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

Variational Quantum Circuits (VQC) are promising models for quantum machine learning, but standard monolithic architectures face an expressivity--trainability dilemma: small circuits can be under-parameterized, while larger circuits are difficult to simulate and optimize. We propose Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC), a modular framework that decomposes high-dimensional inputs into fixed-size local VQC blocks connected by deterministic block-mixing rules. This design keeps each quantum computation local while allowing the number of trainable quantum parameters to scale linearly with input dimension. We evaluate FC-VQC across tabular regression, tabular classification, and spatio-temporal BSDE/PDE approximation. Across the evaluated tasks, FC-VQC improves over monolithic VQC baselines and achieves competitive or improved performance relative to structure-matched deep neural network (DNN) baselines, while using substantially fewer trainable parameters.