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.
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