Use of faulty states in cat-code error correction

Bosonic codes have seen a resurgence in interest for applications as varied as fault-tolerant quantum architectures, quantum enhanced sensing, and entanglement distribution. Cat codes have been proposed as low-level elements in larger architectures, and the theory of rotationally symmetric codes more generally has been significantly expanded in the recent literature. The fault-tolerant preparation and maintenance of cat-code states as a standalone quantum error correction scheme remains, however, limited by the need for robust state preparation and strong intermode interactions. In this work, we consider the teleportation-based correction circuit for cat-code quantum error correction. We show that the class of acceptable ancillary states is broader than is typically acknowledged, and exploit this to propose the use of many-component bridge states, which, though not themselves in the cat-code space, are nonetheless capable of syndrome extraction in the regime where nonlinear interactions are a limiting factor.