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.

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Cite

BibTeX RIS

BibTeX

@misc{ayena2026hybrid,
  title = {{Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction}},
  author = {Koffi Ognandon Ayena and Frédéric Holweck and Serge Iovleff and Amah S d'Almeida},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17358},
  eprint = {2609.17358},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17358},
}

RIS

TY  - UNPB
TI  - Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction
AU  - Koffi Ognandon Ayena
AU  - Frédéric Holweck
AU  - Serge Iovleff
AU  - Amah S d'Almeida
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17358
UR  - https://arxiv.org/abs/2609.17358
AB  - 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.
ER  -

Abstract

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