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We analyze the transformation of QUBO from its conventional Booleanpresentation into an equivalent spin glass problem with coupled $\pm1$ spinvariables exposed to a site-dependent external field. We find that in a widelyused testbed for QUBO these fields tend to be rather large compared to thetypical coupling and many spins in each optimal configurations simply alignwith the fields irrespective of their constraints. Thereby, the testbedinstances tend to exhibit large redundancies - seemingly independent variableswhich contribute little to the hardness of the problem, however. We demonstratevarious consequences of this insight, for QUBO solvers as well as forheuristics developed for finding spin glass ground states. To this end, weimplement the Extremal Optimization (EO) heuristic, in a new adaptation for theQUBO problem. We also propose a novel way to assess the quality of heuristicsfor increasing problem sizes based on asymptotic scaling.

Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem