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arXiv:2505.06799 · Communications Physics

Predicting chaotic dynamics on NISQ hardware with quantum reservoir networks

Erik Connerty, Ethan N. Evans, Gerasimos Angelatos, Vignesh Narayanan

Published May 4, 2026• 0 citations
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Abstract

Abstract Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Here, we propose a quantum reservoir network (QRN) algorithm for prediction and reconstruction of dynamical systems with current quantum hardware. This is developed from the recent NISQRC framework to imbue quantum circuits with a practical fading memory, and we demonstrate its effectiveness on an IBM quantum processor. We apply classical control-theoretic response analysis to characterize the QRN, emphasizing its rich nonlinear dynamics and memory, as well as its ability to be fine-tuned with sparsity and re-uploading blocks. Noisy and noiseless simulations, as well as IBM hardware experiments, demonstrate the capability of our QRN to reconstruct unknown latent variables of the Lorenz system at future timesteps. Our results show that the QRN can operate with persistent memory for over 100 times longer than the median $${{{{\mathcal{T}}}}}_{1}$$ T 1 and $${{{{\mathcal{T}}}}}_{2}$$ T 2 of the QPU, achieving state-of-the-art time-series performance on IBM hardware.

DOI
10.1038/s42005-026-02652-1

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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.
Abstract Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Quantum computers, which replace bits with qubits, hold the potential to overcome these limitations and increase processing power beyond classical systems. Despite this, integrating quantum computing with NNs remains largely unrealized due to challenges such as noise, decoherence, and high error rates in current quantum hardware. In this work, we propose a novel quantum circuit design and implementation algorithm that results in a dynamic quantum echo-state network (QESN). We apply classical control-theoretic response analysis to characterize the QESN, emphasizing its rich nonlinear dynamics and memory. We demonstrate that despite incorporating sparser gate weights for computational efficiency, the QESN preserves its rich dynamicity while enabling system trajectory predictions on any digital quantum computer that can implement a universal gate set. We validate our approach through a comprehensive demonstration of QESNs functioning as quantum observers, applied in both high-fidelity simulations and hardware experiments utilizing data from a prototypical chaotic Lorenz system. Our results show that the QESN can predict long time-series with persistent memory, running over 100 times longer than the median T1 and T2 of the IBM Marrakesh QPU, achieving state-of-the-art performance on superconducting hardware.
Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.
Interest in using quantum computers for the purpose of predicting chaotic partial differential equations (PDEs) has been growing with the advent of newer low-error quantum computers and robust simulation tools. In this paper, we present a method that utilizes a quantum reservoir network (QRN) to predict latent space representations of the high-dimensional chaotic 1-D Kuramoto-Sivashinksy (KS) system. This hybrid approach takes advantage of advancements in classical machine learning (ML) through the use of a classical autoencoder as well as techniques from quantum metrology through the use of a unitary that creates metrologically-useful states. Through rigorous simulation and analysis, we show that the proposed method outperforms alternative QRN implementations without this metrologically-useful state preparation, and also show better performance than classical echo-state networks when weight regularization is not used. Finally, we bring to light potential issues that can arise when using autoencoders within QRC pipelines.
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.
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.