Optimized measurement-free and fault-tolerant quantum error correction for neutral atoms

A major challenge in performing quantum error correction (QEC) is implementing reliable measurements and conditional feed-forward operations. In quantum computing platforms supporting unconditional qubit resets, or a constant supply of fresh qubits, alternative schemes which do not require measurements are possible. In such schemes, the error correction is realized via crafted coherent quantum feedback. We propose implementations of small measurement-free QEC schemes, which are fault-tolerant to circuit-level noise. These implementations are guided by several heuristics to achieve fault-tolerance: redundant syndrome information is extracted, and additional single-shot flag qubits are used. By carefully designing the circuit, the additional overhead of these measurement-free schemes is moderate compared to their conventional measurement-and-feed-forward counterparts. We highlight how this alternative approach paves the way towards implementing resource-efficient measurement-free QEC on neutral-atom arrays.