  In recent years, quantum state engineering and quantum information processing
using microwave fields and photons have received increasing attention. In
addition, multiqubit gates play an important role in quantum information
processing. In this work, we propose to encode a photonic qubit via two
arbitrary orthogonal eigenstates (with eigenvalues 1 and -1, respectively) of
the photon-number parity operator. With such encoding, we then present a
single-step method to realize a multi-target-qubit controlled-phase gate with
one photonic qubit simultaneously controlling n-1 target photonic qubits, by
employing n microwave cavities coupled to one superconducting flux qutrit. This
proposal can be applied not only to implement nonhybrid multi-target-qubit
controlled-phase gates using photonic qubits with various encodings, but also
to realize hybrid multi-target-qubit controlled-phase gates using photonic
qubits with different encodings. The gate realization requires only a
single-step operation. The gate operation time does not increase with the
number of target qubits. Because the qutrit remains in the ground state during
the entire operation, decoherence from the qutrit is greatly suppressed. As an
application, we show how to apply this gate to generate a multicavity
Greenberger-Horne-Zeilinger (GHZ) entangled state with general expression.
Depending on the specific encodings, we further discuss the preparation of
several nonhybrid and hybrid GHZ entangled states of multiple cavities. We
numerically investigate the circuit-QED experimental feasibility of creating a
three-cavity spin-coherent hybrid GHZ state. This proposal can be extended to
accomplish the same tasks in a wide range of physical systems, such as multiple
microwave or optical cavities coupled to a three-level natural or artificial
atom.
