Virtual quantum neural networks
Abstract
Quantum neural networks are a prominent model of quantum machine learning. Their training consists in the minimization of a given loss function over a parametrized family of quantum circuits, mathematically described by unitary operators, or, more generally, completely positive linear maps. In this work, we extend the notion of quantum neural network, using random sampling and classical data processing to enlarge the optimization space in a way that includes linear combinations of completely positive maps. Our extended model, called virtual quantum neural networks, leverages its enlarged optimization space to achieve increased expressivity and improved noise robustness. These benefits are illustrated in three representative tasks: quantum error mitigation, binary classification, and estimation of ground-state energies. Overall, virtual quantum neural networks offer a flexible learning paradigm that expands the space of achievable computations and strengthens the applications of near-term quantum hardware.
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BibTeX
@misc{zhao2026virtual,
title = {{Virtual quantum neural networks}},
author = {Benchi Zhao and Xuanqiang Zhao and Yinan Li and Yingzhou Li and Giulio Chiribella},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11327},
eprint = {2609.11327},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11327},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Virtual quantum neural networks
AU - Benchi Zhao
AU - Xuanqiang Zhao
AU - Yinan Li
AU - Yingzhou Li
AU - Giulio Chiribella
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11327
UR - https://arxiv.org/abs/2609.11327
AB - Quantum neural networks are a prominent model of quantum machine learning. Their training consists in the minimization of a given loss function over a parametrized family of quantum circuits, mathematically described by unitary operators, or, more generally, completely positive linear maps. In this work, we extend the notion of quantum neural network, using random sampling and classical data processing to enlarge the optimization space in a way that includes linear combinations of completely positive maps. Our extended model, called virtual quantum neural networks, leverages its enlarged optimization space to achieve increased expressivity and improved noise robustness. These benefits are illustrated in three representative tasks: quantum error mitigation, binary classification, and estimation of ground-state energies. Overall, virtual quantum neural networks offer a flexible learning paradigm that expands the space of achievable computations and strengthens the applications of near-term quantum hardware.
ER -