  Many results have been recently obtained regarding the power of hypothetical
closed time-like curves (CTCs) in quantum computation. Here we show that the
one-way model of measurement-based quantum computation encompasses in a natural
way the CTC model proposed by Bennett, Schumacher and Svetlichny. We identify a
class of CTCs in this model that can be simulated deterministically and point
to a fundamental limitation of Deutsch's CTC model which leads to predictions
conflicting with those of the one-way model.
