Quantum-inspired tensor networks in machine learning models

arXiv cs.LG / 4/17/2026

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Key Points

Tensor networks, originally developed for many-body quantum physics, provide compressed representations that reduce the otherwise exponential complexity of multiparticle states by focusing on the most relevant dependencies.
Because quantum entanglement is formally similar to statistical correlations, tensor networks have been adopted in machine learning both as alternative model architectures and as decompositions of neural-network components.
The article reviews how tensor networks are being used in machine learning, assessing the current state of the art and where the approach may deliver benefits.
Potential advantages highlighted include improved computational efficiency, greater explainability, and enhanced privacy, but significant challenges remain to be addressed.
The review frames the field as one where insights from quantum many-body theory could enable new methods, while emphasizing the need to overcome practical and theoretical hurdles.

Abstract

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.