  We propose a decoherence-free subspaces (DFS) scheme to realize scalable
quantum computation with trapped ions. The spin-dependent Coulomb interaction
is exploited, and the universal set of unconventional geometric quantum gates
is achieved in encoded subspaces that are immune from decoherence by collective
dephasing. The scalability of the scheme for the ion array system is
demonstrated, either by an adiabatic way of switching on and off the
interactions, or by a fast gate scheme with comprehensive DFS encoding and
noise decoupling techniques.
