  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.
