Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction
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Computer Science > Machine Learning
Title:Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction
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.
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2609.17358 [cs.LG] |
| (or arXiv:2609.17358v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.17358
arXiv-issued DOI via DataCite (pending registration)
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| Journal reference: | The Seventeenth International Conference on Information, Intelligence, Systems and Applications (IISA 2026), Jul 2026, Rhodes Island, Greece, Greece |
Submission history
From: Koffi Ognandon AYENA [view email] [via CCSD proxy][v1] Tue, 15 Sep 2026 15:57:20 UTC (1,287 KB)
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