Spin Hamiltonians with degenerate ground states are one potential system for the storage of quantum information at low temperatures. Trapped ions can be used to simulate the dynamics of these Hamiltonians, but the coherence-preserving properties will be lost. This illustrates that a quantum simulation performed in an interaction frame will not thermalize with its environment.
@article{arxiv.0705.2370,
title = {Energy protection arguments fail in the interaction picture},
author = {Kenneth R. Brown},
journal= {arXiv preprint arXiv:0705.2370},
year = {2009}
}