Processing and Decoding Rydberg Decay Error with MBQC

Achieving fault-tolerant quantum computing with neutral atom necessitates careful consideration of the errors inherent to this system. One typical error is the leakage from Rydberg states during the implementation of multi-qubit gates, which may propagate to multiple correlated errors and deteriorate the performance of error correction. To address this, researchers have proposed an erasure conversion protocol that employs fast leakage detection and continuous atomic replacement to convert leakage errors into benign erasure errors. While this method achieves a high threshold and a favorable error distance d_e = d, its applicability is restricted to certain atom species. In this work, we present a novel approach to manage Rydberg decay errors in measurement-based quantum computation (MBQC). From a hardware perspective, we utilize practical experimental techniques along with an adaptation of the Pauli twirling approximation (PTA) to mitigate the impacts of leakage error, which propagates similarly to Pauli error without degrading the error distance. From a decoding perspective, we leverage the inherent structure of topological cluster states and final leakage detection information to locate propagated errors from Rydberg decay error. This approach eliminates the need for mid-circuit leakage detection, while maintaining an error distance d_e = d and achieving a high threshold of 3.617(3)% per CZ gate for pure Rydberg decay. In the presence of additional Pauli errors, we demonstrate the performance of our protocol in logical error rate within a reasonable range of physical errors and draw a comparison with erasure conversion. The results show a comparable performance within a modest R_e, which reveals possible application of our method in near-term platform.