Effects of Cosine Tapering Window on Quantum Phase Estimation

TL;DR

This paper introduces a modified quantum phase estimation algorithm inspired by classical spectral windowing, achieving significant improvements in cost efficiency and ground state preparation, validated through numerical simulations.

Contribution

It presents a novel modification to QPEA using cosine tapering windows, resulting in cubic cost improvements and an exponential enhancement in ground state preparation methods.

Findings

Cubic reduction in algorithm cost relative to error rate

Exponential improvement in ground state preparation efficiency

Numerical results confirm theoretical scaling predictions

Abstract

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