  We propose a single-step implementation of a muti-target-qubit controlled
phase gate with one cat-state qubit (\textit{cqubit}) simultaneously
controlling $n-1$ target \textit{cqubits}. The two logic states of a
\textit{cqubit} are represented by two orthogonal cat states of a single cavity
mode. In this proposal, the gate is implemented with $n$ microwave cavities
coupled to a superconducting transmon qutrit. Because the qutrit remains in the
ground state during the gate operation, decoherence caused due to the qutrit's
energy relaxation and dephasing is greatly suppressed. The gate implementation
is quite simple because only a single-step operation is needed and neither
classical pulse nor measurement is required. Numerical simulations demonstrate
that high-fidelity realization of a controlled phase gate with one cqubit
simultaneously controlling two target cqubits is feasible with present circuit
QED technology. This proposal can be extended to a wide range of physical
systems to realize the proposed gate, such as multiple microwave or optical
cavities coupled to a natural or artificial three-level atom.
