TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computing

TL;DR

TensorHyper-VQC proposes a tensor-train guided hypernetwork that fully generates VQC parameters on the classical side, decoupling optimization from quantum hardware to combat barren plateaus and noise. Grounded in Neural Tangent Kernel theory, the framework offers provable guarantees on representation, trainability, generalization, and noise robustness, and demonstrates superior performance across quantum-dot classification, Max-Cut optimization, and LiH quantum chemistry tasks, including hardware validation on IBM's 156-qubit Heron. Empirically, it achieves high accuracy with far fewer parameters, shows graceful degradation under noise, and exhibits strong real-device performance without additional mitigation overhead. This approach provides a scalable, hardware-agnostic paradigm for practical quantum machine learning on near-term devices, with broad implications for quantum sensing, optimization, and chemistry simulations.

Abstract

Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to the presence of barren plateaus and its 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.

Figures (3)

• Figure 1: An illustration of the TensorHyper-VQC framework. A classical TT network generates the parameters $\hat{\textbf{w}} = [\alpha^{(1)}_{1:U}, \beta^{(1)}_{1:U}, \gamma^{(1)}_{1:U}, ..., \alpha^{(L)}_{1:U}, \beta^{(L)}_{1:U}, \gamma^{(L)}_{1:U}]^{\top}$ that define the Pauli rotation gates $R_{X}(\alpha^{(l)}_{u}), R_{Y}(\beta^{(l)}_{u}), R_{Z}(\gamma^{(l)}_{u})$ (where $u\in [U], l\in [L]$) in a VQC with $L$ depths and $U$ qubits. The TT-generated parameters are injected into the fixed quantum circuit, which operates solely in inference mode. The loss is computed from quantum measurements, and gradients are backpropagated only through the classical TT-cores. Gaussian noise is injected during training as the input to the TT network. This architecture decouples optimization from quantum hardware, mitigating barren plateaus and improving noise resilience.
• Figure 2: The architecture of variational quantum computing. The classical input data are encoded into quantum states $\vert x_{1} \rangle$, $\vert x_{2} \rangle$, ..., $\vert x_{U} \rangle$ via data encoding (e.g., angle encoding and amplitude encoding). The shaded region denotes $L$ repeated parameterized quantum circuit block, consisting of trainable rotation gates $R_X(\alpha^{(l)}_u)$, $R_{Y}(\beta^{(l)}_{u})$, $R_{Z}(\gamma^{(l)}_{u})$, and entangling layers across quantum channels. These blocks are stacked to increase circuit depth and expressive capacity. Finally, the circuit is measured in the Pauli-Z basis, yielding expectation values $\langle \sigma_{z}^{(1)} \rangle$, $\langle \sigma_{z}^{(2)} \rangle$, ..., $\langle \sigma_{z}^{(U)} \rangle$ that serve as outputs for optimizaiton.
• Figure 3: Comprehensive performance evaluation of TensorHyper-VQC for quantum-dot classification, measured by accuracy on the test dataset. (a) Comparison with standard VQC, MLPHyper-VQC, and TTN+VQC under noiseless conditions, showing faster convergence and higher accuracy; (b) Comparison with classical baselines (ResNet18+LoRA and ResNet50+LoRA), where TensorHyper-VQC achieves superior accuracy with far fewer parameters; (c) Robustness under increasing depolarizing and dephasing noise, maintaining stable performance; (d) Scalability across different qubit counts, with graceful accuracy degradation as system size increases; (e) Comparative analysis under realistic multi-noise conditions, where TensorHyper-VQC outperforms VQC enhanced with LWT, LCF, and REM + ZNE, demonstrating improved trainability and noise resilience; (f) Experimental validation on a 156-qubit IBM quantum processor (Heron r2), confirming its performance advantages and stable convergence without additional mitigation overhead.

Theorems & Definitions (2)

• Corollary 1: Rank-Expressivity Trade-off
• Corollary 2: Expressivity-Generalization Trade-off