VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning

TL;DR

VQC-MLPNet addresses expressivity, trainability, and noise resilience in quantum machine learning by integrating a Variational Quantum Circuit to generate a subset of the classical MLP's first-layer weights during training, while keeping inference fully classical. The authors develop a risk-decomposition framework and NTK-based analysis, showing exponential improvements in representation capacity with circuit depth $L$ and qubits $U$ and establishing favorable training dynamics. Empirically, the method achieves state-of-the-art performance on quantum-dot classification and transcription-factor binding-site prediction using far fewer trainable parameters than all-classical baselines, and maintains robustness under realistic IBM noise. The work demonstrates a scalable, practical pathway for near-term quantum advantage by uniting quantum expressivity with classical nonlinear processing and gradient-based optimization.

Abstract

Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience. We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically. This design preserves scalability, reduces quantum resource demands, and enables practical deployment. We provide a theoretical analysis based on statistical learning and neural tangent kernel theory, establishing explicit risk bounds and demonstrating improved expressivity and trainability compared to purely quantum or existing hybrid approaches. These theoretical insights demonstrate exponential improvements in representation capacity relative to quantum circuit depth and the number of qubits, providing clear computational advantages over standalone quantum circuits and existing hybrid quantum architectures. Empirical results on diverse datasets, including quantum-dot classification and genomic sequence analysis, show that VQC-MLPNet achieves high accuracy and robustness under realistic noise models, outperforming classical and quantum baselines while using significantly fewer trainable parameters.

Figures (3)

• Figure 1: An Illustration of the VQC-MLPNet structure. The VQC-MLPNet architecture is a hybrid quantum-classical neural network where the VQC generates the MLP parameters $\hat{\textbf{W}}^{(1)}$ for its first hidden layer. During training, the VQC uses amplitude encoding to encode $\textbf{W}^{(1)}$. The transformed parameters $\{\alpha_{1:U}, \beta_{1:U}, \gamma_{1:U} \}$ in $f_{\rm vqc}$ are updated through quantum operations before being integrated into the first hidden layer of the MLP. Once trained, the VQC is no longer needed for inference, making the model scalable for deployment.
• Figure 2: The error performance analysis of VQC-MLPNet illustrates the decomposition of total learning error into three key components. Given a target function $h^{*}$, the optimal VQC-MLPNet introduces an approximation error relative to $h^{*}$. The empirical risk minimizer $f_{\boldsymbol{\theta}'}$, obtained from training data, results in a uniform deviation from $f_{\boldsymbol{\theta}^{*}}$. Finally, the algorithmically returned operator $f_{\boldsymbol{\hat{\theta}}}$, derived through gradient-based optimization, incurs an optimization error concerning $f_{\boldsymbol{\theta}'}$.
• Figure 3: The VQC module in the VQC-MLPNet pipeline. Each input weight vector from the MLP's first hidden layer is amplitude-encoded into a quantum state over $U$ qubits. The circuit applies parameterized single-qubit rotations $R_{X}(\alpha_u)$, $R_{Y}(\beta_u)$, $R_{Z}(\gamma_u)$ to over $U$ qubits, optionally followed by entangling layers composed of CNOT gates to capture multi-qubit correlations. The PQC model in the green dashed square is repeatedly copied to build a deeper model. The resulting quantum state is measured through Pauli-Z observables ($\vert z_{1}\rangle$, $\vert z_{2} \rangle$, ..., $\vert z_{U}\rangle$), resulting in the expectation values ($\langle \sigma_{z}^{(1)} \rangle$, $\langle \sigma_{z}^{(2)} \rangle$, ..., $\langle \sigma_{z}^{(U)} \rangle$).