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In the past years, many quantum algorithms have been proposed to tackle hardcombinatorial problems. In particular, the Maximum Independent Set (MIS) is aknown NP-hard problem that can be naturally encoded in Rydberg atom arrays. Byrepresenting a graph with an ensemble of neutral atoms one can leverage Rydbergdynamics to naturally encode the constraints and the solution to MIS. However,the classes of graphs that can be directly mapped ``vertex-to-atom" on standarddevices with 2D capabilities are currently limited to Unit-Disk graphs. In thissetting, the inherent spatial locality of the graphs can be leveraged byclassical polynomial-time approximation schemes (PTAS) that guarantee an$\epsilon$-approximate solution. In this work, we build upon recent progressmade for using 3D arrangements of atoms to embed more complex classes ofgraphs. We report experimental and theoretical results which representimportant steps towards tackling combinatorial tasks on quantum computers forwhich no classical efficient $\varepsilon$-approximation scheme exists.

Exploring the impact of graph locality for the resolution of MIS with neutral atom devices