Estimating the ground-state energy of Hamiltonians in quantum systems is an important task. In this work, we demonstrate that the ground-state energy can be accurately estimated without controlled time evolution by using adiabatic state preparation (ASP) and Ramsey-type measurement. By considering the symmetry of the Hamiltonian governing the time evolution during ASP, we can prepare a superposition of the ground state and reference state whose eigenvalue is known. This enables the estimation of the ground-state energy via Ramsey-type measurement. Furthermore, our method is robust against non-adiabatic transitions, making it suitable for use with early fault-tolerant quantum computers and quantum annealing.
@article{arxiv.2412.19590,
title = {Robust phase estimation of the ground-state energy without controlled time evolution on a quantum device},
author = {Hiroki Kuji and Yuta Shingu and Tetsuro Nikuni and Takashi Imoto and Kenji Sugisaki and Yuichiro Matsuzaki},
journal= {arXiv preprint arXiv:2412.19590},
year = {2025}
}