We propose a simple architecture for 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 photons, which are disentangled from the qubits at the end of each operation. A single photon can generate an entangling controlled phase (C-PHASE) gate between any selected number of qubits in the network and forms the basis for universal quantum computing, distributed over multiple processor units. We analyze this network and we show that the gate fidelity is high, also when more qubits are involved, as requested, e.g., in an efficient Grover search. In our derivation we consider qubit transition energies in the optical regime, however, we stress that it can be readily generalized to other architectures where the nodes may be coupled, e.g., by microwave photons.