On adaptive low-depth quantum algorithms for robust multiple-phase estimation

Understand

This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues.

• We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling.
• The proposed algorithms improve significantly from the idea of single-phase estimation methods by combining carefully designed signal processing routines and an adaptive determination of runtime amplifying factors.
• They address both the {\em integer-power} model, where the unitary $U$ is given as a black box with only integer runtime accessible, and the {\em real-power} model, where $U$ is defined through a Hamiltonian $H$ by $U = \exp(-2\pi\mathrm{i} H)$ with any real runtime allowed.