  Quantum error correction is crucial for any quantum computing platform to
achieve truly scalable quantum computation. The surface code and its variants
have been considered the most promising quantum error correction scheme due to
their high threshold, low overhead, and relatively simple structure that can
naturally be implemented in many existing qubit architectures, such as
superconducting qubits. The recent development of Floquet codes offers another
promising approach. By going beyond the usual paradigm of stabilizer codes,
Floquet codes achieve similar performance while being constructed entirely from
two-qubit measurements. This makes them particularly suitable for platforms
where two-qubit measurements can be implemented directly, such as
measurement-only topological qubits based on Majorana zero modes (MZMs). Here,
we explain how two variants of Floquet codes can be implemented on MZM-based
architectures without any auxiliary qubits for syndrome measurement and with
shallow syndrome extraction sequences. We then numerically demonstrate their
favorable performance. In particular, we show that they improve the threshold
for scalable quantum computation in MZM-based systems by an order of magnitude,
and significantly reduce space and time overheads below threshold.
