Quantum weight enumerators and tensor networks

Abstract: We examine the use of weight enumerators for analyzing tensor network constructions, and specifically the quantum lego framework recently introduced. We extend the notion of quantum weight enumerators to so-called tensor enumerators, and prove that the trace operation on tensor networks is compatible with a trace operation on tensor enumerators. This allows us to compute quantum weight enumerators of larger codes such as the ones constructed through tensor network methods more efficiently. We also provide a general framework for quantum MacWilliams identities that includes tensor enumerators as a special case.