Researchers Establish Riemannian Geometry Framework for Tensor Network Optimization

Researchers at the Complutense University of Madrid, led by Pablo Páez-Velasco, have successfully assigned a Riemannian manifold structure to tensor networks, providing a robust framework for both numerical optimisation and in-depth analysis.

This work directly addresses the inherent gauge freedom within tensor networks, a crucial characteristic, and establishes a Riemannian fundamental theorem applicable to several network families.

Tensor networks, previously understood through fundamental theorems limited to matrix product states and some projected entangled pair states, now extend to several additional families.