Bosonic cyclic codes trade single photon loss detectability for a number of logical phase gates equal to the rotation symmetry order, all via Gaussian rotations, with generalizations of cat and binomial codes.
Jin, General Approach to Error Detection of Bosonic Codes via Phase Estimation, Physical Review Letters135, 10.1103/h6rv-hz81 (2025)
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Bosonic Cyclic Codes: Trading Stabilizers for Gaussian Non-Clifford Phase Gates
Bosonic cyclic codes trade single photon loss detectability for a number of logical phase gates equal to the rotation symmetry order, all via Gaussian rotations, with generalizations of cat and binomial codes.