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One prominent application of near-term quantum computing devices is to solvecombinatorial optimization such as non-deterministic polynomial-time hard(NP-hard) problems. Here we present experiments with Rydberg atoms to solve oneof the NP-hard problems, the maximum independent set (MIS) of graphs. Weintroduce the Rydberg quantum wire scheme with auxiliary atoms to engineerlong-ranged networks of qubit atoms. Three-dimensional (3D) Rydberg-atom arraysare constructed, overcoming the intrinsic limitations of two-dimensionalarrays. We demonstrate Kuratowski subgraphs and a six-degree graph, which arethe essentials of non-planar and high-degree graphs. Their MIS solutions areobtained by realizing a programmable quantum simulator with the quantum-wired3D arrays. Our construction provides a way to engineer many-body entanglement,taking a step toward quantum advantages in combinatorial optimization.

Rydberg Quantum Wires for Maximum Independent Set Problems with Nonplanar and High-Degree Graphs