  We propose an efficient scheme to implement a multiplex-controlled phase gate
with multiple photonic qubits simultaneously controlling one target photonic
qubit based on circuit quantum electrodynamics (QED). For convenience, we
denote this multiqubit gate as MCP gate. The gate is realized by using a
two-level coupler to couple multiple cavities. The coupler here is a
superconducting qubit. This scheme is simple because the gate implementation
requires only \textit{one step} of operation. In addition, this scheme is quite
general because the two logic states of each photonic qubit can be encoded with
a vacuum state and an arbitrary non-vacuum state (e.g., a Fock state, a
superposition of Fock states, a cat state, or a coherent state, etc.) which is
orthogonal or quasi-orthogonal to the vacuum state. The scheme has some
additional advantages: Because only two levels of the coupler are used, i.e.,
no auxiliary levels are utilized, decoherence from higher energy levels of the
coupler is avoided; the gate operation time does not depend on the number of
qubits; and the gate is implemented deterministically because no measurement is
applied. As an example, we numerically analyze the circuit-QED based
experimental feasibility of implementing a three-qubit MCP gate with photonic
qubits each encoded via a vacuum state and a cat state. The scheme can be
applied to accomplish the same task in a wide range of physical system, which
consists of multiple microwave or optical cavities coupled to a two-level
coupler such as a natural or artificial atom.
