Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to barren plateaus and sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided hypernetwork framework that significantly improves the robustness and scalability of VQC. 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. Grounded in 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 TensorHyper-VQC consistently achieves superior performance and robust noise tolerance, including hardware-level validation on a 156-qubit IBM Heron processor. These results position TensorHyper-VQC as a scalable and noise-resilient framework for advancing practical quantum machine learning on near-term devices.

翻译：变分量子计算（VQC）面临着根本性的可扩展性障碍，主要源于贫瘠高原现象和对量子噪声的敏感性。为应对这些挑战，我们提出了TensorHyper-VQC，一种新颖的张量链（TT）引导的超网络框架，该框架显著提升了VQC的鲁棒性和可扩展性。我们的框架将量子电路参数的生成完全委托给一个经典的TT网络，从而有效地将优化过程与量子硬件解耦。这种创新的参数化方法缓解了梯度消失问题，通过结构化的低秩表示增强了噪声鲁棒性，并促进了高效的梯度传播。基于神经正切核与统计学习理论的严格理论分析，为模型的近似能力、优化稳定性和泛化性能提供了坚实的理论保证。在量子点分类、Max-Cut优化和分子量子模拟任务上的大量实证结果表明，TensorHyper-VQC始终能取得更优的性能和强大的噪声容忍度，包括在156量子比特的IBM Heron处理器上进行的硬件级验证。这些成果使TensorHyper-VQC成为一个可扩展且噪声鲁棒的框架，有望推动近期实用量子机器学习的发展。