Training-efficient density quantum machine learning

Quantum machine learning (QML) requires powerful, flexible and efficiently trainable models to be successful in solving challenging problems. We introduce density quantum neural networks, a model family that prepares mixtures of trainable unitaries, with a distributional constraint over coefficients. This framework balances expressivity and efficient trainability, especially on quantum hardware. For expressivity, the Hastings-Campbell Mixing lemma converts benefits from linear combination of unitaries into density models with similar performance guarantees but shallower circuits. For trainability, commuting-generator circuits enable density model construction with efficiently extractable gradients. The framework connects to various facets of QML including post-variational and measurement-based learning. In classical settings, density models naturally integrate the mixture of experts formalism, and offer natural overfitting mitigation. The framework is versatile - we uplift several quantum models into density versions to improve model performance, or trainability, or both. These include Hamming weight-preserving and equivariant models, among others. Extensive numerical experiments validate our findings.

@article{coyle2025_2405.20237,
  title={ Training-efficient density quantum machine learning },
  author={ Brian Coyle and Snehal Raj and Natansh Mathur and El Amine Cherrat and Nishant Jain and Skander Kazdaghli and Iordanis Kerenidis },
  journal={arXiv preprint arXiv:2405.20237},
  year={ 2025 }
}