  In recent years, quantum algorithms have been proposed which use quantum
phase estimation (QPE) coherently as a subroutine without measurement. In order
to do this effectively, the routine must be able to distinguish eigenstates
with success probability close to unity. In this paper, we provide the first
systematic comparison between two approaches towards maximizing this success
probability, one using the quantum singular value transform and the other
leveraging window functions, which have been previously studied as priors of
the phase value distribution. We find that the quantum singular value transform
is significantly outclassed by the window function approach, with the latter
able to achieve between 3 and 5 orders of magnitude improvement in the success
probability with approximately 1/4 the query cost. Our circuit simulation
results indicate that QPE is not a domain which benefits from the integration
of QSVT and we show that the use of the Kaiser window function is currently the
most practical choice for realizing QPE with high success probability.
