Multimode rotationally symmetric bosonic codes from group-theoretic construction

Journal article, 2026

We introduce a family of multimode, rotationally symmetric bosonic codes inspired by the group-theoretic framework introduced by Denys and Leverrier [Phys. Rev. Lett. 133, 240603 (2024)]. Such a construction inverts the traditional paradigm of code design by identifying codes from the requirement that a group of chosen logical gates should be implemented by means of physically simple logical operations, such as linear optics. Leveraging previously unexplored degrees of freedom within this framework, our construction results in codes that display rotational symmetry across multiple modes, while enabling linear-optics implementation of the full Pauli group. These codes exhibit improved protection against dephasing noise, outperforming both single-mode analogues and earlier multimode constructions. Notably, they allow exact correction of correlated dephasing and support qudit encoding in arbitrary dimensions. We analytically construct and numerically benchmark two-mode binomial code instances, and demonstrate that, unlike single-mode rotationally symmetric bosonic codes, these exhibit no trade-off between protection against dephasing and photon loss.