Debjyoti Biswas, Nikhil Sharma, Alberto Salvador, Rui Wang, Mats Granath, Adithi Udupa, Giulia Ferrini

Scalable fault-tolerant quantum computation requires quantum error-correcting codes that simultaneously support universal logical operations, suppress hardware-specific noise, and enable efficient handling of photon-loss errors. Bosonic encodings such as the dual-rail and cat codes each offer attractive features but also exhibit important limitations when used in isolation. The dual-rail code enables efficient single-photon-loss detection by converting leakage out of the computational subspace induced by photon-loss errors into an erasure error. In contrast, the cat code provides a resource-efficient, bias-tailored error-correction scheme with bias-preserving logical gate operations. Here, we introduce the dual-rail cat code (DRCC), a concatenated bosonic encoding that combines an inner cat code with an outer dual-rail structure, thereby inheriting and enhancing the advantages of both constituent codes. We analyse the error-correction properties of the DRCC and propose a deterministic single-photon-loss correction protocol by concatenating it with an outer repetition code. Exploiting the code's intrinsic noise bias, we construct a universal set of logical gates using only beam-splitter interactions and demonstrate that all logical operations preserve the erasure-biased noise structure. The DRCC offers several distinctive advantages, including the absence of relative geometric phases during gate operations, deterministic erasure detection and correction, and simultaneous syndrome extraction without interrupting stabilisation. These features make the DRCC a promising bosonic code for hardware-efficient, bias-preserving, and erasure-resilient fault-tolerant quantum computation.