We present a scheme for generating multiple, strongly interacting qubits in rare-earth-ion-doped inorganic crystals at cryogenic temperatures. Two ground state hyperfine levels, with hour long lifetimes and ms decoherence times are chosen as qubit states. Controlled logic between the qubits is accomplished using the change in permanent dipole moment induced by an optical transition between the ground and excited state of these ions. The scheme is based on existing material data and established measurement techniques and should therefore be straightforward to realise in practice. The procedure used for creating the qubits can be generalised also to other solid state systems.