Closed timelike curves in measurement-based quantum computation

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.