Entangling power of neural networks

Abstract:Characterizing the complexity of correlations between subsystems is a fundamental task across information theory, machine learning, and science. In quantum physics, neural networks have found increasing application in learning wavefunctions. Here we introduce the entangling power of an encoder-decoder neural network, which quantifies its ability to generate entanglement between subsystems, dependent on a latent space dimension $K$ and the complexity class of the decoder. We exactly calculate this quantity for polynomial decoders of degree $p$ acting on a $K$-dimensional latent space. Our results establish the exponential entangling power of neural networks with modest resources. More broadly, our work provides a framework for analyzing correlations in machine learning that generalizes the notion of the Schmidt rank in entanglement theory.

Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)

arXiv:2608.05293 [cond-mat.dis-nn]

(or arXiv:2608.05293v1 [cond-mat.dis-nn] for this version)

https://doi.org/10.48550/arXiv.2608.05293 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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