Geometric Theory of Ising Machines

TL;DR

This paper develops a mathematical framework for designing low-temperature Ising machines, visualizing decision boundaries, and optimizing energy landscapes, advancing the understanding of probabilistic computing devices based on the Ising model.

Contribution

It introduces a diagrammatic visualization tool and proves new theoretical results linking Ising circuits to classifiers and energy landscape optimization.

Findings

Ising circuits generalize 1-NN classifiers with specific structures

Elimination of local minima can be achieved via linear programming

Provides a new visualization method for decision boundaries in Ising circuits

Abstract

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.