities for using quantum reservoir computing with finite samples for time series forecasting on near-term quantum hardware.
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.
The prediction of complex dynamics remains an open problem across many domains of physics, where nonlinearities and multiscale interactions severely limit the reliability of conventional forecasting methods. Quantum Reservoir Computing has emerged as a promising paradigm for information processing by exploiting the nonlinear dynamical evolution of quantum systems to generate expressive feature representations of input signals. Here, we introduce a hybrid quantum-classical reservoir architecture capable of handling multivariate time series through quantum evolution combined with classical memory enhancement. Our model employs a five-qubit transverse-field Ising Hamiltonian with input-modulated dynamics and temporal multiplexing. We apply this framework to two paradigmatic models of chaotic behavior in fluid dynamics, where multiscale dynamics and nonlinearities play a dominant role: a low-dimensional truncation of the two-dimensional Navier-Stokes equations and the Lorenz-63 system. By systematically scanning the quantum system's parameter space, we identify regions that maximize forecasting performance. The observed robustness and reliable performances for both dynamical systems suggest that this hybrid quantum approach offers a flexible platform for modeling complex nonlinear time series.
In chaotic dynamical systems, extreme events manifest in time series as unpredictable large-amplitude peaks. Although deterministic, extreme events appear seemingly randomly, which makes their forecasting difficult. By learning the dynamics from observables (data), reservoir computers can time accurately predict extreme events and chaotic dynamics, but they may require many degrees of freedom (large reservoirs). In this paper, by exploiting quantum-computer ansätze and entanglement, we design reservoir computers with compact reservoirs and accurate prediction capabilities. First, we propose the recurrence-free quantum reservoir computer (RF-QRC) architecture. By developing quantum feature maps and removing recurrent connections, the RF-QRC has quantum circuits with smaller depths. This allows the RF-QRC to scale well with higher-dimensional chaotic systems, which makes it suitable for hardware implementation. Second, we forecast the temporal chaotic dynamics and their long-term statistics of low- and higher-dimensional dynamical systems. We find that RF-QRC requires smaller reservoirs than classical reservoir computers for higher-dimensional systems and the same predictability. Third, we apply the RF-QRC to the time prediction of extreme events in a model of a turbulent shear flow with turbulent bursts. We find that the RF-QRC has longer predictability than the classical reservoir computer for extreme events forecasting. The results and analyses indicate that quantum-computer ansätze offers nonlinear expressivity and computational scalability, which are useful for forecasting chaotic dynamics and extreme events. This work opens new opportunities for using quantum machine learning on near-term quantum computers. Published by the American Physical Society 2024