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We present an algorithm to approximate partition functions of 3-bodyclassical Ising models on two-dimensional lattices of arbitrary genus, in thereal-temperature regime. Even though our algorithm is purely classical, it isdesigned by exploiting a connection to topological quantum systems, namely thecolor codes. The algorithm performance is exponentially better than otherapproaches which employ mappings between partition functions and quantum stateoverlaps. In addition, our approach gives rise to a protocol for quantumsimulation of such Ising models by simply measuring local observables on colorcodes.

Ising models and topological codes: classical algorithms and quantum simulation