Research questionFor a known tensor-network graph, which structural parameters control MPS/TTN overhead and tomography complexity?The same tensor-network state can require different resources when represented as an MPS or TTN, depending on the structure of its underlying graph. That structure also affects how much data and computation are needed to learn the state, including when the input is not exactly representable by the chosen network. Latest papersRecent research connected to this question, newest first.Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomographyThe source studies tensor networks on arbitrary known graphs. It gives bounds involving cutwidth, tree-cutwidth, degree, treewidth, and learning complexity for bond-dimension overhead, TTN grouped-subsystem dimensions, and realisable tomography. Its agnostic setting considers approximating an arbitrary input state by a pure tensor-network state with a specified graph and bond dimension.research paper · Sep 3, 2026