A case study against QSVT: assessment of quantum phase estimation improved by signal processing techniques

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.