Bounding eigenstate overlap from Hamiltonian moments: Success-probability guarantees for quantum phase estimation
Phys. Rev. A 114, 042432 – Published 16 October, 2026
DOI: https://doi.org/10.1103/3n75-vkxf
Abstract
The success probability of quantum phase estimation (QPE) is determined by the overlap of the input state with the target eigenspace. We present a systematically improvable method that, given a finite set of Hamiltonian moments and coarse spectral information, computes certified upper and lower bounds on this spectral weight. Our approach optimizes polynomial majorants and minorants of an energy-window indicator through linear and semidefinite programming, yielding the tightest bounds consistent with the supplied moment and spectral-interval information. We demonstrate the method on strongly correlated molecular Hamiltonians and study how approximate moments obtained from tensor-network contractions affect the certification. The framework provides a general tool for certifying spectral weights from incomplete moment information, with assessment of candidate initial states for QPE as one application.
