Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction

2026-09-15

AI Summary

本文提出了一种混合变分量子电路(HVQC)，通过结合经典仿射后测量层，实现多变量回归和高维数据重建，实验效果优于传统方法。

Abstract

Variational quantum circuits (VQCs) are parameterized quantum circuits optimized classically. We propose a hybrid variational quantum circuit (HVQC) extending VQCs with a classical affine post-measurement layer, enabling vector-valued regression without the linear overhead of independent scalar circuits. Theoretically, we show that elementary one-and two-qubit circuits can approximate quadratic functions and products via data re-uploading and entanglement, providing the foundations of the full architecture. Experimentally, on two synthetic image reconstruction datasets and the Friedman1 benchmark (40,568 test samples), our HVQC matches Gaussian Process Regression and outperforms XGBoost and Random Forest. An ablation study confirms that both quantum and classical components are essential, and results highlight the central role of the feature map in hybrid quantum-classical models.

Problem

• Variational Quantum Circuits
• Multivariate Regression
• High-Dimensional Data Reconstruction

Innovation

• Hybrid Variational Quantum Circuits
• Vector-Valued Regression
• Data Re-uploading
• Entanglement
• Feature Map