Error correction for Rydberg gadget embedding

Rydberg atom arrays are promising platforms for adiabatic quantum computing, as their Hamiltonians naturally encode the NP-hard unit-disk/ball maximum weighted independent set (UD/UB-MWIS) problem. Rydberg gadgets, structured auxiliary atoms, implement non-native interactions that embed problem graphs into UD/UB geometries. However, embeddings require $O(N^2)$ atoms for $O(N)$-size problems, motivating error correction through redundant encoding.

Here, we propose a cluster-based decoding scheme for embedded Rydberg atom arrays. The method exploits that gadgets are grouped into superatoms, allowing exactly one Rydberg excitation via the Rydberg blockade. By counting excitations that yield a nonlinear local syndrome, the algorithm identifies local error clusters and applies corrections when a unique solution exists; otherwise, clusters are iteratively expanded to ensure global consistency.

Numerical simulations under an independent and identically distributed (i.i.d.) error model show threshold-like behavior for both Parity-architecture and crossing-lattice embeddings, with a physical error threshold of approximately 0.3 for all-to-all connected graphs. Our approach is a co-designed architecture bridging hardware and software.