Training-efficient density quantum machine learning

• URL: http://arxiv.org/abs/2405.20237v2
• Date: Fri, 23 May 2025 10:51:37 GMT
• Title: Training-efficient density quantum machine learning
• Authors: Brian Coyle, Snehal Raj, Natansh Mathur, El Amine Cherrat, Nishant Jain, Skander Kazdaghli, Iordanis Kerenidis,
• Abstract summary: We introduce density quantum neural networks, a model family that prepares mixtures of trainable unitaries.<n>This framework balances expressivity and efficient trainability, especially on quantum hardware.
• Score: 2.918930150557355
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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