  We introduce a methodology for generating benchmark problem sets for Ising
machines---devices designed to solve discrete optimization problems cast as
Ising models. In our approach, linear systems of equations are cast as Ising
cost functions. While linear systems are easily solvable, the corresponding
optimization problems are known to exhibit some of the salient features of
NP-hardness, such as strong exponential scaling of heuristic solvers' runtimes
and extensive distances between ground and low-lying excited states. We show
how the proposed technique, which we refer to as `equation planting,' can serve
as a useful tool for evaluating the utility of Ising solvers functioning either
as optimizers or as ground-state samplers. We further argue that
equation-planted problems can be used to probe the mechanisms underlying the
operation of Ising machines.
