Error-detectable logical 2-qubit gates on bosonic qubits

Bosonic error correction in circuit QED has previously been successful at preserving a quantum memory but realizing two-qubit gates in the logical subspace is an outstanding challenge. In particular, we must engineer these operations without succumbing to errors in the requisite nonlinear resource. We present a continuous family of two-qubit gates that satisfy these requirements for bosonic qubits housed in microwave cavities with transmon ancillae for quantum control. Crucially, we have the ability to detect errors in both the cavities and transmon which is vital to preserving the desirable properties of our Bosonic encodings. Our gates require simple hardware - a microwave-actuated beamsplitter interaction between cavities and a transmon ancilla dispersively coupled to only one of the cavities. We show how to construct arbitrary excitation-preserving two-qubit gates for rotation-symmetric codes such as the cat code and other bosonic codes. With appropriate measurements, we can error-detect transmon decay, dephasing and cavity photon loss.