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We propose a single-step implementation of a muti-target-qubit controlledphase gate with one cat-state qubit (\textit{cqubit}) simultaneouslycontrolling $n-1$ target \textit{cqubits}. The two logic states of a\textit{cqubit} are represented by two orthogonal cat states of a single cavitymode. In this proposal, the gate is implemented with $n$ microwave cavitiescoupled to a superconducting transmon qutrit. Because the qutrit remains in theground state during the gate operation, decoherence caused due to the qutrit'senergy relaxation and dephasing is greatly suppressed. The gate implementationis quite simple because only a single-step operation is needed and neitherclassical pulse nor measurement is required. Numerical simulations demonstratethat high-fidelity realization of a controlled phase gate with one cqubitsimultaneously controlling two target cqubits is feasible with present circuitQED technology. This proposal can be extended to a wide range of physicalsystems to realize the proposed gate, such as multiple microwave or opticalcavities coupled to a natural or artificial three-level atom.

One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED