Trainability-Oriented Hybrid Quantum Regression via Geometric Preconditioning and Curriculum Optimization
cs.LG, quant-ph
Submitted: 2026-01-17
Updated: 2026-09-11
License: http://creativecommons.org/publicdomain/zero/1.0/
The gist: 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
Terminology
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.
Sources
- Quantum Neural Ordinary and Partial Differential Equations
- Contextuality and inductive bias in quantum machine learning
- Explainable quantum regression algorithm with encoded data structure
- Multiple Embeddings for Quantum Machine Learning
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