Fixed-Reservoir vs Variational Quantum Architectures for Chaotic Dynamics: Benchmarking QRC and QPINN on the Lorenz System

TL;DR

This study compares fixed-reservoir quantum architectures and variational quantum neural networks for chaotic time-series prediction, demonstrating that fixed-reservoir approaches outperform variational methods in accuracy and training speed on the Lorenz system.

Contribution

It provides a systematic benchmarking of QRC and QPINN architectures, highlighting the advantages of fixed-reservoir quantum models in chaotic dynamics prediction.

Findings

QRC achieves 81% lower test MSE than QPINN.

QRC trains approximately 52,000 times faster than QPINN.

QRC maintains low test MSE across multiple chaotic systems.

Abstract

Deploying quantum machine learning on NISQ devices requires architectures where training overhead does not negate computational advantages. We systematically compare two quantum approaches for chaotic time-series prediction on the Lorenz system: a variational Quantum Physics-Informed Neural Network (QPINN) and a Quantum Reservoir Computing (QRC) framework utilizing a fixed transverse-field Ising Hamiltonian. Under matched resources ($4$--$5$ qubits, $2$--$3$ layers), QRC achieves an $81\%$ lower mean-squared error (test MSE $3.2 \pm 0.6$ vs. $47.9 \pm 36.6$ for QPINN) while training $\sim 52,000\times$ faster ($0.2$\,s vs. $\sim 2.4$\,h per seed). Drawing on the classical delay-embedding principle, we formalize a temporal windowing technique within the QRC pipeline that improves attractor reconstruction by providing bounded, structured input history. Analysis reveals that QPINN instability stems from capacity limitations and competing loss terms rather than barren plateaus; gradient norms remained large ($10^3$--$10^4$), ruling out exponential suppression at this scale. These failure modes are absent by construction in the non-variational QRC approach. We validate robustness across three canonical systems (Lorenz, R\"{o}ssler, and Lorenz-96), where QRC consistently achieves low test MSE ($3.1 \pm 0.6$, $1.8 \pm 0.1$, and $12.4 \pm 0.6$, respectively) with sub-second training. Our findings suggest the fixed-reservoir architecture is a primary driver of QRC's advantage at these scales, warranting further investigation at larger qubit counts and on hardware where quantum-specific advantages are expected to emerge.