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A PTAS for the Classical Ising Spin Glass Problem on the Chimera Graph Structure

We present a polynomial time approximation scheme (PTAS) for the minimum value of the classical Ising Hamiltonian with linear terms on the Chimera graph structure as defined in the recent work of McGeoch and Wang. The result follows from a direct application of the techniques used by Bansal, Bravyi and Terhal who gave a PTAS for the same problem on planar and, in particular, grid graphs. We also show that on Chimera graphs, the trivial lower bound is within a constant factor of the optimum.