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In an effort to overcome the limitations of random spin-glass benchmarks forquantum annealers, focus has shifted to carefully-crafted gadget-based problemswhose logical structure has typically a planar topology. Recent experiments onthese gadget problems using a commercially-available quantum annealer havedemonstrated an impressive performance over a selection of commonly-usedclassical optimization heuristics. Here we show that efficient classicaloptimization techniques, such as minimum-weight perfect matching, can solvethese gadget problems exactly and in polynomial time. We present approaches onhow to mitigate this shortcoming of commonly-used benchmark problems based onplanar logical topologies.

The pitfalls of planar spin-glass benchmarks: Raising the bar for quantum annealers (again)