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.
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.
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.
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
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.
Physical reservoir computing provides a powerful machine learning paradigm that exploits nonlinear physical dynamics for efficient information processing. By incorporating quantum effects, quantum reservoir computing offers superior potential for machine learning applications, as quantum dynamics are exponentially costly to simulate classically. Here, we present a novel quantum reservoir computing approach based on correlated quantum spin systems, exploiting natural quantum many-body interactions to generate reservoir dynamics, thereby circumventing the practical challenges of deep quantum circuits. Our experimental implementation supports nontrivial quantum entanglement and exhibits sufficient dynamical complexity for high-performance machine learning. We achieve state-of-the-art performance in experiments on standard time-series benchmarks, reducing prediction error by 1 to 2 orders of magnitude compared to previous quantum reservoir experiments. In long-term weather forecasting, our 9-spin quantum reservoir delivers greater prediction accuracy than classical reservoirs with thousands of nodes. This represents the first experimental demonstration of quantum machine learning outperforming large-scale classical models on real-world tasks.
The time-index models are a class of time series forecasting models that map time-index features to forecasts in continuous space. Compared to the historical-value models, the time-index models can avoid the effect of data sampling frequency and are usually more expressive. However, the vanilla deep time-index model is weak in modeling the high-frequency components of time series and often requires the introduction of many parameters to enhance the modeling capability. Moreover, the time-index model learns only a mapping relationship and ignores the sequence relationship between temporal features, leading to a weak extrapolation capability in the forecast horizon. In this paper, inspired by the ability of quantum implicit neural representations to model the high-frequency components of signals with fewer parameters, we propose Quantum Time-Index Models with Reservoir (QuantumTime). Specifically, we introduce variational quantum circuits to address the challenge of representing high-frequency components in time series. Then, we introduce a reservoir that empowers QuantumTime with powerful extrapolation capabilities by exploiting the rich dynamical properties of reservoir computing. Ultimately, experiments conducted on chaotic datasets and various real-world datasets demonstrate that QuantumTime achieves highly competitive results compared to the state-of-the-art deep time-index model while reducing training parameters by at least 95%. Our approach provides a paradigm for utilizing potential quantum advantage in practical tasks.
Recent advancements in artificial neural networks have enabled impressive tasks on classical computers, but they demand significant computational resources. While quantum computing offers potential beyond classical systems, the advantages of quantum neural networks (QNNs) remain largely unexplored. In this work, we present and examine a quantum circuit (QC) that implements and aims to improve upon the classical echo-state network (ESN), a type of reservoir-based recurrent neural networks (RNNs), using quantum computers. Typically, ESNs consist of an extremely large reservoir that learns high-dimensional embeddings, enabling prediction of complex system trajectories. Quantum echo-state networks (QESNs) aim to reduce this need for prohibitively large reservoirs by leveraging the unique capabilities of quantum computers, potentially allowing for more efficient and higher performing time-series prediction algorithms. The proposed QESN can be implemented on any digital quantum computer implementing a universal gate set, and does not require any sort of stopping or re-initialization of the circuit, allowing continuous evolution of the quantum state over long time horizons. We conducted simulated QC experiments on the chaotic Lorenz system, both with noisy and noiseless models, to demonstrate the circuit's performance and its potential for execution on noisy intermediate-scale quantum (NISQ) computers.