Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting

Krishna Bhatia; Harsh; Shalini Devendrababu

quant-phAug 24, 2026

Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting

Authors: Krishna Bhatia, Harsh, Shalini Devendrababu

Organizations: QuantumAI Lab, Fractal Analytics, Mumbai, India · Department of Physics, Indian Institute of Technology, Jodhpur, India

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: Dataset overview figures

Panel of Figure 2 — Figure 2: Workflow of the proposed QRC+PIC framework. A quantum reservoir generates rollout predictions that are then refined by a physics-informed corrector.

Model	RMSE $\downarrow$	NRMSE $\downarrow$	Physics residual $\downarrow$
Ridge-AR	1.1777 $\pm$ 0.0000	1.0100 $\pm$ 0.0000	0.6331 $\pm$ 0.0000
QRC+PIC	1.1897 $\pm$ 0.0027	1.0204 $\pm$ 0.0024	0.7035 $\pm$ 0.0498
QRC	1.1971 $\pm$ 0.0044	1.0268 $\pm$ 0.0039	0.7830 $\pm$ 0.0367
Persistence	1.2606 $\pm$ 0.0000	1.0807 $\pm$ 0.0000	0.0715 $\pm$ 0.0000
ESN+PIC	1.5009 $\pm$ 0.0604	1.2871 $\pm$ 0.0516	2.8606 $\pm$ 0.4891
PI-MLP	1.6390 $\pm$ 0.1326	1.4057 $\pm$ 0.1143	2.3110 $\pm$ 0.5685

Table 1: Main KS results (five seeds, test trajectories only)

Panel of Figure 3 — Figure 3: Primary KS figures.

Model	RMSE $\downarrow$	NRMSE $\downarrow$	Physics residual $\downarrow$
Ridge-AR	0.0644 $\pm$ 0.0000	0.2025 $\pm$ 0.0000	0.0298 $\pm$ 0.0000
Persistence	0.1887 $\pm$ 0.0000	0.5836 $\pm$ 0.0000	0.0782 $\pm$ 0.0000
QRC+PIC	0.3458 $\pm$ 0.0010	1.0647 $\pm$ 0.0031	15.0128 $\pm$ 3.4132
MLP-AR	0.3573 $\pm$ 0.0030	1.1164 $\pm$ 0.0089	1.2029 $\pm$ 0.0411
QRC	0.3578 $\pm$ 0.0040	1.1025 $\pm$ 0.0130	177.5869 $\pm$ 35.5570
PI-MLP	0.3861 $\pm$ 0.0436	1.2114 $\pm$ 0.1429	1.3334 $\pm$ 0.1445

Table 2: Auxiliary Burgers results (five seeds, test trajectories only).

Figure 4: Aggregate test metrics with seed-wise error bars for Burgers

Figure 5: KS ablation overview, including lag depth, POD rank, horizon, and physics-loss sensitivity.

Quantum Reservoir Computing

Quantum reservoir computing uses quantum dynamics to transform time-dependent inputs into features for prediction and classification.

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A Quantum Reservoir Architecture for Chaotic Forecasting and a Test of Whether Its High Dimension Helps

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Texas A&M University, College Station, TX, USA

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Open paper AskPDF arXiv

Quantum reservoir computing uses a fixed quantum circuit as a feature generator and trains only a simple linear readout on top of it. This makes it cheap to train and free of the optimisation problems that affect many quantum machine-learning models. A natural worry is that the very large feature space the circuit produces might inflate apparent performance without adding anything real. This paper provides two things. First, it gives a complete, reproducible recipe for one such reservoir applied to forecasting chaotic systems, including how data is fed in, how the circuit is built, and how the readout is trained. Second, it gives a way to tell whether the reservoir's high dimension is actually doing useful work. We grow the size of the prediction problem and the size of the quantum reservoir together, so that extra capacity cannot be the explanation for any improvement, and we track a single stability number that measures how well behaved the readout fit is. On two chaotic test systems, a spatiotemporal chain and a shallow-water fluid model, the quantum reservoir keeps a flat, stable error as both sizes grow, while a matched classical reservoir does not. We report where the classical baseline is in fact stronger, so the comparison is honest. The result is a clean specification plus a diagnostic that other groups can apply to any reservoir whose features have a known scale.

Abstract

Quantum Reservoir Computing

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