Cat qubits are promising candidates to build fault-tolerant quantum hardware. The advantage of this approach lies in the bias of the noise affecting cat qubits: the bit-flips errors are exponentially suppressed with the average number of photons in the cat states, such that the noise is highly dominated by phase-flips even for moderate cat sizes. However, the experimental demonstration of active phase-flip error correction remains challenging.

In this talk, I will discuss the optimal regime of operation of the "cat qubits + repetition code" architecture. More specifically, I will review the different strategies introduced recently to implement fast bias-preserving gates to extract the error syndromes. While implementing fast gates on cat qubits improves the performance of the repetition code, it can lead to quantum states distortion outside of the cat states manifold (state "leakage"). I will discuss the potential problems caused by this leakage and present a method to perform circuit-level simulations of QEC that takes this effect into account.