TensoMeta-VQC: A Tensor-Train-Guided Meta-Learning Framework for Robust and Scalable Variational Quantum Computing

Abstract: Variational Quantum Computing (VQC) faces fundamental barriers in scalability, primarily due to barren plateaus and quantum noise sensitivity. To address these challenges, we introduce TensoMeta-VQC, a novel tensor-train (TT)-guided meta-learning framework designed to improve the robustness and scalability of VQC significantly. Our framework fully delegates the generation of quantum circuit parameters to a classical TT network, effectively decoupling optimization from quantum hardware. This innovative parameterization mitigates gradient vanishing, enhances noise resilience through structured low-rank representations, and facilitates efficient gradient propagation. Based on Neural Tangent Kernel and statistical learning theory, our rigorous theoretical analyses establish strong guarantees on approximation capability, optimization stability, and generalization performance. Extensive empirical results across quantum dot classification, Max-Cut optimization, and molecular quantum simulation tasks demonstrate that TensoMeta-VQC consistently achieves superior performance and robust noise tolerance, establishing it as a principled pathway toward practical and scalable VQC on near-term quantum devices.