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

## TL;DR

This paper reveals that planar spin-glass benchmarks, thought to be challenging for quantum annealers, can be efficiently solved by classical algorithms, highlighting the need for more robust benchmarking methods.

## Contribution

The paper demonstrates that classical algorithms can efficiently solve planar gadget-based spin-glass problems, exposing limitations of current benchmarks for quantum annealers.

## Key findings

- Classical algorithms like minimum-weight perfect matching solve these problems exactly.
- Planar gadget problems are solvable in polynomial time by classical methods.
- Current benchmarks may overestimate quantum annealers' performance.

## Abstract

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.