  We propose a simple interaction protocol to be implemented on a scalable
quantum network, in which the quantum nodes consist of qubit systems confined
in cavities. The nodes are deterministically coupled by transmission and
reflection of a single photon, which is disentangled from the qubits at the end
of the coupling operation. This single photon can generate an entangling
controlled phase (C-PHASE) gate between any selected number of qubits in the
network. Our multi-qubit gate reaches a much higher fidelity compared to
schemes concatenating one-qubit and two-qubit gates; thus it forms an efficient
basis for universal quantum computing distributed over multiple processor
units. In our analysis we consider atomic qubits coupled to optical photons,
while the scheme can be readily generalized to other architectures, such as
superconducting qubit nodes coupled by microwave photons.
