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This study addresses critical trainability bottlenecks in quantum neural networks by introducing a hybrid framework that combines geometric preconditioning with curriculum optimization. The approach demonstrates improved convergence and stability on regression benchmarks, particularly in data-limited regimes where pure quantum models often struggle. By reshaping input representations and adapting training strategies, the method offers a practical pathway for stabilizing variational quantum circuits in scientific machine learning applications.
Trainability-Oriented Hybrid Quantum Regression via Geometric Preconditioning and Curriculum Optimization
arXiv:2601.11942v4 Announce Type: replace-cross Abstract: Quantum neural networks (QNNs) have attracted growing interest for scientific machine learning, yet in regression settings they often suffer from limited trainability under noisy gradients and ill-conditioned optimization. We propose a hybrid quantum--classical regression framework designed to mitigate these bottlenecks. Our model prepends a lightweight classical embedding that acts as a learnable geometric preconditioner, reshaping the input representation to better condition a downstream variational quantum circuit. Building on this architecture, we introduce a curriculum optimization protocol that progressively increases circuit depth and transitions from SPSA-based stochastic exploration to Adam-based gradient fine-tuning. We evaluate the approach on PDE-informed regression benchmarks and standard regression datasets under a fixed training budget in a simulator setting. Empirically, the proposed framework consistently improves over pure QNN baselines and yields more stable convergence in data-limited regimes. We further observe reduced structured errors that are visually correlated with oscillatory components on several scientific benchmarks, suggesting that geometric preconditioning combined with curriculum training is a practical approach for stabilizing quantum regression.
Abstract:Quantum neural networks (QNNs) have attracted growing interest for scientific machine learning, yet in regression settings they often suffer from limited trainability under noisy gradients and ill-conditioned optimization. We propose a hybrid quantum--classical regression framework designed to mitigate these bottlenecks. Our model prepends a lightweight classical embedding that acts as a learnable geometric preconditioner, reshaping the input representation to better condition a downstream variational quantum circuit. Building on this architecture, we introduce a curriculum optimization protocol that progressively increases circuit depth and transitions from SPSA-based stochastic exploration to Adam-based gradient fine-tuning. We evaluate the approach on PDE-informed regression benchmarks and standard regression datasets under a fixed training budget in a simulator setting. Empirically, the proposed framework consistently improves over pure QNN baselines and yields more stable convergence in data-limited regimes. We further observe reduced structured errors that are visually correlated with oscillatory components on several scientific benchmarks, suggesting that geometric preconditioning combined with curriculum training is a practical approach for stabilizing quantum regression.
Machine Learning (cs.LG); Quantum Physics (quant-ph)
arXiv:2601.11942 [cs.LG]
(or arXiv:2601.11942v4 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2601.11942 Focus to learn more arXiv-issued DOI via DataCite
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