The Impossibility of the Counterfactual Computation for all Possible Outcomes

Recent proposal for counterfactual computation [Hosten et al., Nature, 439, 949 (2006)] is analyzed. It is argued that the method does not provide counterfactual computation for all possible outcomes. The explanation involves a novel paradoxical feature of pre- and post-selected quantum particles: the particle can reach a certain location without being on the path that leads to this location.