A Unified Protocol for Arbitrary Z Rotations of a Class of Bosonic cQED Qubits

Bosonic-qubit encodings provide diverse approaches to storing and processing quantum information, with logical operations often implemented through encoding-specific physical strategies. Here, we identify a class of bosonic Fock-based qubits in circuit QED for which distinct implementations of arbitrary Z rotations share a common structure. We formulate this structure as a six-step protocol that provides a unified procedure for implementing arbitrary Z rotations across this class of bosonic cQED qubits. The applicability of the protocol is determined by a specific condition on the encoding, providing a criterion for identifying bosonic Fock-based cQED qubits that admit the common implementation.