Trainability-Oriented Hybrid Quantum Regression via Geometric Preconditioning and Curriculum Optimization

• URL: http://arxiv.org/abs/2601.11942v1
• Date: Sat, 17 Jan 2026 07:32:18 GMT
• Title: Trainability-Oriented Hybrid Quantum Regression via Geometric Preconditioning and Curriculum Optimization
• Authors: Qingyu Meng, Yangshuai Wang,
• Abstract summary: Quantum neural networks (QNNs) have attracted growing interest for scientific machine learning.<n>In regression settings they often suffer from limited trainability under noisy gradients and ill-conditioned optimization.<n>We propose a hybrid quantum-classical regression framework designed to mitigate these bottlenecks.
• Score: 0.6445605125467574
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

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