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Architectures for quantum computing based on neutral atoms have risen toprominence as candidates for both near and long-term applications. Thesedevices are particularly well suited to solve independent set problems, as thecombinatorial constraints can be naturally encoded in the low-energy Hilbertspace due to the Rydberg blockade mechanism. Here, we approach this connectionwith a focus on a particular device architecture and explore the ubiquity andutility of independent set problems by providing examples of real-worldapplications. After a pedagogical introduction of basic graph theory conceptsof relevance, we briefly discuss how to encode independent set problems inRydberg Hamiltonians. We then outline the major classes of independent setproblems and include associated example applications with industry and socialrelevance. We determine a wide range of sectors that could benefit fromefficient solutions of independent set problems -- from telecommunications andlogistics to finance and strategic planning -- and display some generalstrategies for efficient problem encoding and implementation on neutral-atomplatforms.

Industry applications of neutral-atom quantum computing solving independent set problems