Beyond the Classical Ceiling: Multi-Layer Fully-Connected Variational Quantum Circuits

Standard Variational Quantum Circuits (VQCs) struggle to scale to high-dimensional data due to the "curse of dimensionality," which manifests as exponential simulation costs $mathcal{O}(2^d$) and untrainable Barren Plateaus. Existing solutions often bypass this by relying on classical neural networks for feature compression, obscuring the true quantum capability. In this work, we propose the Multi-Layer Fully-Connected VQC (FC-VQC), a modular architecture that performs end-to-end quantum learning without trainable classical encoders. By restricting local Hilbert space dimensions while enabling global feature interaction via structured block mixing, our framework achieves linear scalability mathcal{O}(d). We empirically validate this approach on standard benchmarks and a high-dimensional industrial task: 300-asset Option Portfolio Pricing. In this regime, the FC-VQC breaks the "Classical Ceiling," outperforming state-of-the-art Gradient Boosting baselines (XGBoost/CatBoost) while exhibiting approx 17times greater parameter efficiency than Deep Neural Networks. These results provide concrete evidence that pure, modular quantum architectures can effectively learn industrial-scale feature spaces that are intractable for monolithic ansatzes.