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The noise bias is adapted for neutral-atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions and are thus expected to be the dominant source of noise. Careful design of the gates allows us to further reduce the noise model to Pauli-                     <a:math xmlns:a=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\">                       <a:mi>Z</a:mi>                     </a:math>                     errors. In addition, the presented circuits are robust to arbitrary single-qubit gate errors, and we demonstrate that the break-even point can be significantly improved compared to fully fault-tolerant measurement-free schemes. 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