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Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

Parameterised graph theory studies how the complexity of graph-theoretic problems depends on structural parameters of the input graph. This perspective has proved useful in analysing tensor-network simulation (Markov and Shi, 2008). Its implications for tensor-network representations and tomography are less well understood. In particular, which graph parameters determine whether a tensor-network state (TNS) admits a tractable matrix product state (MPS) or tree tensor network (TTN) representation, and which control the complexity of learning the state? We address these questions using parameter

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