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The requirements for fault-tolerant quantum error correction can besimplified by leveraging structure in the noise of the underlying hardware. Inthis work, we identify a new type of structured noise motivated by neutral atomqubits, biased erasure errors, which arises when qubit errors are dominated bydetectable leakage from only one of the computational states of the qubit. Westudy the performance of this model using gate-level simulations of the XZZXsurface code. Using the predicted erasure fraction and bias of metastable$^{171}$Yb qubits, we find a threshold of 8.2% for two-qubit gate errors, whichis 1.9 times higher than the threshold for unbiased erasures, and 7.5 timeshigher than the threshold for depolarizing errors. Surprisingly, the improvedthreshold is achieved without bias-preserving controlled-not gates, and insteadresults from the lower noise entropy in this model. We also introduce an XZZXcluster state construction for measurement-based error correction,hybrid-fusion, that is optimized for this noise model. By combining fusionoperations and deterministic entangling gates, this construction preserves theintrinsic symmetry of the XZZX code, leading to a higher threshold of 10.3% andenabling the use of rectangular codes with fewer qubits. We discuss a potentialphysical implementation using a single plane of atoms and moveable tweezers.

High threshold codes for neutral atom qubits with biased erasure errors