Programmable neutral atom arrays show great promise for fault-tolerant quantum computing. A dominant physical error on this platform is qubit leakage and loss, notably decay errors from the Rydberg state during two-qubit gates. Such leakage events are particularly detrimental as they propagate, generating correlated errors that severely degrade the effective error distance of quantum error correction codes. Here, we present a novel approach to address Rydberg decay errors leveraging measurement-based quantum computation. Our scheme strategically exploits the inherent geometric structure of topological cluster states and only uses final leakage detection information to locate propagated errors originating from Rydberg decay. This eliminates the need for complex and atom-species-specific midcircuit leakage detection, offering broader applicability, e.g., to the well-established Rb atom platform. We demonstrate a high error threshold of 3.65% per cz gate for pure Rydberg decay and achieve a favorable error distance $d_e\approx d$. Our method compares favorably with state-of-the-art erasure conversion protocols in the subthreshold performance, offering comparable or marginally larger logical error rates while significantly reducing experimental overhead.

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• Measurement-based quantum computing
• Quantum computation
• Quantum error correction