Double-bracket quantum imaginary-time evolution (DB-QITE) is a quantum algorithm which coherently implements steps in the Riemannian steepest-descent direction for the energy cost function. DB-QITE is derived from Brockett's double-bracket flow which exhibits saddle points where gradients vanish. In this work, we perform numerical simulations of DB-QITE and describe signatures of transitioning through the vicinity of such saddle points. We provide an explicit gate count analysis using quantum compilation programmed in Qrisp.
Cite
@article{arxiv.2504.01065,
title = {Role of Riemannian geometry in double-bracket quantum imaginary-time evolution},
author = {René Zander and Raphael Seidel and Li Xiaoyue and Marek Gluza},
journal= {arXiv preprint arXiv:2504.01065},
year = {2026}
}