Fault-tolerant performance and decoding thresholds

Establish the fault-tolerant properties of the one-, two-, and three-step Floquet Majorana XYZ protocols under realistic data and measurement errors, including decoding thresholds for their time-dependent instantaneous stabilizer groups and logical representatives.

Background

The paper constructs one-, two-, and three-step Floquet codes from the Majorana XYZ subsystem code and exactly characterizes their parity-dependent logical structures and distances. However, the reported distance results are instantaneous code distances; the paper does not analyze fault-tolerant operation in the presence of data-qubit or measurement errors, nor does it provide decoders or threshold estimates for the evolving stabilizer groups and logical operators.

The authors identify the development of such an analysis as the most important unresolved direction, specifically calling for fault-tolerance results and decoding thresholds under realistic error models.