We study a hybrid proposal--correction architecture for reduced-order PDE forecasting in which a pure-state quantum reservoir computer (QRC) predicts latent coefficient dynamics and a PINN-based physics-informed corrector (PIC) refines local rollout windows. The method is evaluated on Burgers and Kuramoto--Sivashinsky (KS), with KS as the primary chaotic benchmark. On KS, QRC+PIC consistently improves over QRC alone in RMSE, NRMSE, and PDE residual, while Burgers highlights a regime in which simple baselines remain strong. These results suggest that QRC proposals with local physics-informed correction are a viable benchmark-dependent reduced-order forecasting strategy.
Journal reference
Advances in Quantum Neural and Reinforcement Learning, Communications in Computer and Information Science, vol. 3063, Springer Singapore, 2026
Comments
11 pages, 5 figures. Accepted at QNRL@WCCI 2026. To appear in Advances in Quantum Neural and Reinforcement Learning, Communications in Computer and Information Science, vol. 3063, Springer Singapore, 2026
We study a hybrid proposal--correction architecture for reduced-order PDE forecasting in which a pure-state quantum reservoir computer (QRC) predicts latent coefficient dynamics and a PINN-based physics-informed corrector (PIC) refines local rollout windows. The method is evaluated on Burgers and Kuramoto--Sivashinsky (KS), with KS as the primary chaotic benchmark. On KS, QRC+PIC consistently improves over QRC alone in RMSE, NRMSE, and PDE residual, while Burgers highlights a regime in which simple baselines remain strong. These results suggest that QRC proposals with local physics-informed correction are a viable benchmark-dependent reduced-order forecasting strategy.
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.
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.
Quantum reservoir computing (QRC) uses fixed quantum dynamics as a high-dimensional temporal feature map and trains only a lightweight classical readout. QRC is attractive for near-term quantum machine learning, but its performance depends strongly on architecture choices such as input encoding, reservoir depth, entanglement topology, measurement features, state-reset policy, feature construction, and readout regularization. We introduce \method, a simulator-based benchmark that formulates QRC design as constrained black-box architecture search and evaluates whether large language models can act as proposal controllers for this search problem. The benchmark compares five policies under identical evaluation budgets: random search, evolutionary search, Bayesian/TPE optimization, a feedback-based LLM agent, and \hybrid, which combines LLM proposals with memory, mutation, crossover, duplicate avoidance, and exploration. On NARMA10, Mackey-Glass forecasting, and temporal parity, \hybrid{} is the most consistent policy: it ranks first on NARMA10 and temporal parity and second on Mackey-Glass, narrowly behind evolutionary search. Under a 25-evaluation budget and three seeds, \hybrid{} improves over random search on all tasks, including a 23.6\% relative reduction in Mackey-Glass error. The results do not show that LLMs are universal QRC optimizers; rather, they show that generative models can be useful high-level controllers when embedded inside validated, reproducible hybrid search loops.
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 provides an alternative to recurrent neural networks by overcoming the common problems of backpropagation through time and by training only a simple readout layer. The emerging field of quantum computing offers a new computing paradigm that promises to enhance learning through richer feature representations. In this work, we investigate quantum reservoir computing for time-series forecasting. We explore and benchmark four different architectures that combine single or multiple (distributed) reservoirs with single or multiple (distributed) ridge-regression readout layers. We evaluate these architectures using ideal and hardware-informed noisy simulations, and include both hybrid and fully quantum variants, with classical reservoir counterparts serving as a baseline. The results indicate that quantum-enhanced configurations consistently improve forecasting accuracy by reducing the mean absolute error (MAE) and the root mean squared error (RMSE) up to 78.8% and 72.3%, respectively, while distributed architectures effectively enable scaling by utilizing multiple quantum resources in a hardware-agnostic manner. These findings support distributed quantum reservoir computing as a promising, modular approach for forecasting on the quantum platforms of the noisy intermediate-scale quantum (NISQ) era.
Motivated by the perspective of advanced time-series prediction and exploitation of Quantum Reservoir Computing (QRC), we explored the design and implementation of a Hybrid Photonic-Quantum Reservoir Computing (HPQRC) paradigm. It brings together the high-speed parallelism of photonic systems with the quantum reservoir's capacity of modeling complex, nonlinear dynamics, and hence acts as a powerful tool for performing real-time prediction in resource resource-constrained environment with low latency. We have engineered a solution using this architecture to address issues like computational bottlenecks, energy inefficiency, and sensitivity to noise that are common in existing reservoir computing models. Our simulation results show that HPQRC attains much higher accuracy with lower computational time than both classical and quantum-only models. This model is robust when environments are noisy and scales well across large datasets, and therefore is suitable for application on diverse problems such as financial forecasting, industrial automation, and smart sensor networks. Our results substantiate that HPQRC performs significantly faster than traditional architectures and could be a viable and highly scalable platform for actual edge computing systems. Overall, HPQRC demonstrates significant advancements in time series modeling capabilities. In combination with enhanced predictive accuracy with reduced computational requirements, HPQRC establishes itself as an effective analytical tool for complex dynamic systems that require both precision and processing efficiency.