Geometric Theory of Ising Machines

We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a physical system allows efficient and distributed computation, but the design of the energy function is a difficult puzzle. We introduce a diagrammatic device that allows us to visualize the decision boundaries for Ising circuits. It is then used to prove two results: (1) Ising circuits are a generalization of 1-NN classifiers with a certain special structure, and (2) Elimination of local minima in the energy landscape can be formulated as a linear programming problem.