  We propose a quantum-information processor that consists of decoherence-free
logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity
single-qubit operations are performed deterministically within a
decoherence-free subsystem without leakage via global addressing of bichromatic
laser fields. Two-qubit operations are realized locally with four physical
qubits, and between separated logical qubits using linear optics. We show how
to prepare cluster states using this method. We include all
non-nearest-neighbor effects in our calculations, and we assume the qubits are
not located in the Dicke limit. Although our proposal is general to any system
of dipole-coupled qubits, throughout the paper we use nitrogen-vacancy (NV)
centers in diamond as an experimental context for our theoretical results.
