  A cluster state cannot be a unique ground state of a two-body interacting
Hamiltonian. Here, we propose the creation of a cluster state of logical qubits
encoded in spin-1/2 particles by adiabatically weakening two-body interactions.
The proposal is valid for any spatial dimensional cluster states. Errors
induced by thermal fluctuations and adiabatic evolution within finite time can
be eliminated ensuring fault-tolerant quantum computing schemes.
