  We give an iterative algorithm for phase estimation of a parameter theta,
which is within a logarithmic factor of the Heisenberg limit. Unlike other
methods, we do not need any entanglement or an extra rotation gate which can
perform arbitrary rotations with almost perfect accuracy: only a single copy of
the unitary channel and basic measurements are needed. Simulations show that
the algorithm is successful. We also look at iterative phase estimation when
depolarizing noise is present. It is seen that the algorithm is still
successful provided the number of iterative stages is below a certain
threshold.
