  Projective measurements with high quantum efficiency is often assumed to be
required for efficient circuit based quantum computing. We argue that this is
not the case and show that this fact has actually be known previously though
not deeply explored. We examine this issue by giving an example of how to
perform the quantum ordering finding algorithm efficiently using non-local weak
measurements given that the measurements used are of bounded weakness and some
fixed but arbitrary probability of success less than unity is required. We also
show that it is possible to perform the same computation with only local weak
measurements but this must necessarily introduce an exponential overhead.
