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Computing quantum entanglement with machine learning

Andrea Bulgarelli
Elia Cellini
Karl Jansen
Stefan Kühn
Alessandro Nada
Shinichi Nakajima
Kim A. Nicoli
Marco Panero

December 12, 2025

Entanglement calculations in quantum field theories are extremely challenging and typically rely on the replica trick, where the problem is rephrased in a study of defects. We demonstrate that the use of deep generative models drastically outperforms standard Monte Carlo algorithms. Remarkably, such a machine-learning method enables high-precision estimates of Rényi entropies in three dimensions for very large lattices. Moreover, we propose a new paradigm for studying lattice defects with flow-based sampling.