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We present a simple construction that maps quantum circuits to graphs andvice-versa. Inspired by the results of D.A. Lidar linking the Ising partitionfunction with quadratically signed weight enumerators (QWGTs), we also presenta BQP-complete problem for the additive approximation of a function overhypergraphs related to the generating function of Eulerian subgraphs forordinary graphs. We discuss connections with the Ising partition function.

A BQP-complete problem related to the Ising model partition function via a new connection between quantum circuits and graphs