Scalable quantum computation in decoherence-free subspaces with trapped ions

We propose a decoherence-free subspace (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent laser-ion coupling is exploited in the presence of Coulomb interactions. A 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 an ion-array system is demonstrated, either by adiabatically switching on and off the interactions, or by a fast gate scheme with DFS encoding and noise-decoupling techniques.