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arXiv:2602.16623

Scalable Quantum Machine Learning via Multi-layer Fully-Connected Variational Quantum Circuits

Howard Su, Chen-Yu Liu, Samuel Yen-Chi Chen, Kuan-Cheng Chen, Huan-Hsin Tseng

quant-phSubmitted Feb 18, 2026• Announced Feb 19, 2026• 0 citations• Revised Sep 28, 2026 (v3)
v1 · Feb 18, 2026v2 · May 10, 2026v3 · Sep 28, 2026
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Abstract

Variational quantum circuits (VQCs) face an expressivity-trainability dilemma and scalability challenges. We propose Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC), a general-purpose quantum machine learning framework that connects local VQC blocks through measurement, deterministic parameter-free routing, and re-encoding. All trainable model parameters reside within the quantum blocks, without trainable classical neural components. We study fully connected, sliding-window, and parallel block mixing and analyze computational costs, conditional error propagation, and block information exchange. Using classical simulation, we evaluate tabular regression and classification, with our main comparison addressing spatio-temporal function approximation for the Black--Scholes, Burgers, and time-dependent oscillatory PDEs with up to $144$ spatial dimensions. Comparisons include neural-network, explicit angle-feature, tensor-network, and gradient-boosted-tree baselines. The results show that FC-VQC achieves the lowest trajectory relative MAE for all PDEs at the higher dimensions $d\in\{81,144\}$. Gradient-dynamics and depolarizing-noise experiments provide complementary empirical diagnostics of trainability and preliminary noise sensitivity.

Comments
54 pages, 11 figures, 29 tables. Main text: 9 pages

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