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

TL;DR

This paper introduces a new connection between quantum circuits and graphs, establishing a BQP-complete problem related to the Ising model partition function and hypergraph functions, advancing understanding of quantum-classical mappings.

Contribution

It presents a simple construction linking quantum circuits to graphs and a BQP-complete problem related to hypergraph functions and the Ising model.

Findings

Mapping between quantum circuits and graphs established

BQP-complete problem for hypergraph functions introduced

Connections with Ising partition function discussed

Abstract

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