Protecting bosonic codes from ancilla-induced logical errors with continuous-variable flags

Bosonic codes have emerged as a promising strategy for achieving fault-tolerant quantum computation with significantly reduced hardware overhead. These continuous-variable encodings use the large dimension of a quantum system's Hilbert space to redundantly store and process quantum information, often relying on ancillary qubits to detect errors on the bosonic encoding. Recent experiments have demonstrated such architectures with ancillary transmons, for the autonomous stabilization of GKP states (Sivak et al., Nature 2023) and for the stabilization of cat qubits concatenated in a repetition code (Putterman et al., Nature 2025). However, the logical lifetime of these codes is often limited by errors on these ancillary qubits, which can propagate to the bosonic code and lead to logical errors. One existing solution to counter such error propagation involves using the second excited state of transmons with a matching dispersive shift to provide first-order protection from transmon decays.

In this work, we present an alternative solution based on continuous-variable flags, showing that it is possible to detect and correct ancilla-induced logical errors using this mode. Specifically, we demonstrate how this approach can be applied in circuit quantum electrodynamics architectures to reduce transmon-induced errors during syndrome measurements of both rotation-symmetric and translation-symmetric bosonic codes.