Publication

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

11/07/2019

Ryan L. Mann and Michael J. Bremner

Quantum, 3, 162 (2019)

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. Furthermore, we prove that for this class of Ising models the partition function does not vanish. Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing the leading coefficients of graph polynomials on bounded degree graphs. Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum circuits.

University: University of Technology Sydney

Authors Centre Participants: Dr. Ryan Mann, Prof. Michael Bremner

Source: Other

Publication Type: Refereed Journal article

DOI Link: DOI Link

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