A new connection between quantum circuits, graphs and the Ising partition function

Authors:
Joseph Geraci
Affiliations:
Department of Mathematics, University of Toronto, Toronto, Canada and CQIST --- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, USA
Venue:
Quantum Information Processing
Year:
2008

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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 problem for the additive approximation of a function over hypergraphs related to the generating function of Eulerian subgraphs for ordinary graphs. Further, if E is an oracle that returns approximations of this function, we prove that PE = BQP. We also discuss connections with the Ising partition function.