Effects of cosine tapering window on quantum phase estimation

We provide a modification to the quantum phase estimation algorithm (QPEA) inspired on classical windowing methods for spectral density estimation. From this we obtain an upper bound in cost that implies cubic improvement with respect algorithm's error rate. Numerical evaluation of costs also demonstrates improvement. Moreover, similar techniques, detail iterative projective measurement method ground state preparation gives exponential over previous bounds using QPEA. tests confirm expected scaling behavior are obtained. For these numerical have used Lattice Thirring model as testing ground. Using well-known perturbation theory results, show how more appropriately estimate instead evolution operator error.