Local Rydberg blockade regimes for disk graph embedding and quantum optimization
Rydberg atom arrays are a powerful platform for solving combinatorial optimization problems, owing to the Rydberg blockade mechanism, which imposes effective constraints on simultaneous atomic excitations. These constraints have enabled the encoding of the Maximum Independent Set (MIS) problem on unit disk graphs, where atoms interact within a fixed, globally defined blockade radius. However, this restriction limits the class of addressable problems. A natural extension is to consider disk graphs, which generalize unit disk graphs by allowing arbitrary disk radii and correspond to the intersection graphs of disks in the plane. Embedding such graphs in Rydberg systems requires moving beyond the standard, globally uniform blockade model. In this work, we introduce a local Rydberg blockade regime, which emerges when local drives are applied to different pairs of atoms involved in a potential interaction. We develop a general theoretical framework for this regime and propose two novel metrics, the correlation matrix and the maximum independence violation, to quantify the quality of the embedding. Using these metrics, we demonstrate that disk graphs can be meaningfully embedded into Rydberg atom arrays under local drive schemes, thereby expanding the landscape of quantum-addressable optimization problems. Finally, when evaluating approximate solutions of the MIS problem, characterized by near-optimal independent sets, local drive approaches exhibit significantly improved performance over global ones. These results highlight the practical advantage of local blockade engineering for approximate combinatorial optimization and open a path toward leveraging the analog capabilities of Rydberg platforms beyond conventional geometric constraints.