Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction

Approximation of a tensor network by approximating (e.g., factorizing) one or more its constituent tensors can be improved canceling the leading-order error due to constituents’ approximation. The utility such robust approximation is demonstrated for canonical polyadic (CP) (density-fitting) factorized two-particle Coulomb interaction tensor. resulting algebraic (grid-free) tensor, closely related factorization appearing in pseudospectral and hypercontraction approaches, efficient accurate, with significantly reduced rank compared naive (nonrobust) Application particle–particle ladder term coupled-cluster singles doubles reduces size complexity from O (N6) (N5) robustness ensuring negligible errors chemically relevant energy differences using CP ranks approximately equal density-fitting basis.