Modeling logical performance of concatenated cat codes

Bosonic cat qubits are a promising physical platform for quantum computing, since the cats' large noise bias can enable more hardware-efficient quantum error correction. In fact, a simple repetition code already suffices to correct the cats' dominant errors. In this talk, we describe theoretical modeling of the repetition cat code experiment in [Putterman et al., arXiv:2409.13025]. In particular, we show how logical error is accurately predicted by simple phenomenological models, and discuss limits on repetition code performance. We chart a path for overcoming these limitations by extending from repetition cat codes to surface cat codes.