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

In an effort to overcome the limitations of random spin-glass benchmarks for quantum annealers, focus has shifted to carefully-crafted gadget-based problems whose logical structure has typically a planar topology. Recent experiments on these gadget problems using a commercially-available quantum annealer have demonstrated an impressive performance over a selection of commonly-used classical optimization heuristics. Here we show that efficient classical optimization techniques, such as minimum-weight perfect matching, can solve these gadget problems exactly and in polynomial time. We present approaches on how to mitigate this shortcoming of commonly-used benchmark problems based on planar logical topologies.