Role of Riemannian geometry in double-bracket quantum imaginary-time evolution

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.

💡 Research Summary

This paper introduces a non‑variational quantum algorithm—double‑bracket quantum imaginary‑time evolution (DB‑QITE)—that implements imaginary‑time evolution (ITE) by exploiting the double‑bracket flow (DBF) originally studied by Brockett. The authors first recast ITE in terms of a matrix‑valued ordinary differential equation ∂τρ =